From afee8eae7813d815f5a636cd7bf2bda2bbe933cf Mon Sep 17 00:00:00 2001 From: Carlo Date: Fri, 26 Jun 2026 00:21:51 +0200 Subject: [PATCH 1/9] ema --- Companion/world_model/jepa_world_model.ipynb | 3122 ++++++++++++++++++ 1 file changed, 3122 insertions(+) create mode 100644 Companion/world_model/jepa_world_model.ipynb diff --git a/Companion/world_model/jepa_world_model.ipynb b/Companion/world_model/jepa_world_model.ipynb new file mode 100644 index 000000000..6fe22e4dd --- /dev/null +++ b/Companion/world_model/jepa_world_model.ipynb @@ -0,0 +1,3122 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "1c41d949", + "metadata": {}, + "source": [ + "# Measuring Particle Diffusion with a JEPA world model\n", + "\n", + "
\n", + "\"Open\n", + "If using Colab/Kaggle: You need to uncomment the code in the cell below this one.\n", + "
" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "42aabbb3", + "metadata": {}, + "outputs": [], + "source": [ + "# !pip install deeptrack deeplay torch torchvision matplotlib scikit-learn # Uncomment if using Colab/Kaggle." + ] + }, + { + "cell_type": "markdown", + "id": "1adfb1f1", + "metadata": {}, + "source": [ + "Joint Embedding Predictive Architectures (JEPAs) allow an AI system to learn how the world works purely by observing it, creating an internal \"world model\" without requiring human labels.\n", + "\n", + "In this notebook, you will use a JEPA world model to analyze a stochastic physical system: the Brownian diffusion of a particle. You will see how predicting in an abstract latent space—rather than predicting raw pixels—lets a neural network represent the statistics of an inherently unpredictable process, instead of chasing an exact future it has no way of knowing. By the end, you will test whether the model's representation captures something physically meaningful, by training a small linear probe to extract the particle's diffusion coefficient ($D$) straight from its abstract representation—a quantity the network was never directly trained to predict." + ] + }, + { + "cell_type": "markdown", + "id": "db87d875", + "metadata": {}, + "source": [ + "
\n", + "Note: This companion example extends several concepts introduced throughout the book, specifically, encoder-decoder architectures (Chapter 4) and particle diffusion (Chapter 11). Unlike several examples in the book, the network is trained not to reproduce its input but to predict its own future latent representations, learning an implicit model of the system's dynamics directly from simulated video.\n", + "\n", + "**Deep Learning Crash Course** \n", + "Giovanni Volpe, Benjamin Midtvedt, Jesús Pineda, Henrik Klein Moberg, Harshith Bachimanchi, Joana B. Pereira, Carlo Manzo \n", + "No Starch Press, San Francisco (CA), 2026 \n", + "ISBN-13: 9781718503922 \n", + "\n", + "[https://nostarch.com/deep-learning-crash-course](https://nostarch.com/deep-learning-crash-course)\n", + "\n", + "You can find the other notebooks on the [Deep Learning Crash Course GitHub page](https://github.com/DeepTrackAI/DeepLearningCrashCourse).\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "53fb6d56", + "metadata": {}, + "source": [ + "## Understanding JEPA World Models\n", + "Many artificial intelligence problems require an understanding of how a surrounding environment evolves. For instance, a robot navigating a room needs to anticipate collisions, a self-driving car needs to predict pedestrian movements, and an automated microscope needs to track how moving cells or particles spread over time.\n", + "\n", + "To make sense of the world, humans and animals rely on an internal World Model—a mental simulator that uses past observations to predict future outcomes. In machine learning, building an effective world model generally involves balancing two competing realities:\n", + "\n", + "1. Unpredictable Specifics: High-frequency, chaotic, or stochastic details where the exact future state is fundamentally uncertain (e.g., the exact, jittery trajectory of a single diffusing particle).\n", + "\n", + "2. Predictable Statistics: Structural invariants or global properties that govern how that uncertainty behaves over time (e.g., the environmental diffusion coefficient, $D$).\n", + "\n", + "Traditional predictive machine learning models typically try to predict the future down to the exact pixel. Given a video sequence, a generative network (like a standard Video Autoencoder or GAN) attempts to reconstruct subsequent frames pixel-by-pixel. However, in stochastic environments, predicting every single pixel is fundamentally a losing game. Because the exact path of a random particle cannot be known in advance, pixel-space models suffer from the \"blurry image\" problem—they mathematically average all possible futures, resulting in a faded, low-utility smudge.\n", + "\n", + "Joint Embedding Predictive Architectures (JEPAs) solve this dilemma by changing where the prediction happens. Instead of training a network to generate future raw pixels, a JEPA passes the data through an encoder and performs its predictions entirely within an abstract representation space (latent space).\n", + "\n", + "Crucially, this architecture does not magically look \"through\" the randomness to find a hidden, clean physical signal. In a system like diffusion, the randomness **is** the physical signal. Instead, the JEPA learns to represent the macroscopic statistics of the uncertainty. By optimizing to predict future latent states without memorizing unpredictable pixel-level specifics, the model naturally captures how the system spreads globally, allowing us to accurately extract underlying properties like $D$—matching the realistic performance boundaries of a truly chaotic system." + ] + }, + { + "cell_type": "markdown", + "id": "210a80b2", + "metadata": {}, + "source": [ + "### The Generative Dead End: Why Pixel Prediction Fails\n", + "Historically, the most intuitive way to build an AI world model from video data was to use generative modeling. Given a sequence of past video frames, a neural network is optimized to output the exact raw pixels of the subsequent frames.\n", + "\n", + "While visually striking when successful, Yann LeCun argues that generative pixel-level prediction is a fundamental engineering bottleneck—and an unfeasible strategy for learning physics—for two major reasons:\n", + "\n", + "- The Nuisance Variable Problem: A single pixel value can change drastically due to irrelevant factors like a shifting shadow, a camera sensor's grain, or background leaves rustling in the wind. Generative models waste immense computational capacity trying to reconstruct these high-frequency, non-essential \"nuisance variables.\"\n", + "\n", + "- The Multimodal Uncertainty Trap: In a stochastic or chaotic environment, the exact future cannot be perfectly known. If a particle is undergoing random thermal collisions, it has infinite possible paths. When a pixel-level model tries to handle multiple possible futures simultaneously, the mathematical average of those futures results in a blurred, low-utility average image—a faded smudge." + ] + }, + { + "cell_type": "markdown", + "id": "682eec1f", + "metadata": {}, + "source": [ + "### The JEPA Paradigm: Moving to Representation Space\n", + "Joint Embedding Predictive Architectures (JEPAs) circumvent the flaws of generative modeling by changing where the prediction takes place. Instead of predicting the future in high-dimensional pixel space, a JEPA predicts the future in a lower-dimensional, abstract representation space (latent space).\n", + "\n", + "The JEPA framework relies on a highly synchronized multi-network system:\n", + "\n", + "- The Context Encoder: Takes a history of frames (e.g., a 10-frame window) and flattens them into an abstract latent state vector, $z_0$, summarizing everything important about the system's current state.\n", + "\n", + "- The Target Encoder: Processes the actual future frames and extracts their true abstract latent representation, $z_1$. Crucially, this encoder does not backpropagate gradients directly; its weights are updated as a slow Exponential Moving Average (EMA) of the Context Encoder to serve as a stable, moving anchor.\n", + "\n", + "- The Latent Predictor: Receives the present latent state $z_0$ and a time horizon conditioning parameter ($\\delta$), and is tasked with guessing the future abstract state $\\hat{z}_1$.\n", + "\n", + "Because a JEPA is tasked with predicting abstract features rather than exact pixel locations, it naturally learns to discard individual pixel-level unpredictabilities. Instead, it captures the macroscopic statistics of the system's uncertainty. It learns to represent how space and uncertainty scale over time relative to environmental constants (like the diffusion coefficient, $D$).By bypassing the need to generate images, the network is free to focus entirely on learning the mathematical structure of the physical environment, creating an elegant, robust window into self-supervised physical common sense." + ] + }, + { + "cell_type": "markdown", + "id": "b4448972", + "metadata": {}, + "source": [ + "### The JEPA Optimization Objective: Loss and the Collapse Problem\n", + "\n", + "In traditional generative world models, the loss function is simple: it is usually a Mean Squared Error (MSE) calculated between the predicted pixels and the true future pixels. The raw pixel grid acts as a natural anchor that prevents the model from doing anything lazy.\n", + "\n", + "In a JEPA, however, there is **no pixel decoder**. The loss is calculated entirely within the abstract latent space:\n", + "$$\n", + "L_{\\text{pred}} = \\|\\hat{z}_1 - z_1\\|^2\n", + "$$\n", + "\n", + "Where $\\hat{z}_1$ is the predicted future representation and $z_1$ is the true future representation produced by the target encoder. This design poses a massive mathematical danger known as **Representation Collapse**.\n", + "\n", + "### The Danger of Trivial Representations\n", + "Because both the context encoder and the target encoder are neural networks that we control, the model can discover a massive \"shortcut\" to drive the prediction error to zero: **it can learn to output a constant vector for every single frame.** If the encoders map every single image sequence—regardless of whether the particle is moving fast, slow, left, or right—to the exact same vector (e.g., $z = [0, 0, \\dots, 0]$), then the predictor can simply output zero. The prediction error becomes exactly zero, but the representations are completely useless, carrying zero information about the physics of the environment.\n", + "\n", + "To build a meaningful world model, we must force the latent representations to be highly informative while minimizing prediction error. JEPA achieves this by introducing explicit **anti-collapse regularization** adapted from self-supervised frameworks like **VICReg** (Variance-Invariance-Covariance Regularization)." + ] + }, + { + "cell_type": "markdown", + "id": "54332dbf", + "metadata": {}, + "source": [ + "### The Three Pillars of the JEPA Loss Function\n", + "\n", + "To prevent collapse and force the model to capture the true underlying physics, the total loss function is broken down into three distinct mathematical objectives: **Invariance (Prediction)**, **Variance**, and **Covariance**.\n", + "\n", + "$$\\mathcal{L}_{\\text{total}} = \\alpha \\mathcal{L}_{\\text{pred}} + \\beta \\mathcal{L}_{\\text{var}} + \\gamma \\mathcal{L}_{\\text{cov}}$$\n", + "\n", + "#### 1. The Invariance Loss ($\\mathcal{L}_{\\text{pred}}$)\n", + "This is the core predictive world-model objective. It minimizes the Mean Squared Error between the predicted future latent state $\\hat{z}_1$ and the actual target latent state $z_1$:\n", + "\n", + "$$\\mathcal{L}_{\\text{pred}} = \\frac{1}{B}\\sum_{i=1}^{B} \\|\\hat{z}_{1,i} - z_{1,i}\\|^2$$\n", + "\n", + "It forces the predictor to understand temporal dynamics. To minimize this, the model must calculate how a physical history transforms across an elapsed time horizon $\\delta$.\n", + "\n", + "#### 2. The Variance Regularizer ($\\mathcal{L}_{\\text{var}}$)\n", + "To prevent the encoders from collapsing into a single static point, the variance regularizer forces the latent vectors across a training batch to vary. It calculates the standard deviation $\\sigma$ of each latent dimension across the batch and penalizes it if it drops below a target threshold (typically $1.0$):\n", + "\n", + "$$\\mathcal{L}_{\\text{var}} = \\frac{1}{d}\\sum_{j=1}^{d} \\max\\left(0, 1 - \\sigma(z_{\\cdot, j})\\right)$$\n", + "\n", + "It acts as an expansive force. It explicitly forbids the encoders from squeezing all physical images into a single point, ensuring that different physical behaviors are mapped to distinct, unique locations in latent space.\n", + "\n", + "#### 3. The Covariance Regularizer ($\\mathcal{L}_{\\text{cov}}$)\n", + "Even with high variance, a model can cheat by making all latent variables track the exact same signal (e.g., if dimension 1 tracks particle position, dimensions 2 through 16 might redundantly copy dimension 1). The covariance loss penalizes the off-diagonal elements of the latent covariance matrix:\n", + "\n", + "$$\\mathcal{L}_{\\text{cov}} = \\frac{1}{d}\\sum_{j \\neq k} \\left(\\text{Cov}(z)_{j,k}\\right)^2$$\n", + "\n", + "It acts as an information decoherer. It forces the different dimensions of your latent space to be linearly independent of one another. This maximizes the \"capacity\" of the embedding space, pushing the model to cleanly separate different orthogonal physical features (like tracking the particle's spatial $x,y$ position in some dimensions, and isolating the global diffusion rate $D$ in others)." + ] + }, + { + "cell_type": "markdown", + "id": "6c5bc4d2", + "metadata": {}, + "source": [ + "## Simulating particle-diffusion videos\n", + "\n", + "You'll simulate short video clips of a Brownian particle in a box, where the diffusion coefficient $D$ varies from\n", + "clip to clip. The world model will never be told $D$ directly — it has to infer it implicitly from how \"jittery\"\n", + "the particle's motion looks across frames. This is exactly the kind of latent physical parameter a JEPA-style model\n", + "should be able to recover from dynamics alone." + ] + }, + { + "cell_type": "raw", + "id": "f7a7e826", + "metadata": { + "vscode": { + "languageId": "raw" + } + }, + "source": [ + "You'll separate the **true physics simulation** (the Brownian\n", + "motion integration) from **rendering** (DeepTrack2's optics pipeline). This is convenient pedagogically: we always\n", + "have access to ground truth `positions`, which we'll use later only to *evaluate* what the world model has learned,\n", + "never during self-supervised training." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "c125997d", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "IMAGE_SIZE = 64 # image size in pixels, corresponds to the box size \n", + "N_FRAMES = 20 # frames per clip\n", + "DELTA_T = 1.0 # time between frames (arbitrary units)\n", + "\n", + "def reflect(pos, lo, hi):\n", + " \"\"\"Reflect a scalar position back into [lo, hi] if it overshoots.\"\"\"\n", + " span = hi - lo\n", + " pos = pos - lo\n", + " pos = np.abs(pos) # reflect off lo\n", + " pos = pos % (2 * span)\n", + " pos = np.where(pos > span, 2 * span - pos, pos) # reflect off hi\n", + " return pos + lo\n", + "\n", + "def simulate_trajectory(D, n_frames=N_FRAMES, image_size=IMAGE_SIZE,\n", + " delta_t=DELTA_T, margin=4):\n", + " \"\"\"Simulate a single Brownian trajectory with reflective boundaries.\n", + "\n", + " Returns:\n", + " positions: (n_frames, 2) true (x, y) positions in pixel units\n", + " \"\"\"\n", + " pos = np.array([image_size // 2, image_size // 2]) # start in the center\n", + " # pos = np.random.uniform(margin, image_size - margin, size=2)\n", + " positions = [pos.copy()]\n", + " for _ in range(n_frames - 1):\n", + " step = np.sqrt(2 * D * delta_t) * np.random.randn(2)\n", + " pos = pos + step\n", + " pos[0] = reflect(pos[0], margin, image_size - margin)\n", + " pos[1] = reflect(pos[1], margin, image_size - margin)\n", + " positions.append(pos.copy())\n", + " return np.array(positions)" + ] + }, + { + "cell_type": "markdown", + "id": "db40d752", + "metadata": {}, + "source": [ + "## Optical Rendering through a Fluorescence Microscope" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "1b22485e", + "metadata": {}, + "outputs": [], + "source": [ + "import deeptrack as dt\n", + "\n", + "def render_trajectory(positions, image_size=IMAGE_SIZE):\n", + " \"\"\"Render a sequence of (x, y) positions into a video of a fluorescent particle.\n", + "\n", + " Returns:\n", + " frames: (n_frames, image_size, image_size) float32 array in [0, 1]\n", + " \"\"\"\n", + " current_position = {\"value\": positions[0]}\n", + "\n", + " optics = dt.Fluorescence(\n", + " NA=0.8,\n", + " wavelength=560e-9,\n", + " resolution=1e-7,\n", + " magnification=1,\n", + " output_region=(0, 0, image_size, image_size),\n", + " )\n", + " particle = dt.PointParticle(\n", + " position=lambda: current_position[\"value\"],\n", + " position_unit=\"pixel\",\n", + " intensity=200,\n", + " )\n", + " pipeline = optics(particle)\n", + "\n", + " frames = []\n", + " for p in positions:\n", + " current_position[\"value\"] = p\n", + " frame = pipeline.update()()\n", + " frames.append(np.asarray(frame).squeeze())\n", + " frames = np.stack(frames).astype(\"float32\")\n", + " frames = frames / (frames.max() + 1e-8)\n", + " return frames" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "5e3b7036", + "metadata": {}, + "outputs": [], + "source": [ + "def make_particle_clip(D, n_frames=N_FRAMES, image_size=IMAGE_SIZE, delta_t=DELTA_T):\n", + " \"\"\"Simulate and render one video clip of a single Brownian particle.\n", + "\n", + " Returns:\n", + " frames: (n_frames, image_size, image_size) float32 array in [0, 1]\n", + " positions: (n_frames, 2) true (x, y) positions in pixel units\n", + " \"\"\"\n", + " positions = simulate_trajectory(D, n_frames, image_size, delta_t)\n", + " frames = render_trajectory(positions, image_size)\n", + " return frames, positions" + ] + }, + { + "cell_type": "raw", + "id": "4a36d8ac", + "metadata": { + "vscode": { + "languageId": "raw" + } + }, + "source": [ + "IMAGE_SIZE = 64\n", + "N_FRAMES = 24 # frames per clip\n", + "DELTA_T = 1.0 # time between frames (arbitrary units)\n", + "D_RANGE = (0.1, 10.0) # diffusion coefficient range, varied per clip\n", + "WINDOW = 10 \n", + "\n", + "def reflect(pos, lo, hi):\n", + " \"\"\"Reflect a scalar position back into [lo, hi] if it overshoots.\"\"\"\n", + " span = hi - lo\n", + " pos = pos - lo\n", + " pos = np.abs(pos) # reflect off lo\n", + " pos = pos % (2 * span)\n", + " pos = np.where(pos > span, 2 * span - pos, pos) # reflect off hi\n", + " return pos + lo\n", + "\n", + "def make_particle_clip(D, n_frames=N_FRAMES, image_size=IMAGE_SIZE, delta_t=DELTA_T):\n", + " \"\"\"Simulate one video clip of a single Brownian particle with diffusion coefficient D.\n", + "\n", + " Returns:\n", + " frames: (n_frames, image_size, image_size) float32 array in [0, 1]\n", + " positions: (n_frames, 2) true (x, y) positions in pixel units\n", + " \"\"\"\n", + "\n", + " margin = 4\n", + " pos = np.random.uniform(margin, image_size - margin, size=2)\n", + " current_position = {\"value\": pos}\n", + "\n", + " optics = dt.Fluorescence(\n", + " NA=0.8,\n", + " wavelength=560e-9,\n", + " resolution=1e-7,\n", + " magnification=1,\n", + " output_region=(0, 0, image_size, image_size),\n", + " )\n", + "\n", + " particle = dt.PointParticle(\n", + " position=lambda: current_position[\"value\"],\n", + " position_unit=\"pixel\",\n", + " intensity=200,\n", + " )\n", + "\n", + " pipeline = optics(particle)\n", + "\n", + " # Pre-compute the true Brownian trajectory ourselves (Euler-Maruyama),\n", + " # then re-render the particle at each position. This keeps the physics\n", + " # explicit and lets us keep ground-truth positions for the probing step.\n", + " # pos = np.array([image_size / 2, image_size / 2], dtype=np.float64)\n", + " positions = [pos.copy()]\n", + " for _ in range(n_frames - 1):\n", + " step = np.sqrt(2 * D * delta_t) * np.random.randn(2)\n", + " pos = pos + step\n", + " pos[0] = reflect(pos[0], 4, image_size - 4)\n", + " pos[1] = reflect(pos[1], 4, image_size - 4)\n", + " positions.append(pos.copy())\n", + " positions = np.array(positions)\n", + "\n", + " frames = []\n", + " for p in positions:\n", + " current_position[\"value\"] = p\n", + " frame = pipeline.update()()\n", + " frames.append(np.asarray(frame).squeeze())\n", + " frames = np.stack(frames).astype(\"float32\")\n", + " frames = frames / (frames.max() + 1e-8)\n", + " return frames, positions\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "18cf80d7", + "metadata": {}, + "source": [ + "### Visualize an Example Clip" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "d3933ac1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
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The `DiffusionClipDataset()` handles this by dynamically generating video clips on the fly and slicing them into specific temporal windows. For every index sampled, the dataset performs the following operations:\n", + "\n", + "- Simulates a Full Video: It draws a random environmental diffusion coefficient ($D$) from our specified range and generates a continuous trajectory of N_FRAMES.\n", + "\n", + "- Establishes the Present Anchor: It randomly selects a frame index $t_0$ to represent the \"present moment.\" To ensure there are enough past frames to fill our context window, $t_0$ is constrained to look back at least `window` frames.\n", + "\n", + "- Samples a Random Future Horizon: It randomly samples a time gap ($\\delta$) ranging from $1$ to the maximum remaining frames in the clip. This sets our future target frame at $t_1 = t_0 + \\delta$.\n", + "\n", + "- Assembles the Tensors:\n", + "\n", + " - x0 (Context Window): A sequence of 10 consecutive frames leading up to and including the present moment ($[t_0 - 9, \\dots, t_0]$).\n", + " - x1 (Target Window): A sequence of 10 consecutive frames leading up to and including the future moment ($[t_1 - 9, \\dots, t_1]$).\n", + " - Conditioning & Ground Truths: It extracts the elapsed time gap delta_t ($\\Delta t$), the true environmental rate D_true ($D$), and the precise 2D spatial positions (pos0, pos1) of the particle at both timestamps for downstream verification." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "29ae5714", + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "\n", + "WINDOW = 10 # window size for sampling clips\n", + "D_RANGE = (0.1, 10.0) # range of diffusion coefficients to sample from\n", + "\n", + "class DiffusionClipDataset(torch.utils.data.Dataset):\n", + " def __init__(self, n_clips=2000, n_frames=N_FRAMES, image_size=IMAGE_SIZE,\n", + " d_range=D_RANGE, window=WINDOW):\n", + " self.n_clips = n_clips\n", + " self.n_frames = n_frames\n", + " self.image_size = image_size\n", + " self.d_range = d_range\n", + " self.window = window\n", + "\n", + " def __len__(self):\n", + " return self.n_clips\n", + "\n", + " def __getitem__(self, idx):\n", + " D = np.random.uniform(*self.d_range)\n", + " frames, positions = make_particle_clip(D, self.n_frames, self.image_size)\n", + "\n", + " w = self.window\n", + " t0 = np.random.randint(w - 1, self.n_frames - w )\n", + " delta = np.random.randint(w, self.n_frames - t0)\n", + " t1 = t0 + delta\n", + "\n", + " x0 = torch.from_numpy(frames[t0 - w + 1 : t0 + 1]).float() # (w, H, W)\n", + " x1 = torch.from_numpy(frames[t1 - w + 1 : t1 + 1]).float() # (w, H, W)\n", + "\n", + " delta_t = torch.tensor([delta], dtype=torch.float32)\n", + " D_true = torch.tensor([D], dtype=torch.float32)\n", + " pos0 = torch.from_numpy(positions[t0]).float()\n", + " pos1 = torch.from_numpy(positions[t1]).float()\n", + "\n", + " return x0, x1, delta_t, D_true, pos0, pos1\n", + "\n", + "train_ds = DiffusionClipDataset(n_clips=2000)\n", + "val_ds = DiffusionClipDataset(n_clips=400)\n", + "\n", + "train_loader = torch.utils.data.DataLoader(train_ds, batch_size=32, shuffle=True)\n", + "val_loader = torch.utils.data.DataLoader(val_ds, batch_size=32, shuffle=False)\n" + ] + }, + { + "cell_type": "markdown", + "id": "ff89d73b", + "metadata": {}, + "source": [ + "## Understanding World Models\n", + "\n", + "We will build a **Joint-Embedding Predictive Architecture (JEPA)**:\n", + "- an **encoder** $E_\\theta$ that maps a video frame to a latent state $z_t = E_\\theta(x_t)$\n", + "- a **target encoder** $E_{\\bar\\theta}$ (an EMA copy of $E_\\theta$, no gradient) that produces the *prediction target*\n", + "- a **predictor** $P_\\phi$ that predicts $\\hat z_{t+\\Delta t} = P_\\phi(z_t, \\Delta t)$\n", + "- training signal: $\\hat z_{t+\\Delta t} \\approx E_{\\bar\\theta}(x_{t+\\Delta t})$, **not** pixel reconstruction\n", + "\n", + "The key pedagogical point: we never ask the model to reconstruct pixels. Diffusion videos are mostly noise/texture —\n", + "not worth modeling. We ask the model to predict *its own representation* of the future. We will see this is harder to\n", + "get right (it can collapse to a trivial constant) and we'll fix that with an EMA target + a variance regularizer\n", + "(VICReg-style), in the spirit of I-JEPA / V-JEPA.\n", + "\n", + "### Roadmap\n", + "1. Simulate particle-diffusion videos with **DeepTrack2** (vary the diffusion coefficient $D$)\n", + "2. Build encoder / target-encoder / predictor\n", + "3. Train self-supervised with a latent-prediction loss + anti-collapse regularization\n", + "4. **Probe**: train a tiny linear head latent → true $D$, true position — this is the moment we check whether the\n", + " world model \"discovered\" physics\n", + "5. Visualize latent trajectories vs. true trajectories\n", + "6. **Ablation**: remove the EMA target / regularizer and watch the representation collapse\n", + "7. (Optional, advanced) Differentiable-simulator comparison: optimize $D$ directly through DeepTrack2's\n", + " gradient-preserving pipeline and compare to what the learned world model infers" + ] + }, + { + "cell_type": "markdown", + "id": "c111c0ee", + "metadata": {}, + "source": [ + "## 3. The world model: encoder, EMA target encoder, predictor\n", + "\n", + "We build everything with **Deeplay**, so each block is a swappable, composable module. The encoder is a small CNN;\n", + "the predictor is an MLP that takes $(z_t, \\Delta t)$ and outputs $\\hat z_{t+\\Delta t}$.\n", + "\n", + "Two design choices worth flagging:\n", + "- **EMA target encoder**: the target representation $E_{\\bar\\theta}(x_{t+\\Delta t})$ is produced by a *momentum copy*\n", + " of the encoder, updated as $\\bar\\theta \\leftarrow \\tau \\bar\\theta + (1-\\tau)\\theta$, with **no gradient** flowing\n", + " through it. This is the standard trick (BYOL/I-JEPA/V-JEPA) to prevent the trivial collapse \"encoder outputs a\n", + " constant, predictor learns the constant, loss = 0\".\n", + "- **Variance regularization** (VICReg-style): we additionally penalize the embeddings if their per-dimension\n", + " variance across the batch collapses toward 0. This is a second, complementary defense against collapse, and lets\n", + " us demonstrate what happens when we strip each one out (Section 6).\n" + ] + }, + { + "cell_type": "markdown", + "id": "fcdd01ba", + "metadata": {}, + "source": [ + "## Framing the Architecture: Why We Condition on Time ($\\Delta t$)\n", + "\n", + "When applying Joint Embedding Predictive Architectures to video data (such as Meta's V-JEPA), it is common practice to use fixed-size context and target windows. For example, a model might take a fixed block of frames and learn to predict a subsequent, fixed block of frames. Because the time gap between the context and the target is always identical, the predictor network does not need to know when it is predicting; it only needs to learn a static temporal mapping.\n", + "\n", + "However, because our goal is to recover the underlying physics of diffusion, we introduce a deliberate modification to the standard literature setup: **we explicitly condition our Latent Predictor on a variable time horizon ($\\Delta t$).**\n", + "\n", + "Instead of predicting a single fixed future block, our model is given a 10-frame context window and asked to predict anywhere from 1 to 14 frames into the future, with the exact horizon sampled randomly for every training example.\n", + "\n", + "### The Pedagogical Value of Variable Horizons\n", + "\n", + "We make this architectural departure for two reasons:\n", + "\n", + "1. **Discouraging a \"Memorized Displacement\" Shortcut:** In pure Brownian motion, the environmental diffusion coefficient ($D$) is not a static displacement; it is the proportionality constant that dictates how the uncertainty scales over time ($\\sigma^2 \\sim 2D\\Delta t$). If the time gap were always fixed, the model could satisfy the prediction objective by memorizing a one-off displacement scale for that specific horizon, without ever needing a notion of rate. By varying $\\Delta t$, the model is instead asked to be consistent across many different horizons simultaneously—a design intended to encourage it to internalize a generalizable rate, rather than a single fixed-horizon shortcut.\n", + "2. **Visualizing the Arrow of Diffusion:** Conditioning on $\\Delta t$ lets us evaluate the model's performance as a function of elapsed time. This makes it possible to directly plot how latent prediction error grows as the horizon expands—a quantifiable window into how a world model handles accumulating stochastic uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "924e8d3b", + "metadata": {}, + "outputs": [], + "source": [ + "import deeplay as dl\n", + "from typing import Optional\n", + "from torch import nn\n", + "import torch.nn.functional as F\n", + "\n", + "\n", + "LATENT_DIM = 64\n", + "\n", + "class WorldModel(dl.Application):\n", + " def __init__(self, latent_dim=LATENT_DIM, ema_tau=0.99, lam=1.0, mu=1.0, nu=0.01, use_ema=True,\n", + " optimizer=None, **kwargs):\n", + "\n", + " self.encoder = dl.ConvolutionalEncoder2d(\n", + " in_channels=WINDOW,\n", + " hidden_channels=[32, 64],\n", + " out_channels=128,\n", + " postprocess=dl.Layer(nn.AdaptiveAvgPool2d, 1),\n", + " )\n", + " self.encoder.strided(stride=2, apply_to_first_layer=True, apply_to_last_layer=True)\n", + " self.encoder_proj = nn.Sequential(\n", + " nn.Linear(128, latent_dim),\n", + " nn.BatchNorm1d(latent_dim),\n", + " )\n", + "\n", + " self.predictor = dl.MultiLayerPerceptron(\n", + " in_features=latent_dim + 1,\n", + " hidden_features=[128, 128],\n", + " out_features=latent_dim,\n", + " )\n", + " self.predictor[\"blocks\", :-1].all.normalized(nn.BatchNorm1d)\n", + " self.predictor[\"blocks\", :-1].configure(order=[\"layer\", \"normalization\", \"activation\"])\n", + "\n", + "\n", + " self.use_ema = use_ema\n", + " self.ema_tau = ema_tau\n", + " self.lam = lam\n", + " self.mu = mu\n", + " self.nu = nu\n", + "\n", + " if self.use_ema:\n", + " self.target_encoder = dl.ConvolutionalEncoder2d(\n", + " in_channels=WINDOW,\n", + " hidden_channels=[32, 64],\n", + " out_channels=128,\n", + " postprocess=dl.Layer(nn.AdaptiveAvgPool2d, 1),\n", + " )\n", + " self.target_encoder.strided(stride=2, apply_to_first_layer=True, apply_to_last_layer=True)\n", + " self.target_proj = nn.Sequential(\n", + " nn.Linear(128, latent_dim),\n", + " nn.BatchNorm1d(latent_dim),\n", + " )\n", + " else:\n", + " self.target_encoder = self.encoder\n", + " self.target_proj = self.encoder_proj\n", + "\n", + " super().__init__(**kwargs)\n", + "\n", + " self.optimizer = optimizer or dl.Adam(lr=1e-4)\n", + "\n", + " @self.optimizer.params\n", + " def params(self):\n", + " return self.parameters()\n", + "\n", + " self._target_synced = False\n", + "\n", + " def encode(self, x):\n", + " z = self.encoder_proj(self.encoder(x).flatten(1))\n", + " return F.normalize(z, dim=-1)\n", + "\n", + " def encode_target(self, x):\n", + " z = self.target_proj(self.target_encoder(x).flatten(1))\n", + " return F.normalize(z, dim=-1)\n", + "\n", + " def forward(self, x0, x1, delta_t):\n", + " z0 = self.encode(x0)\n", + " z1_pred = self.predictor(torch.cat([z0, delta_t / N_FRAMES], dim=-1))\n", + " z1_pred = F.normalize(z1_pred, dim=-1) # predictor output must match target's scale\n", + " if self.use_ema:\n", + " with torch.no_grad():\n", + " z1_target = self.encode_target(x1)\n", + " else:\n", + " z1_target = self.encode_target(x1)\n", + " return z0, z1_pred, z1_target\n", + " \n", + " def variance_loss(self, z, gamma=None):\n", + " if gamma is None:\n", + " gamma = 1.0 / (z.shape[-1] ** 0.5) # ~0.125 for latent_dim=64\n", + " std = z.std(dim=0) + 1e-4\n", + " return F.relu(gamma - std).mean()\n", + "\n", + " # def covariance_loss(self, z):\n", + " # z = z - z.mean(dim=0)\n", + " # n, d = z.shape\n", + " # cov = (z.T @ z) / (n - 1)\n", + " # off_diag = cov.flatten()[:-1].view(d - 1, d + 1)[:, 1:].flatten()\n", + " # return (off_diag ** 2).sum() / d\n", + " \n", + " def covariance_loss(self, z):\n", + " z = z - z.mean(dim=0)\n", + " cov = (z.T @ z) / (z.shape[0] - 1)\n", + " off_diag = cov - torch.diag(torch.diagonal(cov))\n", + " return (off_diag ** 2).sum() / z.shape[1]\n", + "\n", + " def compute_loss(self, z0, z1_pred, z1_target):\n", + " pred_loss = F.mse_loss(z1_pred, z1_target)\n", + " loss = {\"pred\": self.lam * pred_loss}\n", + " if self.mu > 0:\n", + " reg_loss = self.variance_loss(z0) + self.variance_loss(z1_pred)\n", + " loss[\"reg\"] = self.mu * reg_loss\n", + " if self.nu > 0:\n", + " cov_loss = self.covariance_loss(z0) + self.covariance_loss(z1_pred)\n", + " loss[\"cov\"] = self.nu * cov_loss\n", + " return loss\n", + "\n", + " def _shared_step(self, batch, stage):\n", + " x0, x1, delta_t, D_true, pos0, pos1 = batch\n", + " z0, z1_pred, z1_target = self(x0, x1, delta_t)\n", + " loss = self.compute_loss(z0, z1_pred, z1_target)\n", + " for name, v in loss.items():\n", + " self.log(f\"{stage}_{name}\", v, on_step=True, on_epoch=True,\n", + " prog_bar=True, logger=True)\n", + " return sum(loss.values())\n", + "\n", + " def training_step(self, batch, batch_idx):\n", + " return self._shared_step(batch, \"train\")\n", + "\n", + " def validation_step(self, batch, batch_idx):\n", + " return self._shared_step(batch, \"val\")\n", + "\n", + " def on_train_batch_end(self, outputs, batch, batch_idx):\n", + " if self.use_ema:\n", + " self.update_target()\n", + "\n", + " # @torch.no_grad()\n", + " # def update_target(self):\n", + " # if not self._target_synced:\n", + " # self.target_encoder.load_state_dict(self.encoder.state_dict())\n", + "\n", + " @torch.no_grad()\n", + " def update_target(self):\n", + " if not self._target_synced:\n", + " self.target_encoder.load_state_dict(self.encoder.state_dict())\n", + " self.target_proj.load_state_dict(self.encoder_proj.state_dict())\n", + " for p in list(self.target_encoder.parameters()) + list(self.target_proj.parameters()):\n", + " p.requires_grad_(False)\n", + " self._target_synced = True\n", + " return\n", + " for p, p_t in zip(self.encoder.parameters(), self.target_encoder.parameters()):\n", + " p_t.data.mul_(self.ema_tau).add_(p.data, alpha=1 - self.ema_tau)\n", + " for p, p_t in zip(self.encoder_proj.parameters(), self.target_proj.parameters()):\n", + " p_t.data.mul_(self.ema_tau).add_(p.data, alpha=1 - self.ema_tau)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "12a0bd11", + "metadata": {}, + "outputs": [], + "source": [ + "from lightning.pytorch.callbacks import Callback\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.metrics import r2_score\n", + "\n", + "class ProbeMonitorCallback(Callback):\n", + " def __init__(self, check_every_n_epochs=1, n_clips=300):\n", + " self.check_every_n_epochs = check_every_n_epochs\n", + " self.n_clips = n_clips\n", + " self.history = []\n", + "\n", + " @torch.no_grad()\n", + " def _collect_probe_data(self, model):\n", + " model.eval()\n", + " Z, Z2, DT, DS, POS = [], [], [], [], []\n", + " ds = DiffusionClipDataset(n_clips=self.n_clips)\n", + " loader = torch.utils.data.DataLoader(ds, batch_size=32, shuffle=False)\n", + " for x0, x1, delta_t, D_true, pos0, pos1 in loader:\n", + " x0, x1 = x0.to(model.device), x1.to(model.device)\n", + " z0 = model.encode(x0)\n", + " z1 = model.encode(x1)\n", + " Z.append(z0.cpu()); Z2.append(z1.cpu())\n", + " DT.append(delta_t); DS.append(D_true); POS.append(pos0)\n", + " return torch.cat(Z), torch.cat(Z2), torch.cat(DT), torch.cat(DS), torch.cat(POS)\n", + "\n", + " def on_train_epoch_end(self, trainer, pl_module):\n", + " epoch = trainer.current_epoch\n", + " if (epoch + 1) % self.check_every_n_epochs != 0:\n", + " return\n", + "\n", + " Z0, Z1, DT_, D_, POS0 = self._collect_probe_data(pl_module)\n", + " feat_D = torch.cat([Z0, Z1, DT_], dim=1).numpy()\n", + " target_D = D_.numpy().ravel()\n", + "\n", + " Xtr, Xte, ytr, yte = train_test_split(feat_D, target_D, test_size=0.25, random_state=0)\n", + " probe = Ridge(alpha=1.0).fit(Xtr, ytr)\n", + " r2 = r2_score(yte, probe.predict(Xte))\n", + "\n", + " self.history.append((epoch, r2))\n", + " pl_module.log(\"probe_D_r2\", r2, prog_bar=True, on_step=False, on_epoch=True)\n", + " print(f\" [epoch {epoch}] D probe R^2 = {r2:.3f}\")\n", + "\n", + " pl_module.train()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5a15788b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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+       "┃   ┃ Name           ┃ Type                   ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
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+       "│ 0 │ encoder        │ ConvolutionalEncoder2d │ 95.3 K │ train │     0 │\n",
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Trainable params: 241 K                                                                                            \n",
+       "Non-trainable params: 0                                                                                            \n",
+       "Total params: 241 K                                                                                                \n",
+       "Total estimated model params size (MB): 0                                                                          \n",
+       "Modules in train mode: 47                                                                                          \n",
+       "Modules in eval mode: 0                                                                                            \n",
+       "Total FLOPs: 0                                                                                                     \n",
+       "
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/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/\n",
+       "_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and \n",
+       "treespec.is_leaf()` instead.\n",
+       "
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/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/co\n",
+       "nnectors/data_connector.py:434: The 'val_dataloader' does not have many workers which may be a bottleneck. Consider\n",
+       "increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n",
+       "
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/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/co\n",
+       "nnectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. \n",
+       "Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve \n",
+       "performance.\n",
+       "
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  [epoch 0] D probe R^2 = 0.592\n",
+       "
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  [epoch 1] D probe R^2 = 0.668\n",
+       "
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  [epoch 2] D probe R^2 = 0.445\n",
+       "
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  [epoch 3] D probe R^2 = 0.536\n",
+       "
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  [epoch 4] D probe R^2 = 0.566\n",
+       "
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  [epoch 5] D probe R^2 = 0.656\n",
+       "
\n" + ], + "text/plain": [ + " [epoch 5] D probe R^2 = 0.656\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "probe_monitor = ProbeMonitorCallback(check_every_n_epochs=1, n_clips=300)\n", + "\n", + "model = WorldModel(optimizer=dl.Adam(lr=1e-4)).create()\n", + "history = model.fit(train_ds, val_data=val_ds, max_epochs=15, batch_size=32, accelerator = \"auto\", callbacks=[probe_monitor])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8f9b1333", + "metadata": {}, + "outputs": [], + "source": [ + "epochs, r2s = zip(*probe_monitor.history)\n", + "plt.plot(epochs, r2s, marker=\"o\")\n", + "plt.xlabel(\"epoch\"); plt.ylabel(\"D probe R²\")\n", + "plt.title(\"Probe R² over training\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5a64741e", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "50d5e387", + "metadata": {}, + "source": [ + "## 4. Loss: latent prediction + anti-collapse regularizer\n", + "\n", + "$$ \\mathcal{L} = \\underbrace{\\|\\hat z_{t+\\Delta t} - \\text{sg}(z_{t+\\Delta t})\\|^2}_{\\text{prediction loss}} \\;+\\; \\lambda \\underbrace{\\sum_d \\max(0,\\, \\gamma - \\text{std}(z_{\\cdot, d}))}_{\\text{variance regularizer (VICReg-style)}} $$\n", + "\n", + "`sg` = stop-gradient (handled here by the target encoder having `requires_grad=False` and being updated only via EMA).\n", + "The variance term pushes each latent dimension to keep some spread *within the batch*, so it can't collapse to a\n", + "single point for every input.\n" + ] + }, + { + "cell_type": "markdown", + "id": "c4e78483", + "metadata": {}, + "source": [ + "## 6. Probing: did the world model discover physics?\n", + "\n", + "We freeze the encoder and fit a small linear/MLP probe from $z_t$ alone to:\n", + "- the true diffusion coefficient $D$ (a *global* property of the clip)\n", + "- the true particle position (a property of the single frame)\n", + "\n", + "If the encoder's latent space is rich enough to predict $D$ well, the self-supervised prediction objective has\n", + "forced the model to represent something about the *dynamics regime* of the clip — not just the current pixel\n", + "pattern. This is the chapter's main \"aha\" moment.\n", + "\n", + "Note: $D$ is a property of the *whole clip*, not a single frame, so to probe it fairly we feed the probe a short\n", + "window of frames (or, more simply here, two latents $z_t, z_{t+\\Delta t}$ and let it use their difference).\n" + ] + }, + { + "cell_type": "markdown", + "id": "336727af", + "metadata": {}, + "source": [ + "# diagnosstic 1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ff4e8986", + "metadata": {}, + "outputs": [], + "source": [ + "## Diagnostic: is D actually recoverable from raw pixel displacements?\n", + "#\n", + "# This bypasses the model entirely. We simulate many clips at different D,\n", + "# compute the raw pixel displacement statistics directly from the rendered\n", + "# frames (via simple centroid tracking, NOT from the ground-truth `positions`\n", + "# array -- we want to know what's visible in the IMAGES, since that's all the\n", + "# encoder ever sees), and check whether D is recoverable from that signal.\n", + "#\n", + "# If this comes back with a weak/no relationship, the bottleneck is the\n", + "# rendering/resolution regime, not the world-model architecture, and no\n", + "# amount of context_k or loss tuning will fix it -- you'd need to change the\n", + "# image_size, the D range, or the optics (PSF size, magnification, etc.).\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "def centroid_from_frame(frame, threshold_rel=0.3):\n", + " \"\"\"Cheap centroid estimate directly from pixel intensities (mimics what\n", + " any reasonable encoder could in principle extract from a single frame).\"\"\"\n", + " thresh = frame.max() * threshold_rel\n", + " mask = frame > thresh\n", + " if mask.sum() == 0:\n", + " mask = frame > 0\n", + " ys, xs = np.nonzero(mask)\n", + " weights = frame[ys, xs]\n", + " if weights.sum() == 0:\n", + " return np.array([np.nan, np.nan])\n", + " cy = np.average(ys, weights=weights)\n", + " cx = np.average(xs, weights=weights)\n", + " return np.array([cx, cy])\n", + "\n", + "\n", + "def measure_pixel_displacement_vs_D(n_clips=200, k=14, n_frames=N_FRAMES):\n", + " Ds, true_disps, pix_disps = [], [], []\n", + "\n", + " for _ in range(n_clips):\n", + " D = np.random.uniform(*D_RANGE)\n", + " frames, positions = make_particle_clip(D, n_frames=n_frames)\n", + "\n", + " t0s = np.random.randint(0, n_frames - k, size=3)\n", + " for t0 in t0s:\n", + " true_disp = np.linalg.norm(positions[t0 + k] - positions[t0])\n", + "\n", + " c0 = centroid_from_frame(frames[t0])\n", + " c1 = centroid_from_frame(frames[t0 + k])\n", + " if np.any(np.isnan(c0)) or np.any(np.isnan(c1)):\n", + " continue\n", + " pix_disp = np.linalg.norm(c1 - c0)\n", + "\n", + " Ds.append(D)\n", + " true_disps.append(true_disp)\n", + " pix_disps.append(pix_disp)\n", + "\n", + " return np.array(Ds), np.array(true_disps), np.array(pix_disps)\n", + "\n", + "\n", + "Ds, true_disps, pix_disps = measure_pixel_displacement_vs_D(n_clips=200, k=14)\n", + "\n", + "print(f\"n samples: {len(Ds)}\")\n", + "print(f\"correlation(D, true_disp) = {np.corrcoef(Ds, true_disps)[0, 1]:.3f} \"\n", + " f\"(sanity check -- should be strongly positive by construction)\")\n", + "print(f\"correlation(D, pix_disp) = {np.corrcoef(Ds, pix_disps)[0, 1]:.3f} \"\n", + " f\"(THIS is what matters -- can pixels alone reveal D?)\")\n", + "print(f\"correlation(true_disp, pix_disp) = {np.corrcoef(true_disps, pix_disps)[0, 1]:.3f} \"\n", + " f\"(how faithfully does rendering preserve the true displacement?)\")\n", + "\n", + "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n", + "\n", + "axes[0].scatter(Ds, true_disps, s=8, alpha=0.4)\n", + "axes[0].set_xlabel(\"D\"); axes[0].set_ylabel(\"true displacement (k frames)\")\n", + "axes[0].set_title(\"Ground truth: D vs true displacement\")\n", + "\n", + "axes[1].scatter(Ds, pix_disps, s=8, alpha=0.4, color=\"orange\")\n", + "axes[1].set_xlabel(\"D\"); axes[1].set_ylabel(\"pixel-centroid displacement (k frames)\")\n", + "axes[1].set_title(\"From RENDERED PIXELS: D vs measured displacement\")\n", + "\n", + "axes[2].scatter(true_disps, pix_disps, s=8, alpha=0.4, color=\"green\")\n", + "lims = [0, max(true_disps.max(), pix_disps.max())]\n", + "axes[2].plot(lims, lims, \"r--\", alpha=0.5)\n", + "axes[2].set_xlabel(\"true displacement\"); axes[2].set_ylabel(\"pixel-centroid displacement\")\n", + "axes[2].set_title(\"Rendering fidelity check\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e32e6b7e", + "metadata": {}, + "source": [ + "# diagnostic" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "baa9a949", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "train_pred = history.history[\"train_pred_epoch\"][\"value\"]\n", + "train_reg = history.history.get(\"train_reg_loss_val\")\n", + "\n", + "plt.figure(figsize=(6, 4))\n", + "plt.plot(train_pred, label=\"pred_loss\")\n", + "if train_reg is not None:\n", + " plt.plot(train_reg, label=\"reg_loss\")\n", + "plt.xlabel(\"epoch\"); plt.ylabel(\"loss\"); plt.legend()\n", + "plt.title(\"Training loss breakdown\")\n", + "plt.show()\n", + "\n", + "print(f\"pred_loss: first={train_pred[0]:.4f} last={train_pred[-1]:.4f}\")\n", + "print(f\" -> dropped to {100 * train_pred[-1] / train_pred[0]:.1f}% of initial value\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c791ea9", + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "\n", + "@torch.no_grad()\n", + "def check_latent_variance(model, n_clips=300):\n", + " model.eval()\n", + " ds = DiffusionClipDataset(n_clips=n_clips)\n", + " loader = torch.utils.data.DataLoader(ds, batch_size=32, shuffle=False)\n", + " Zs = []\n", + " for x0, x1, delta_t, D_true, pos0, pos1 in loader:\n", + " x0 = x0.to(model.device)\n", + " Zs.append(model.encode(x0).cpu())\n", + " Z = torch.cat(Zs)\n", + " return Z, Z.std(dim=0)\n", + "\n", + "Z0_check, per_dim_std = check_latent_variance(model)\n", + "print(f\"Per-dim std -- mean: {per_dim_std.mean():.4f}, min: {per_dim_std.min():.4f}, max: {per_dim_std.max():.4f}\")\n", + "\n", + "gamma = 1.0 # whatever you set in variance_loss\n", + "near_floor = (per_dim_std - gamma).abs() < 0.1\n", + "print(f\"Dims near the regularizer floor: {near_floor.sum().item()} / {len(per_dim_std)}\")\n", + "\n", + "# Confirm it's not just stochastic noise in eval mode\n", + "x0_sample, *_ = next(iter(torch.utils.data.DataLoader(DiffusionClipDataset(n_clips=4), batch_size=4)))\n", + "x0_sample = x0_sample.to(model.device)\n", + "z_a, z_b = model.encode(x0_sample), model.encode(x0_sample)\n", + "print(f\"Repeat-forward diff (should be ~0): {(z_a - z_b).abs().max().item():.6f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "899a11b5", + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA\n", + "pca = PCA().fit(Z0_check.numpy())\n", + "print(np.cumsum(pca.explained_variance_ratio_)[:10])" + ] + }, + { + "cell_type": "markdown", + "id": "71b3e56f", + "metadata": {}, + "source": [ + "# test" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c8491ab5", + "metadata": {}, + "outputs": [], + "source": [ + "@torch.no_grad()\n", + "def collect_probe_data(model, n_clips=600):\n", + " model.eval()\n", + " Z, Z2, DT, DS, POS = [], [], [], [], []\n", + " ds = DiffusionClipDataset(n_clips=n_clips)\n", + " loader = torch.utils.data.DataLoader(ds, batch_size=32, shuffle=False)\n", + " for x0, x1, delta_t, D_true, pos0, pos1 in loader:\n", + " x0, x1 = x0.to(model.device), x1.to(model.device)\n", + " z0 = model.encode(x0)\n", + " z1 = model.encode(x1)\n", + " Z.append(z0.cpu()); Z2.append(z1.cpu())\n", + " DT.append(delta_t); DS.append(D_true); POS.append(pos0)\n", + " return (torch.cat(Z), torch.cat(Z2), torch.cat(DT), torch.cat(DS), torch.cat(POS))\n", + "\n", + "\n", + "Z0, Z1, DT_, D_, POS0 = collect_probe_data(model)\n", + "\n", + "# Feature for the D-probe: concatenate z0, z1, and delta_t (so the probe can use\n", + "# \"how much did the latent move, given how much time passed\" -- exactly the\n", + "# quantity that defines a diffusion coefficient).\n", + "feat_D = torch.cat([Z0, Z1, DT_], dim=1).numpy()\n", + "target_D = D_.numpy().ravel()\n", + "\n", + "feat_pos = Z0.numpy()\n", + "target_pos = POS0.numpy()\n", + "\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.metrics import r2_score\n", + "\n", + "Xtr, Xte, ytr, yte = train_test_split(feat_D, target_D, test_size=0.25, random_state=0)\n", + "probe_D = Ridge(alpha=1.0).fit(Xtr, ytr)\n", + "pred_D = probe_D.predict(Xte)\n", + "print(f\"D probe R^2 = {r2_score(yte, pred_D):.3f}\")\n", + "\n", + "Xtr2, Xte2, ytr2, yte2 = train_test_split(feat_pos, target_pos, test_size=0.25, random_state=0)\n", + "probe_pos = Ridge(alpha=1.0).fit(Xtr2, ytr2)\n", + "pred_pos = probe_pos.predict(Xte2)\n", + "print(f\"position probe R^2 = {r2_score(yte2, pred_pos):.3f}\")\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n", + "axes[0].scatter(yte, pred_D, s=10, alpha=0.5)\n", + "axes[0].plot([yte.min(), yte.max()], [yte.min(), yte.max()], \"r--\")\n", + "axes[0].set_xlabel(\"true D\"); axes[0].set_ylabel(\"predicted D\"); axes[0].set_title(\"D probe\")\n", + "\n", + "axes[1].scatter(yte2[:, 0], pred_pos[:, 0], s=10, alpha=0.5, label=\"x\")\n", + "axes[1].scatter(yte2[:, 1], pred_pos[:, 1], s=10, alpha=0.5, label=\"y\")\n", + "axes[1].plot([0, IMAGE_SIZE], [0, IMAGE_SIZE], \"r--\")\n", + "axes[1].set_xlabel(\"true position\"); axes[1].set_ylabel(\"predicted position\")\n", + "axes[1].legend(); axes[1].set_title(\"position probe\")\n", + "plt.tight_layout(); plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "8830f506", + "metadata": {}, + "source": [ + "## 7. Visualizing latent trajectories\n", + "\n", + "A qualitative check: encode every frame of a single clip and look at the latent trajectory (via PCA), next to the\n", + "true (x, y) trajectory. A good world model's latent trajectory should \"look like\" a (possibly distorted/rotated)\n", + "version of the true motion — smooth, continuous, and varying systematically with $D$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d518d0d1", + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA\n", + "\n", + "@torch.no_grad()\n", + "# def encode_full_clip(model, D):\n", + "# frames, positions = make_particle_clip(D)\n", + "# x = torch.from_numpy(frames).unsqueeze(1).to(model.device) # (T, 1, H, W)\n", + "# z = model.encode(x).cpu().numpy() # <-- was model.encoder(x)\n", + "# return z, positions\n", + "def encode_full_clip(model, D, w=WINDOW):\n", + " frames, positions = make_particle_clip(D)\n", + " windows = np.stack([frames[i - w + 1 : i + 1] for i in range(w - 1, len(frames))])\n", + " x = torch.from_numpy(windows).float().to(model.device)\n", + " z = model.encode(x).cpu().numpy()\n", + " return z, positions[w - 1:]\n", + "\n", + "\n", + "model.eval()\n", + "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n", + "for ax, D_val in zip(axes, [0.1, 0.8, 1.8]):\n", + " z, positions = encode_full_clip(model, D_val)\n", + " z_pca = PCA(n_components=2).fit_transform(z)\n", + " ax.plot(positions[:, 0], positions[:, 1], \"o-\", label=\"true (x, y)\", alpha=0.6)\n", + " ax2 = ax.twinx().twiny()\n", + " ax2.plot(z_pca[:, 0], z_pca[:, 1], \"x--\", color=\"orange\", label=\"latent (PCA)\", alpha=0.8)\n", + " ax.set_title(f\"D = {D_val}\")\n", + "plt.tight_layout(); plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "98793cbb", + "metadata": {}, + "source": [ + "## 8. Ablation: what happens without the anti-collapse defenses?\n", + "\n", + "We retrain two broken variants:\n", + "- **No EMA target** (predictor and target encoder share weights and gradients — a classic recipe for collapse)\n", + "- **No variance regularizer** ($\\lambda = 0$)\n", + "\n", + "Watch the prediction loss: it can go to (near) zero *for the wrong reason* — the encoder learns to output a\n", + "near-constant vector, which is trivially easy to \"predict\". The probe R² is the tell: collapse gives low prediction\n", + "loss but a useless representation (probe R² near zero).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7950d7cf", + "metadata": {}, + "outputs": [], + "source": [ + "class WorldModelNoEMA(WorldModel):\n", + " \"\"\"Target encoder IS the online encoder (no separate weights, no stop-gradient).\"\"\"\n", + " def forward(self, x0, x1, delta_t):\n", + " z0 = self.encoder(x0)\n", + " z1_pred = self.predictor(z0, delta_t)\n", + " z1_target = self.encoder(x1) # gradient flows here too -- no stop-gradient!\n", + " return z0, z1_pred, z1_target\n", + "\n", + " @torch.no_grad()\n", + " def update_target(self):\n", + " pass # nothing to update; there is no separate target encoder\n", + "\n", + "\n", + "def quick_eval_probe(model, n_clips=400):\n", + " Z0, Z1, DT_, D_, POS0 = collect_probe_data(model, n_clips=n_clips)\n", + " feat_D = torch.cat([Z0, Z1, DT_], dim=1).numpy()\n", + " Xtr, Xte, ytr, yte = train_test_split(feat_D, D_.numpy().ravel(), test_size=0.25, random_state=0)\n", + " probe = Ridge(alpha=1.0).fit(Xtr, ytr)\n", + " return r2_score(yte, probe.predict(Xte))\n", + "\n", + "\n", + "# Variant A: no EMA target (collapse-prone)\n", + "model_no_ema = WorldModelNoEMA().to(device)\n", + "hist_no_ema = train_world_model(model_no_ema, train_loader, val_loader, n_epochs=10, lam=1.0)\n", + "r2_no_ema = quick_eval_probe(model_no_ema)\n", + "print(f\"No-EMA variant: final pred_loss={hist_no_ema['pred_loss'][-1]:.4f}, probe R^2={r2_no_ema:.3f}\")\n", + "\n", + "# Variant B: no variance regularizer (lam=0), EMA kept\n", + "model_no_reg = WorldModel().to(device)\n", + "hist_no_reg = train_world_model(model_no_reg, train_loader, val_loader, n_epochs=10, lam=0.0)\n", + "r2_no_reg = quick_eval_probe(model_no_reg)\n", + "print(f\"No-regularizer variant: final pred_loss={hist_no_reg['pred_loss'][-1]:.4f}, probe R^2={r2_no_reg:.3f}\")\n", + "\n", + "print(f\"Full model probe R^2 was: {r2_score(yte, pred_D):.3f}\")\n", + "print(\"Compare: low pred_loss + low probe R^2 == collapse, not a good world model.\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "9ccc5cd8", + "metadata": {}, + "source": [ + "## 9. (Optional, advanced) Analysis-by-synthesis through the differentiable simulator\n", + "\n", + "DeepTrack2's pipeline is gradient-preserving. As a contrast to the *learned* world model, we can directly optimize a\n", + "diffusion coefficient by backpropagating an image-reconstruction loss through the simulator itself (\"analysis by\n", + "synthesis\" / differentiable rendering), and compare the result to what our learned model's probe infers from the\n", + "same clip. This connects the chapter back to your earlier \"classical differentiable simulation\" material and shows\n", + "two different routes to the same physical insight: a model that *learned* to infer $D$ implicitly, vs. optimization\n", + "that infers $D$ explicitly via a differentiable forward model.\n", + "\n", + "We leave this as an extension for the reader / next revision of the notebook — it requires exposing $D$ as a\n", + "`torch.nn.Parameter` inside the simulation step rather than a plain numpy float, which depends on how your local\n", + "DeepTrack2/Deeplay version exposes differentiable parameters in `pipeline.update()`.\n" + ] + }, + { + "cell_type": "markdown", + "id": "bd779ae9", + "metadata": {}, + "source": [ + "## 10. Summary & what to try next\n", + "\n", + "- We trained a JEPA-style world model that predicts **latent** futures, not pixels, on simulated diffusion videos.\n", + "- The EMA target + variance regularizer were both necessary to avoid collapse — the ablation made this concrete.\n", + "- A simple linear probe shows the latent space encodes the diffusion coefficient $D$ and the particle's position,\n", + " even though neither was ever a training target.\n", + "\n", + "**Extensions worth trying:**\n", + "- Multiple particles per clip → forces a decision between a single global latent vs. per-particle \"slots\" (a natural\n", + " segue into object-centric / slot-based world models)\n", + "- Add DeepTrack2's optical aberrations/noise to make the rendering more realistic, and see whether the probe R² for\n", + " $D$ degrades — a nice lesson on how much \"physics signal\" survives realistic imaging noise\n", + "- Replace the CNN encoder with a small ViT (swap-in, thanks to Deeplay's modularity) and compare probe quality\n", + "- Try predicting multiple $\\Delta t$ steps ahead recurrently, and see how prediction error grows with horizon —\n", + " this is the classic compounding-error problem in world models\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "deeptrack_dev (3.12.8)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From a08c097a416087cf85cc09fcc755baba58366f8a Mon Sep 17 00:00:00 2001 From: Carlo Date: Fri, 26 Jun 2026 00:41:54 +0200 Subject: [PATCH 2/9] lr --- Companion/world_model/jepa_world_model.ipynb | 2529 +++++++++--------- 1 file changed, 1248 insertions(+), 1281 deletions(-) diff --git a/Companion/world_model/jepa_world_model.ipynb b/Companion/world_model/jepa_world_model.ipynb index 6fe22e4dd..d3803b371 100644 --- a/Companion/world_model/jepa_world_model.ipynb +++ b/Companion/world_model/jepa_world_model.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 1, "id": "42aabbb3", "metadata": {}, "outputs": [], @@ -192,7 +192,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 2, "id": "c125997d", "metadata": {}, "outputs": [], @@ -241,7 +241,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 3, "id": "1b22485e", "metadata": {}, "outputs": [], @@ -282,7 +282,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 4, "id": "5e3b7036", "metadata": {}, "outputs": [], @@ -385,7 +385,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 5, "id": "d3933ac1", "metadata": {}, "outputs": [ @@ -577,42 +577,42 @@ "\n", "\n", "
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above elements are created before\n", " the object is initialized. */\n", " setTimeout(function() {\n", - " anim8f0d1f221d7846cdb0371d3b2d7fc656 = new Animation(frames, img_id, slider_id, 149.0,\n", + " animb7102eda2f634148949c5749bd25124c = new Animation(frames, img_id, slider_id, 149.0,\n", " loop_select_id);\n", " }, 0);\n", " })()\n", @@ -2037,7 +2030,7 @@ "" ] }, - "execution_count": 14, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -2093,7 +2086,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 6, "id": "29ae5714", "metadata": {}, "outputs": [], @@ -2374,7 +2367,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "12a0bd11", "metadata": {}, "outputs": [], @@ -2430,6 +2423,13 @@ "id": "5a15788b", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:76: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default\n" + ] + }, { "data": { "text/html": [ @@ -2495,7 +2495,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "6eeb719f92c8407fba118296cbf2ac58", + "model_id": "27747b3be8144f7084ed9b4e722f0c81", "version_major": 2, "version_minor": 0 }, @@ -2562,11 +2562,11 @@ { "data": { "text/html": [ - "
  [epoch 0] D probe R^2 = 0.592\n",
+       "
  [epoch 0] D probe R^2 = 0.334\n",
        "
\n"
       ],
       "text/plain": [
-       "  [epoch 0] D probe R^2 = 0.592\n"
+       "  [epoch 0] D probe R^2 = 0.334\n"
       ]
      },
      "metadata": {},
@@ -2575,63 +2575,11 @@
     {
      "data": {
       "text/html": [
-       "
  [epoch 1] D probe R^2 = 0.668\n",
+       "
  [epoch 1] D probe R^2 = 0.516\n",
        "
\n"
       ],
       "text/plain": [
-       "  [epoch 1] D probe R^2 = 0.668\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
  [epoch 2] D probe R^2 = 0.445\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "  [epoch 2] D probe R^2 = 0.445\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
  [epoch 3] D probe R^2 = 0.536\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "  [epoch 3] D probe R^2 = 0.536\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
  [epoch 4] D probe R^2 = 0.566\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "  [epoch 4] D probe R^2 = 0.566\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
  [epoch 5] D probe R^2 = 0.656\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "  [epoch 5] D probe R^2 = 0.656\n"
+       "  [epoch 1] D probe R^2 = 0.516\n"
       ]
      },
      "metadata": {},
@@ -2641,7 +2589,7 @@
    "source": [
     "probe_monitor = ProbeMonitorCallback(check_every_n_epochs=1, n_clips=300)\n",
     "\n",
-    "model = WorldModel(optimizer=dl.Adam(lr=1e-4)).create()\n",
+    "model = WorldModel(optimizer=dl.Adam(lr=1e-3)).create()\n",
     "history = model.fit(train_ds, val_data=val_ds, max_epochs=15, batch_size=32, accelerator = \"auto\", callbacks=[probe_monitor])"
    ]
   },
@@ -2894,7 +2842,26 @@
    "execution_count": null,
    "id": "c8491ab5",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "D probe  R^2 = 0.564\n",
+      "position probe  R^2 = 0.003\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "@torch.no_grad()\n",
     "def collect_probe_data(model, n_clips=600):\n",

From 491e2933708298409efdc78ba1b69e689f656185 Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Sun, 23 Aug 2026 10:46:12 +0200
Subject: [PATCH 3/9] jepa

---
 Companion/cc_jepa/jepa.ipynb                 | 6822 ++++++++++++++++++
 Companion/world_model/jepa_world_model.ipynb | 3089 --------
 2 files changed, 6822 insertions(+), 3089 deletions(-)
 create mode 100644 Companion/cc_jepa/jepa.ipynb
 delete mode 100644 Companion/world_model/jepa_world_model.ipynb

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
new file mode 100644
index 000000000..069f6ddd9
--- /dev/null
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -0,0 +1,6822 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "506ba7f1",
+   "metadata": {},
+   "source": [
+    "# Building a World Model with a Joint-Embedding Predictive Architecture (JEPA)\n",
+    "\n",
+    "
\n",
+    "\"Open\n",
+    "If using Colab/Kaggle: You need to uncomment the code in the cell below this one.\n",
+    "
"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "a4994aa9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# !pip install deeplay  # Uncomment if using Colab/Kaggle."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31e63fc4",
+   "metadata": {},
+   "source": [
+    "A central hypothesis in self-supervised learning is that systems can build broad, general knowledge of the world largely from observation, without needing labels for everything they're meant to learn. Joint-Embedding Predictive Architectures (JEPAs) put this into practice by predicting the representation of one part of an input from another, rather than reconstructing the raw input itself.\n",
+    "\n",
+    "In this notebook, you'll use a JEPA to build a small world model of a bouncing particle, a simplified but genuine testbed for self-supervised video representation learning. You'll see how training a predictor entirely in latent space — to predict the representation of future frames instead of the pixels themselves — lets a network learn where an object is and how fast it's moving without ever being given position or velocity labels, compare the model's predicted trajectory against the true simulated one, and investigate how far the network can roll a scene forward in time from just two seed frames."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07068274",
+   "metadata": {},
+   "source": [
+    "
\n",
+    "Note: This companion example extends several ideas introduced throughout the book, specifically, using convolutional networks to extract local image features (Chapter 3), self-supervised learning to train without labels (Chapter 6), attention and transformers to relate those features across space and time (Chapter 8), and learning to emulate the evolution of physical systems (Chapters 11 and 14).\n",
+    "\n",
+    "**Deep Learning Crash Course**  \n",
+    "Giovanni Volpe, Benjamin Midtvedt, Jesús Pineda, Henrik Klein Moberg, Harshith Bachimanchi, Joana B. Pereira, Carlo Manzo  \n",
+    "No Starch Press, San Francisco (CA), 2026  \n",
+    "ISBN-13: 9781718503922  \n",
+    "\n",
+    "[https://nostarch.com/deep-learning-crash-course](https://nostarch.com/deep-learning-crash-course)\n",
+    "\n",
+    "You can find the other notebooks on the [Deep Learning Crash Course GitHub page](https://github.com/DeepTrackAI/DeepLearningCrashCourse).\n",
+    "
"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc4ae3c1",
+   "metadata": {},
+   "source": [
+    "## Understanding Joint-Embedding Predictive Architectures\n",
+    "\n",
+    "Several theories in cognitive science propose that humans build an internal model of the world by integrating raw sensory input into a representation that predicts what will happen next, and that this internal model shapes perception itself, moment to moment. If an artificial agent could learn a world model the same way, directly from raw sensory data and without manual labels, it could understand its surroundings, anticipate what happens next, and plan for situations it has never encountered before.\n",
+    "\n",
+    "Video is a good place to start: it captures how a scene evolves directly, frame by frame. A natural first attempt would be to train a network to predict future frames directly, pixel by pixel. Imagine watching a short clip of a ball rolling across a table: even without seeing what happens next, you can be fairly confident about where it will be a moment later and how fast it's moving. What you can't predict is much less important, the exact play of light on its surface, or a faint shadow shifting as the camera trembles slightly. Forcing a network to predict pixels forces it to get all of this right, including the parts that were never predictable in the first place. In practice, this backfires: since the network can't know how the unpredictable details will turn out, it hedges its bets and produces a blurry average over the possibilities, spending most of its capacity guessing at things that were never guessable, instead of learning the structure, like the ball's position and motion, that actually matters.\n",
+    "\n",
+    "Joint-Embedding Predictive Architectures take a different, non-generative approach to the same problem: rather than predicting future pixels, they predict the future's internal representation, a compressed description that keeps only what's predictable and discards the rest. Because the network never has to reconstruct fine, unpredictable detail, it can dedicate its capacity to the underlying structure of the scene, which is exactly what lets a JEPA-trained network learn about an object's position, velocity, or identity without ever being told these are the things to look for."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23bfe323",
+   "metadata": {},
+   "source": [
+    "### Defining the Problem\n",
+    "\n",
+    "Consider an agent that only has access to a stream of raw observations (e.g., a video) of some dynamical system, with no information about the physical rules that govern it. The problem is to learn, directly from these observations and without any labels, a representation that captures the system's underlying state, such as the position and velocity of the objects it contains, and that can be used to predict how that state will evolve over time."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "72c2d7b7",
+   "metadata": {},
+   "source": [
+    "### Encoders, Predictors, and Training\n",
+    "\n",
+    "A JEPA is built from three parts: two encoders and a predictor. It takes two inputs, $x$ and $y$, and passes each through an encoder to produce two representations, $s_x$ and $s_y$. $x$ is usually called the *context*, since it's what the model is given, and $y$ the *target*, since it's what has to be predicted. The same terms apply to their representations: $s_x$ is the context representation, $s_y$ is the target representation.\n",
+    "\n",
+    "The two encoders don't need to share an architecture or parameters, which is what lets $x$ and $y$ come from entirely different signals or two different views of the same scene. A predictor module then learns to produce $s_y$ from $s_x$. Because $x$ doesn't always determine $y$ exactly, the predictor can also take a latent variable $z$ as input, letting it represent several plausible outcomes rather than being forced to commit to one.\n",
+    "\n",
+    "Masking is one common way to create that split: by holding part of the input back from the context encoder, there's something genuinely left to predict, rather than reconstruct from something already fully visible. Holding out whole contiguous blocks, rather than scattering individually hidden patches, matters too: if the model could attend to a token right next to a hidden one, it could get away with simple local interpolation instead of learning how the scene actually evolves.\n",
+    "\n",
+    "To prevent the model from collapsing to a trivial solution, such as mapping every input to the same constant representation, the target encoder is never trained directly. Instead, it's a slowly updated exponential moving average (EMA) of the context encoder, so the prediction target evolves gradually and stays consistent throughout training.\n",
+    "\n",
+    "The predictor is trained by comparing its predicted representation to the target encoder's actual representation, using a simple distance in representation space rather than a pixel-wise loss."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c74cb685",
+   "metadata": {},
+   "source": [
+    "## The Physical System\n",
+    "\n",
+    "You'll apply these ideas to a small, concrete system: a single bead moving at constant velocity inside a square box, bouncing off the walls."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1f8afc2d",
+   "metadata": {},
+   "source": [
+    "The first step is to define the ground-truth physics: a bead moves at a constant, randomly chosen integer-pixel velocity and bounces elastically off the image boundary, reversing whichever velocity component hit the wall."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "9dea3f77",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "IMAGE_SIZE = 24\n",
+    "N_FRAMES = 20\n",
+    "DELTA_T = 1.0\n",
+    "MARGIN = 0\n",
+    "\n",
+    "DISCRETE_VELOCITIES = np.array([\n",
+    "    [-1, -1], [-1, 0], [-1, 1],\n",
+    "    [ 0, -1],          [ 0, 1],\n",
+    "    [ 1, -1], [ 1, 0], [ 1, 1],\n",
+    "    [-2,  0], [ 2,  0], [ 0, -2], [ 0,  2],\n",
+    "    [-2, -1], [-2,  1], [ 2, -1], [ 2,  1],\n",
+    "    [-1, -2], [-1,  2], [ 1, -2], [ 1,  2],\n",
+    "], dtype=np.int32)\n",
+    "\n",
+    "def random_discrete_velocity():\n",
+    "    return DISCRETE_VELOCITIES[np.random.randint(len(DISCRETE_VELOCITIES))].copy()\n",
+    "\n",
+    "def reflect_grid(pos, vel, lower, upper):\n",
+    "    \"\"\"Reflect one integer coordinate in the inclusive [lower, upper] range.\"\"\"\n",
+    "    if pos < lower:\n",
+    "        return lower + (lower - pos), -vel\n",
+    "    if pos > upper:\n",
+    "        return upper - (pos - upper), -vel\n",
+    "    return pos, vel\n",
+    "\n",
+    "def simulate_trajectory(radius,\n",
+    "                        image_size=IMAGE_SIZE, n_frames=N_FRAMES,\n",
+    "                        delta_t=DELTA_T, margin=MARGIN,\n",
+    "                        seed=None):\n",
+    "    \"\"\"One fixed-shape bead moving on an integer pixel grid.\"\"\"\n",
+    "    if seed is not None:\n",
+    "        np.random.seed(seed)\n",
+    "    \n",
+    "    radius_pixels = int(np.floor(radius))\n",
+    "    lower = margin + radius_pixels\n",
+    "    upper = image_size - margin - 1 - radius_pixels\n",
+    "    if lower >= upper:\n",
+    "        raise ValueError(\"Image is too small for this bead radius and margin.\")\n",
+    "\n",
+    "    pos = np.random.randint(lower, upper + 1, size=2, dtype=np.int32)\n",
+    "    vel = random_discrete_velocity()\n",
+    "\n",
+    "    positions = [pos.copy()]\n",
+    "    velocities = [vel.copy()]\n",
+    "   \n",
+    "    for _ in range(n_frames - 1):\n",
+    "        pos = pos + vel\n",
+    "\n",
+    "        pos[0], vel[0] = reflect_grid(pos[0], vel[0], lower, upper)\n",
+    "        pos[1], vel[1] = reflect_grid(pos[1], vel[1], lower, upper)\n",
+    "\n",
+    "        positions.append(pos.copy())\n",
+    "        velocities.append(vel.copy())\n",
+    "\n",
+    "\n",
+    "    return (np.array(positions, dtype=np.float32),\n",
+    "            np.array(velocities, dtype=np.float32))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "50581c2a",
+   "metadata": {},
+   "source": [
+    "The next step is turning positions into pixels. `render_trajectories` draws the bead as a soft, radially-fading disc.\n",
+    "\n",
+    "You'll also add distractors, small flickering rectangles appearing, disappearing, and relocating unpredictably from frame to frame. \n",
+    "\n",
+    "`make_clip` ties it together: one simulated trajectory, rendered both with and without distractors, alongside the ground-truth position and velocity."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7f80d1e0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "BEAD_RADIUS = 4.5\n",
+    "BEAD_INTENSITY = 0.7\n",
+    "DISTRACTOR_INTENSITY = 1.0\n",
+    "\n",
+    "def render_trajectories(positions, radius=BEAD_RADIUS, image_size=IMAGE_SIZE,\n",
+    "                        intensity=BEAD_INTENSITY, sigma=None):\n",
+    "    \"\"\"Render a video of a circular bead with a radial intensity falloff.\"\"\"\n",
+    "\n",
+    "    if sigma is None:\n",
+    "        sigma = radius / 2.0  # ~14% of peak intensity right at the edge\n",
+    "    yy, xx = np.meshgrid(np.arange(image_size), np.arange(image_size), indexing=\"ij\")\n",
+    "    frames = np.zeros((len(positions), image_size, image_size), dtype=np.float32)\n",
+    "    for t, (row, col) in enumerate(positions):\n",
+    "        dist_sq = (yy - row) ** 2 + (xx - col) ** 2\n",
+    "        bead = dist_sq <= radius ** 2\n",
+    "        frames[t, bead] = intensity * np.exp(-dist_sq[bead] / (2 * sigma ** 2))\n",
+    "    return frames\n",
+    "\n",
+    "\n",
+    "def sample_distractor_rects(image_size=IMAGE_SIZE, n_min=1, n_max=3, side_min=1, side_max=4):\n",
+    "    \"\"\"Sample a random number of small, static rectangular distractors.\"\"\"\n",
+    "\n",
+    "    n = np.random.randint(n_min, n_max + 1)\n",
+    "    rects = []\n",
+    "    for _ in range(n):\n",
+    "        h = np.random.randint(side_min, side_max + 1)\n",
+    "        w = np.random.randint(side_min, side_max + 1)\n",
+    "        row0 = np.random.randint(0, image_size - h + 1)\n",
+    "        col0 = np.random.randint(0, image_size - w + 1)\n",
+    "        rects.append((row0, col0, h, w))\n",
+    "    return rects\n",
+    "\n",
+    "def add_flickering_distractors(frames, p_present=0.75, n_min=1, n_max=4,\n",
+    "                                side_min=1, side_max=3, intensity=DISTRACTOR_INTENSITY):\n",
+    "    \"\"\"Stamp random rectangular distractors onto a random subset of frames.\"\"\"\n",
+    "\n",
+    "    out = frames.copy()\n",
+    "    T, H, W = frames.shape\n",
+    "    for t in range(T):\n",
+    "        if np.random.rand() > p_present:\n",
+    "            continue\n",
+    "        rects = sample_distractor_rects(image_size=H, n_min=n_min, n_max=n_max,\n",
+    "                                         side_min=side_min, side_max=side_max)\n",
+    "        for row0, col0, h, w in rects:\n",
+    "            out[t, row0:row0 + h, col0:col0 + w] = np.maximum(\n",
+    "                out[t, row0:row0 + h, col0:col0 + w], intensity\n",
+    "            )\n",
+    "    return out\n",
+    "\n",
+    "def make_clip(radius=BEAD_RADIUS):\n",
+    "    \"\"\"Simulate one trajectory and return matched views.\"\"\"\n",
+    "    \n",
+    "    positions, vel = simulate_trajectory(radius)\n",
+    "    clean = render_trajectories(positions, radius)\n",
+    "    w_distractors = add_flickering_distractors(clean)\n",
+    "    return clean, w_distractors, positions, vel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "551fb934",
+   "metadata": {},
+   "source": [
+    "A quick visual sanity check: this animates one clip side by side, clean and with distractors, along with the ground-truth velocity and speed at each frame."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "43847c1c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "
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+       "  \n",
+       "  
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+       "    \n",
+       "    
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+       "      \n",
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+       "    
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+       "    
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+       "      \n",
+       "    
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+       "  
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+       "\n",
+       "\n",
+       "\n"
+      ],
+      "text/plain": [
+       ""
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib import animation\n",
+    "from IPython.display import HTML\n",
+    "\n",
+    "clean_frames, w_distractors_frames, positions, vel = make_clip()\n",
+    "\n",
+    "fig, axes = plt.subplots(1, 2, figsize=(9, 4.5))\n",
+    "im_clean = axes[0].imshow(clean_frames[0], cmap=\"gray\", vmin=0, vmax=1)\n",
+    "im_w_distractors = axes[1].imshow(w_distractors_frames[0], cmap=\"gray\", vmin=0, vmax=1)\n",
+    "axes[0].set_title(\"Clean view\")\n",
+    "axes[1].set_title(\"With distractors view\")\n",
+    "for ax in axes:\n",
+    "    ax.axis(\"off\")\n",
+    "\n",
+    "def update(i):\n",
+    "    im_clean.set_data(clean_frames[i])\n",
+    "    im_w_distractors.set_data(w_distractors_frames[i])\n",
+    "    row_velocity, col_velocity = vel[i]\n",
+    "    speed = np.linalg.norm(vel[i])\n",
+    "    fig.suptitle(\n",
+    "        f\"Frame {i}   |   velocity = ({row_velocity:+.0f}, {col_velocity:+.0f})\"\n",
+    "        f\"   |   speed = {speed:.2f}   \"\n",
+    "    )\n",
+    "    return [im_clean, im_w_distractors]\n",
+    "\n",
+    "anim = animation.FuncAnimation(\n",
+    "    fig, update, frames=len(clean_frames), interval=150, blit=False\n",
+    ")\n",
+    "plt.close(fig)\n",
+    "\n",
+    "HTML(anim.to_jshtml())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f798aacd",
+   "metadata": {},
+   "source": [
+    "The following helper function ties everything together: simulate a trajectory, render both clean and distractor views, and repeat for as many clips as needed, saving the result to disk in one call."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "07c28293",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import torch\n",
+    "\n",
+    "def build_and_save_dataset(path, n_clips=5000, radius=BEAD_RADIUS):\n",
+    "    \"\"\"Generate n_clips random trajectories, render both clean and distractor \n",
+    "    views for each, and save everything to `path` as a single .pt file.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    clean_clips, w_distractors_clips = [], []\n",
+    "    positions_list, velocities_list = [], []\n",
+    "    for _ in range(n_clips):\n",
+    "        clean, w_distractors, positions, vel = make_clip(radius)\n",
+    "        clean_clips.append(torch.from_numpy(clean).unsqueeze(0))\n",
+    "        w_distractors_clips.append(torch.from_numpy(w_distractors).unsqueeze(0))\n",
+    "        positions_list.append(torch.from_numpy(positions))\n",
+    "        velocities_list.append(torch.from_numpy(vel))\n",
+    "\n",
+    "    clean_clips = torch.stack(clean_clips).float()\n",
+    "    torch.save({\n",
+    "        \"clips_clean\": clean_clips,\n",
+    "        \"clips_w_distractors\": torch.stack(w_distractors_clips).float(),\n",
+    "        \"positions\": torch.stack(positions_list).float(),\n",
+    "        \"velocities\": torch.stack(velocities_list).float(),\n",
+    "    }, path)\n",
+    "    print(f\"saved {n_clips} clips to {path}\")\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a10ecfc",
+   "metadata": {},
+   "source": [
+    "With the function defined, generate the train, validation, and test splits. Each is saved to disk once, so re-running this notebook later loads the existing files instead of resimulating everything from scratch."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "9d9ad66c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Datasets already exist. Skipping dataset generation.\n"
+     ]
+    }
+   ],
+   "source": [
+    "import os\n",
+    "from os.path import exists\n",
+    "\n",
+    "os.makedirs(\"datasets/bouncing bead with distractors\", exist_ok=True)\n",
+    "\n",
+    "if exists(\"datasets/bouncing bead with distractors/particles_train.pt\") and exists(\"datasets/bouncing bead with distractors/particles_val.pt\") and exists(\"datasets/bouncing bead with distractors/particles_test.pt\"):\n",
+    "    print(\"Datasets already exist. Skipping dataset generation.\")\n",
+    "else:\n",
+    "    build_and_save_dataset(\"datasets/bouncing bead with distractors/particles_train.pt\", n_clips=10000)\n",
+    "    build_and_save_dataset(\"datasets/bouncing bead with distractors/particles_val.pt\", n_clips=2000)\n",
+    "    build_and_save_dataset(\"datasets/bouncing bead with distractors/particles_test.pt\", n_clips=1000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ddd653ee",
+   "metadata": {},
+   "source": [
+    "The class `ParticlesDataset` wraps a saved file for training. With `p_distractors=0`, it returns clean clips only. With `p_distractors>0`, each clip has some probability of using its distractor-contaminated view as context instead of the clean one, while the clean view is always kept as what the encoder is trained to reconstruct.\n",
+    "\n",
+    "For now, you'll start with clean clips."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "b4cf3ddc",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "train_ds: 10000 clips\n",
+      "val_ds:   2000 clips\n",
+      "test_ds:  1000 clips\n",
+      "clip shape: torch.Size([1, 20, 24, 24])\n",
+      "positions shape: torch.Size([20, 2])\n",
+      "velocities shape: torch.Size([20, 2])\n"
+     ]
+    }
+   ],
+   "source": [
+    "class ParticlesDataset(torch.utils.data.Dataset):\n",
+    "    \"\"\"Clean baseline dataset, or paired context/target views for JEPA fine-tuning.\"\"\"\n",
+    "    def __init__(self, path, p_distractors=0.0, seed=0):\n",
+    "        data = torch.load(path)\n",
+    "        self.clean = data.get(\"clips_clean\")\n",
+    "        self.positions = data[\"positions\"]\n",
+    "        self.velocities = data[\"velocities\"]\n",
+    "        self.p_distractors = p_distractors\n",
+    "        if p_distractors > 0.0:\n",
+    "            self.w_distractors = data[\"clips_w_distractors\"]\n",
+    "            rng = np.random.default_rng(seed)\n",
+    "            self.use_w_distractors_context = rng.random(len(self.clean)) < p_distractors\n",
+    "\n",
+    "    def __len__(self):\n",
+    "        return len(self.clean)\n",
+    "\n",
+    "    def __getitem__(self, idx):\n",
+    "        if self.p_distractors > 0.0:\n",
+    "            context = self.w_distractors[idx] if self.use_w_distractors_context[idx] else self.clean[idx]\n",
+    "            return self.clean[idx], context, self.positions[idx], self.velocities[idx]\n",
+    "        return self.clean[idx], self.positions[idx], self.velocities[idx]\n",
+    "\n",
+    "train_ds = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_train.pt\")\n",
+    "val_ds = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_val.pt\")\n",
+    "test_ds = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_test.pt\")\n",
+    "\n",
+    "print(f\"train_ds: {len(train_ds)} clips\")\n",
+    "print(f\"val_ds:   {len(val_ds)} clips\")\n",
+    "print(f\"test_ds:  {len(test_ds)} clips\")\n",
+    "\n",
+    "clip0, pos0, vel0 = train_ds[0]\n",
+    "print(\"clip shape:\", clip0.shape)      # (1, N_FRAMES, H, W)\n",
+    "print(\"positions shape:\", pos0.shape)  # (N_FRAMES, 2)\n",
+    "print(\"velocities shape:\", vel0.shape)  # (N_FRAMES, 2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "468bd129",
+   "metadata": {},
+   "source": [
+    "## Pretraining\n",
+    "\n",
+    "Training happens in two stages: pretraining and rollout, echoing what V-JEPA2-AC calls pretraining and post-training. First, the context and target encoders and a predictor are trained together, self-supervised, on the masked-prediction task described earlier, that's pretraining, covered in this section. This predictor's job is to force a good representation to emerge, not to be used afterward: once pretraining is done, only the context encoder is kept. The target encoder was only ever an EMA-updated training aid, and the pretraining predictor is discarded along with it. The rollout stage, covered later, builds an entirely new predictor on top of the frozen context encoder to forecast forward in time, unlike V-JEPA2-AC's post-training, it isn't action-conditioned, it's pure passive dynamics, since this notebook's bead has no actions to take."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "deb4d992",
+   "metadata": {},
+   "source": [
+    "### Masking the Clips\n",
+    "\n",
+    "As described earlier, the context encoder needs part of the input held back, otherwise there's nothing left to predict, and here's the concrete scheme that does the holding back for these clips.\n",
+    "\n",
+    "The masking scheme below follows V-JEPA's actual recipe: two mask groups sampled together for every clip, several small, scattered blocks (\"short\") and one large block (\"long\"), so the model learns from both an easier and a harder version of the same task in every training step. Each block is held out from the context encoder across the whole clip, block-shaped as described earlier, while the target encoder always sees the complete, unmasked clip.\n",
+    "\n",
+    "Despite the names, \"short\" and \"long\" refer to spatial range, not time. Both mask groups span the entire clip; what differs is how far a masked patch sits from the nearest visible one, a few small, scattered blocks keep every hidden patch close to visible content (short-range), while one large block forces the model to infer content far from anything it can see (long-range)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "67adc09b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "\n",
+    "MASK_GROUPS = [(\"short\", 4, 0.1), (\"long\", 1, 0.5)]\n",
+    "\n",
+    "\n",
+    "def _block_side(s_grid, coverage):\n",
+    "    \"\"\"Side length of a square block covering roughly `coverage` fraction\n",
+    "    of the grid.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    area = coverage * s_grid * s_grid\n",
+    "    side = max(1, min(s_grid, round(math.sqrt(area))))\n",
+    "    return side\n",
+    "\n",
+    "def sample_masks(B, t_grid, s_grid, rng=None, min_visible=2):\n",
+    "    \"\"\"Sample one short-range and one long-range mask (see MASK_GROUPS),\n",
+    "    each reused identically across the whole batch. A short retry loop\n",
+    "    guards against masking away more than `min_visible` cells.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    rng = rng or np.random.default_rng()\n",
+    "    groups = []\n",
+    "\n",
+    "    for label, n_blocks, coverage in MASK_GROUPS:\n",
+    "        side = _block_side(s_grid, coverage)\n",
+    "\n",
+    "        for _ in range(20):   # retry a few times if we mask too much\n",
+    "            mask = np.zeros((s_grid, s_grid), dtype=bool)\n",
+    "            for _ in range(n_blocks):\n",
+    "                top = rng.integers(0, s_grid - side + 1)\n",
+    "                left = rng.integers(0, s_grid - side + 1)\n",
+    "                mask[top:top+side, left:left+side] = True\n",
+    "            if (~mask).sum() >= min_visible:\n",
+    "                break\n",
+    "\n",
+    "        masked_cells = np.flatnonzero(mask)\n",
+    "        visible_cells = np.flatnonzero(~mask)\n",
+    "\n",
+    "        t_offsets = np.arange(t_grid) * (s_grid * s_grid)\n",
+    "        ctx = np.sort((t_offsets[:, None] + visible_cells[None, :]).ravel())\n",
+    "        pred = np.sort((t_offsets[:, None] + masked_cells[None, :]).ravel())\n",
+    "\n",
+    "        groups.append({\n",
+    "            \"label\": label,\n",
+    "            \"ctx\": [ctx.tolist()] * B,\n",
+    "            \"pred\": [pred.tolist()] * B,\n",
+    "        })\n",
+    "    return groups"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e43f8375",
+   "metadata": {},
+   "source": [
+    "Let's see what these masks actually look like on real clips. The cell below overlays the masked regions in red on a sample clip, for both the short- and long-range groups, confirming visually that \"short\" scatters several small blocks while \"long\" covers one large region, and that both stay in the same place across every frame.\n",
+    "\n",
+    "Before any of this can run, the video needs to be broken into tokens, the discrete units a transformer actually operates on. Treating every individual pixel as its own token would be far too many for a transformer to handle, and a single pixel carries almost no information about the scene on its own anyway. Instead, the clip is divided into small spatial patches, `patch_size` × `patch_size` pixels each. Each patch is then extended across a few consecutive frames, `t_patch` frames at a time, into a tubelet: a small chunk of space and time treated as a single unit. Each tubelet becomes one token, and `s_grid` and `t_grid` are simply how many of these tokens fit across space and across time."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "3d93bd73",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "num_frames = N_FRAMES\n",
+    "batch_size = 8\n",
+    "patch_size = 6\n",
+    "image_size = 24\n",
+    "t_patch = 2\n",
+    "\n",
+    "loader = torch.utils.data.DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
+    "batch = next(iter(loader))\n",
+    "if len(batch) == 4:\n",
+    "    _, videos, positions, velocities = batch\n",
+    "else:\n",
+    "    videos, positions, velocities = batch\n",
+    "\n",
+    "t_grid = num_frames // t_patch\n",
+    "s_grid = image_size // patch_size\n",
+    "\n",
+    "groups = sample_masks(videos.size(0), t_grid, s_grid)\n",
+    "n_groups = len(groups)\n",
+    "\n",
+    "n_frames_total = videos.shape[2]\n",
+    "frame_indices = list(range(0, n_frames_total, 2))   # every 2nd frame\n",
+    "n_display_frames = len(frame_indices)\n",
+    "\n",
+    "sample_i = 0\n",
+    "fig, axes = plt.subplots(n_groups, n_display_frames,\n",
+    "                         figsize=(1.6 * n_display_frames, 2.0 * n_groups),\n",
+    "                         squeeze=False)\n",
+    "\n",
+    "for row, group in enumerate(groups):\n",
+    "    masked_spatial = np.unique(np.array(group[\"pred\"][sample_i]) % (s_grid * s_grid))\n",
+    "    mask_grid = np.zeros((s_grid, s_grid), dtype=bool)\n",
+    "    mask_grid.flat[masked_spatial] = True\n",
+    "    mask_pixels = np.repeat(np.repeat(mask_grid, patch_size, axis=0), patch_size, axis=1)\n",
+    "\n",
+    "    for col, t in enumerate(frame_indices):\n",
+    "        ax = axes[row, col]\n",
+    "        ax.imshow(videos[sample_i, 0, t].cpu(), cmap=\"gray\", vmin=0, vmax=1)\n",
+    "        overlay = np.zeros((*mask_pixels.shape, 4))\n",
+    "        overlay[mask_pixels] = [1, 0, 0, 0.35]\n",
+    "        ax.imshow(overlay)\n",
+    "        ax.axis(\"off\")\n",
+    "        if col == 0:\n",
+    "            ax.set_ylabel(group[\"label\"], rotation=0, ha=\"right\", va=\"center\")\n",
+    "        if row == 0:\n",
+    "            ax.set_title(f\"t={t}\", fontsize=8)\n",
+    "\n",
+    "plt.suptitle(\"JEPA spatial masks: red = masked tokens\", y=1.02)\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d9026b7a",
+   "metadata": {},
+   "source": [
+    "### The Encoder\n",
+    "\n",
+    "With tokenization defined, the next step is turning those tokens into representations, this is where the encoder itself lives.\n",
+    "\n",
+    "The building blocks here are self-attention transformer blocks: each token looks at every other token in the sequence and decides how much to weight each one when updating its own representation, letting information flow between distant patches directly, rather than only through the fixed, local neighborhoods a convolutional network would use. Transformers have no inherent sense of position, though: attention treats a sequence of tokens as an unordered set unless told otherwise. `pos_embed_3d` fixes this by giving every token a fixed sin/cos embedding based on where it sits in space and time, the same idea used in the original Transformer paper, extended here from one dimension to three. `Block` is the standard building block used throughout this notebook: self-attention followed by an MLP, both with residual connections. The same class reappears in the predictor later.\n",
+    "\n",
+    "`VideoEncoder` ties it together: `tubelet_proj` turns the clip into tubelet tokens, positional embeddings get added, and the result runs through a stack of `Block`s. Its `forward` method supports more than one use case on purpose: encoding the whole clip at once (the default), encoding a single temporal group in isolation via `t_offset` (used later to keep the rollout predictor from leaking information from future frames), and encoding only a subset of tokens via `idx` (used for masking, this is what the context encoder calls with only the visible tokens). The same class serves as both the context encoder and the target encoder, just used differently."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "027f07d3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import torch.nn as nn\n",
+    "import torch.nn.functional as F\n",
+    "\n",
+    "def pos_embed_3d(t, h, w, dim, t_frac=0.25):\n",
+    "    \"\"\"Combined temporal + spatial sin/cos positional embedding for video tokens.\"\"\"\n",
+    "    td = int(dim * t_frac); td += td % 2; sd = dim - td\n",
+    "\n",
+    "    # Temporal component\n",
+    "    pos_t = torch.arange(t).unsqueeze(1).float()\n",
+    "    div_t = torch.exp(torch.arange(0, td, 2).float() * (-math.log(10000.) / td))\n",
+    "    pe_t = torch.zeros(t, td)\n",
+    "    pe_t[:, 0::2] = torch.sin(pos_t * div_t)\n",
+    "    pe_t[:, 1::2] = torch.cos(pos_t * div_t)\n",
+    "\n",
+    "    # Spatial component\n",
+    "    sub = sd // 4\n",
+    "    yy, xx = [x.reshape(-1).float() for x in torch.meshgrid(torch.arange(h), torch.arange(w), indexing=\"ij\")]\n",
+    "    div_s = torch.exp(torch.arange(0, sub * 2, 2).float() * (-math.log(10000.) / (sub * 2)))\n",
+    "    pe_s = torch.cat([torch.sin(yy[:, None] * div_s), torch.cos(yy[:, None] * div_s),\n",
+    "                       torch.sin(xx[:, None] * div_s), torch.cos(xx[:, None] * div_s)], dim=-1)\n",
+    "\n",
+    "    # Combine: broadcast temporal across all spatial positions, spatial across all timesteps\n",
+    "    pe = torch.zeros(t * h * w, dim)\n",
+    "    pe[:, :td] = pe_t.unsqueeze(1).expand(t, h * w, td).reshape(-1, td)\n",
+    "    pe[:, td:] = pe_s.unsqueeze(0).expand(t, h * w, sd).reshape(-1, sd)\n",
+    "    return pe\n",
+    "\n",
+    "class Block(nn.Module):\n",
+    "    def __init__(self, dim, heads, mlp=4.0):\n",
+    "        super().__init__()\n",
+    "        self.n1, self.n2 = nn.LayerNorm(dim, eps=1e-6), nn.LayerNorm(dim, eps=1e-6)\n",
+    "        self.attn = nn.MultiheadAttention(dim, heads, batch_first=True)\n",
+    "        self.mlp = nn.Sequential(nn.Linear(dim, int(dim * mlp)), nn.GELU(), nn.Linear(int(dim * mlp), dim))\n",
+    "\n",
+    "    def forward(self, x, attn_mask=None):\n",
+    "        h = self.n1(x)\n",
+    "        x = x + self.attn(h, h, h, attn_mask=attn_mask, need_weights=False)[0]\n",
+    "        return x + self.mlp(self.n2(x))\n",
+    "\n",
+    "\n",
+    "class VideoEncoder(nn.Module):\n",
+    "    def __init__(self, num_frames=20, t_patch=2, img_size=24, patch_size=6,\n",
+    "                 in_chans=1, dim=128, depth=6, heads=4):\n",
+    "        super().__init__()\n",
+    "        self.t_grid = num_frames // t_patch; self.s_grid = img_size // patch_size\n",
+    "        self.n_patches = self.t_grid * self.s_grid * self.s_grid\n",
+    "        self.t_patch = t_patch; self.patch_size = patch_size; self.dim = dim\n",
+    "        self.tubelet_proj = nn.Conv3d(in_chans, dim,\n",
+    "                                      kernel_size=(t_patch, patch_size, patch_size),\n",
+    "                                      stride=(t_patch, patch_size, patch_size))\n",
+    "        self.register_buffer(\"pos\", pos_embed_3d(self.t_grid, self.s_grid, self.s_grid, dim))\n",
+    "        self.blocks = nn.ModuleList([Block(dim, heads) for _ in range(depth)])\n",
+    "        self.norm = nn.LayerNorm(dim, eps=1e-6)\n",
+    "\n",
+    "\n",
+    "    def forward(self, videos, idx=None, t_offset=0):\n",
+    "        tokens = self.tubelet_proj(videos).flatten(2).transpose(1, 2)\n",
+    "        B, N, D = tokens.shape\n",
+    "\n",
+    "        if idx is None:\n",
+    "            S = self.s_grid * self.s_grid\n",
+    "            if N == S:\n",
+    "                # Single-group encode (e.g. leakage-safe rollout encoding)\n",
+    "                idx = torch.arange(t_offset * S, t_offset * S + N, device=videos.device).expand(B, -1)\n",
+    "            else:\n",
+    "                # Full-clip encode (default path, N = T*S)\n",
+    "                idx = torch.arange(N, device=videos.device).expand(B, -1)\n",
+    "            x = tokens + self.pos[idx]\n",
+    "        else:\n",
+    "            x = tokens.gather(1, idx.unsqueeze(-1).expand(-1, -1, D)) + self.pos[idx]\n",
+    "\n",
+    "        for blk in self.blocks:\n",
+    "            x = blk(x)\n",
+    "        return self.norm(x)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc2f5b01",
+   "metadata": {},
+   "source": [
+    "### The Predictor\n",
+    "\n",
+    "The predictor's job, as described earlier, is to infer the representation of the masked positions from the visible ones. Concretely: the encoded context tokens are projected down to the predictor's own, smaller, working dimension, and every masked position gets filled with a copy of the same learnable `mask_token`, a placeholder that carries no information about what's actually there, only its position, added the same way positional embeddings were added in the encoder. Context tokens and mask tokens are concatenated into one sequence and run through the same kind of self-attention blocks as the encoder, letting the mask tokens attend to the visible context, and to each other, to infer what should fill each gap. Only the mask-token positions are read out at the end and projected back up to the encoder's dimension, giving the predicted representation for each masked position."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "cd3d9dfe",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class Predictor(nn.Module):\n",
+    "    def __init__(self, t_grid, s_grid, enc_dim=128, dim=64, depth=4, heads=4):\n",
+    "        super().__init__()\n",
+    "        self.in_proj = nn.Linear(enc_dim, dim); self.out_proj = nn.Linear(dim, enc_dim)\n",
+    "        self.mask_token = nn.Parameter(torch.zeros(1, 1, dim)); nn.init.trunc_normal_(self.mask_token, std=0.02)\n",
+    "        self.register_buffer(\"pos\", pos_embed_3d(t_grid, s_grid, s_grid, dim))\n",
+    "        self.blocks = nn.ModuleList([Block(dim, heads) for _ in range(depth)])\n",
+    "        self.norm = nn.LayerNorm(dim, eps=1e-6)\n",
+    "\n",
+    "    def forward(self, ctx, ctx_idx, tgt_idx):\n",
+    "        B, T = ctx.size(0), tgt_idx.size(1)\n",
+    "        x = torch.cat([self.in_proj(ctx) + self.pos[ctx_idx],\n",
+    "                       self.mask_token.expand(B, T, -1) + self.pos[tgt_idx]], dim=1)\n",
+    "        for blk in self.blocks: x = blk(x)\n",
+    "        return self.out_proj(self.norm(x[:, -T:]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "299fe29e",
+   "metadata": {},
+   "source": [
+    "### The Pretraining Model\n",
+    "\n",
+    "`PretrainingModel` assembles everything from this section into one trainable object: a context encoder, an EMA-updated target encoder, and a predictor.\n",
+    "\n",
+    "Each training step samples a fresh short-range and long-range mask, encodes the context video using only its visible tokens, and asks the predictor to infer the masked positions' representations. Those predictions are compared against the target encoder's own encoding of the complete, clean, unmasked clip, using a simple L1 distance in representation space. Both mask groups are trained on in the same step; their losses are logged separately, since long-range masking is the harder of the two tasks and it's worth seeing whether the model struggles more with one than the other.\n",
+    "\n",
+    "`update_target` implements the exponential moving average described earlier: the first call copies the context encoder's weights over directly, so both encoders start identical, and every call after that nudges the target encoder a small step toward the context encoder's current weights, keeping the prediction target stable and slow-moving rather than tied to whatever the context encoder looks like at this exact instant."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "6ff7f0b7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import deeplay as dl\n",
+    "\n",
+    "class PretrainingModel(dl.Application):\n",
+    "    def __init__(self, num_frames=N_FRAMES, img_size=IMAGE_SIZE, t_patch=2, patch_size=6,\n",
+    "                 dim=128, depth=6, heads=4, ema_tau=0.998, optimizer=None, **kwargs):\n",
+    "\n",
+    "        self.ctx_enc = VideoEncoder(num_frames=num_frames, t_patch=t_patch, img_size=img_size,\n",
+    "                                     patch_size=patch_size, dim=dim, depth=depth, heads=heads)\n",
+    "        self.tgt_enc = VideoEncoder(num_frames=num_frames, t_patch=t_patch, img_size=img_size,\n",
+    "                                     patch_size=patch_size, dim=dim, depth=depth, heads=heads)\n",
+    "        for p in self.tgt_enc.parameters():\n",
+    "            p.requires_grad_(False)\n",
+    "\n",
+    "        self.predictor = Predictor(t_grid=self.ctx_enc.t_grid, s_grid=self.ctx_enc.s_grid, enc_dim=dim)\n",
+    "\n",
+    "        self.ema_tau = ema_tau\n",
+    "        self._target_synced = False\n",
+    "\n",
+    "        super().__init__(**kwargs)\n",
+    "\n",
+    "        self.optimizer = optimizer or dl.Adam(lr=3e-4)\n",
+    "\n",
+    "        @self.optimizer.params\n",
+    "        def params(self):\n",
+    "            return self.parameters()\n",
+    "\n",
+    "    def _shared_step(self, batch, stage):\n",
+    "        if len(batch) == 4:\n",
+    "            # videos_clean, videos_ctx, _, _ = batch\n",
+    "            _, videos_ctx, _, _ = batch\n",
+    "            videos_clean = videos_ctx            \n",
+    "        else:\n",
+    "            videos_clean, _, _ = batch\n",
+    "            videos_ctx = videos_clean\n",
+    "\n",
+    "        device = videos_ctx.device\n",
+    "        D = self.ctx_enc.dim\n",
+    "\n",
+    "        groups = sample_masks(videos_ctx.size(0), self.ctx_enc.t_grid, self.ctx_enc.s_grid)\n",
+    "\n",
+    "        with torch.no_grad():\n",
+    "            full_tgt = F.layer_norm(self.tgt_enc(videos_clean), (D,))\n",
+    "\n",
+    "        losses = {}\n",
+    "        for g in groups:\n",
+    "            ci = torch.tensor(g[\"ctx\"], device=device)\n",
+    "            ti = torch.tensor(g[\"pred\"], device=device)\n",
+    "            tgt_tokens = full_tgt.gather(1, ti.unsqueeze(-1).expand(-1, -1, D))\n",
+    "            pred_tokens = self.predictor(self.ctx_enc(videos_ctx, ci), ci, ti)\n",
+    "            losses[g[\"label\"]] = F.l1_loss(pred_tokens, tgt_tokens)\n",
+    "\n",
+    "        for name, v in losses.items():\n",
+    "            self.log(f\"{stage}_{name}_loss\", v, on_step=True, on_epoch=True, prog_bar=True, logger=True)\n",
+    "\n",
+    "        return sum(losses.values()) / len(losses)\n",
+    "\n",
+    "    def training_step(self, batch, batch_idx):\n",
+    "        return self._shared_step(batch, \"train\")\n",
+    "\n",
+    "    def validation_step(self, batch, batch_idx):\n",
+    "        return self._shared_step(batch, \"val\")\n",
+    "\n",
+    "    def on_train_batch_end(self, outputs, batch, batch_idx):\n",
+    "        self.update_target()\n",
+    "\n",
+    "    @torch.no_grad()\n",
+    "    def update_target(self):\n",
+    "        if not self._target_synced:\n",
+    "            self.tgt_enc.load_state_dict(self.ctx_enc.state_dict())\n",
+    "            self._target_synced = True\n",
+    "            return\n",
+    "        for p, pt in zip(self.ctx_enc.parameters(), self.tgt_enc.parameters()):\n",
+    "            pt.data.mul_(self.ema_tau).add_(p.data, alpha=1 - self.ema_tau)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d9f47c82",
+   "metadata": {},
+   "source": [
+    "Let's make pretraining actually happen."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "c9090a44",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:76: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default\n",
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃   ┃ Name          ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│ 0 │ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 1 │ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 2 │ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│ 3 │ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 4 │ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 5 │ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 6 │ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "
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+      ],
+      "text/plain": [
+       "┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName         \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m6\u001b[0m\u001b[2m \u001b[0m│ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
Trainable params: 1.4 M                                                                                            \n",
+       "Non-trainable params: 1.2 M                                                                                        \n",
+       "Total params: 2.6 M                                                                                                \n",
+       "Total estimated model params size (MB): 10                                                                         \n",
+       "Modules in train mode: 161                                                                                         \n",
+       "Modules in eval mode: 0                                                                                            \n",
+       "Total FLOPs: 0                                                                                                     \n",
+       "
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+      ],
+      "text/plain": [
+       "\u001b[1mTrainable params\u001b[0m: 1.4 M                                                                                            \n",
+       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
+       "\u001b[1mTotal params\u001b[0m: 2.6 M                                                                                                \n",
+       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 10                                                                         \n",
+       "\u001b[1mModules in train mode\u001b[0m: 161                                                                                         \n",
+       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
+       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "9dda25001c404d65bf176dcc55b92c20",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "model = PretrainingModel(ema_tau=0.999, optimizer=dl.Adam(lr=3e-4))\n",
+    "summary = model.fit(train_ds, max_epochs=30, batch_size=16, accelerator=\"auto\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9743f78",
+   "metadata": {},
+   "source": [
+    "Let's define a reusable helper for the loss curves..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "f692f783",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_loss_curves(summary, keys, titles=None, figsize=None):\n",
+    "    \"\"\"Plot one subplot per loss key substring found in `summary.history`.\n",
+    "\n",
+    "    `keys` is a list of substrings to search for (e.g. [\"short\", \"long\"]\n",
+    "    for pretraining, or [\"tf\", \"roll\"] for rollout later).\n",
+    "    \"\"\"\n",
+    "    n = len(keys)\n",
+    "    titles = titles or keys\n",
+    "    fig, axes = plt.subplots(1, n, figsize=figsize or (5.5 * n, 4))\n",
+    "    if n == 1:\n",
+    "        axes = [axes]\n",
+    "\n",
+    "    for ax, key_substr, title in zip(axes, keys, titles):\n",
+    "        for key in summary.history.keys():\n",
+    "            if key_substr in key and key.endswith(\"_epoch\"):\n",
+    "                ax.plot(summary.history[key][\"value\"], label=key)\n",
+    "        ax.set_xlabel(\"epoch\"); ax.set_ylabel(\"loss\"); ax.set_title(title)\n",
+    "        ax.legend(fontsize=8)\n",
+    "\n",
+    "    plt.tight_layout()\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d331d3a8",
+   "metadata": {},
+   "source": [
+    "... and display the curves.\n",
+    "\n",
+    "Both curves show a similar shape: a sharp early drop, a rise, then a slow decline. The initial drop isn't genuine learning, it's representation collapse: early in training, the untrained predictor's gradients can pull the encoder toward mapping every input to nearly the same constant representation, which is trivially easy to \"predict\" and drives the loss down fast for the wrong reason. As the EMA-updated target stabilizes and the representation starts differentiating again, escaping that collapse, the loss rises, before beginning a slower, genuine decline as the model actually learns to solve the masked-prediction task (Ennadir, Zólyomi, and Smirnov, 2026)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "10ddc233",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_loss_curves(summary, keys=[\"short\", \"long\"], titles=[\"Short-term loss\", \"Long-term loss\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e091439d",
+   "metadata": {},
+   "source": [
+    "### Evaluating the Representation with Linear Probing\n",
+    "\n",
+    "Up to this point, the model was trained without ever being told what position or velocity are. \n",
+    "\n",
+    "> So how do you check whether that self-supervised representation actually captured them?\n",
+    "\n",
+    "The standard approach in self-supervised learning is linear probing: freeze the trained encoder entirely, and fit a simple linear model on top of its output to predict the quantity of interest, using a small amount of labeled data the encoder itself never saw during training. The key word is linear. A powerful, nonlinear probe could potentially extract position and velocity from almost any representation, however disorganized, by doing the hard work of reconstruction itself, which would say more about the probe than about the representation. A linear probe has no such flexibility: if it succeeds, that's evidence the encoder already arranged the information in an accessible, roughly linear way on its own, without ever being asked to."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f6245e87",
+   "metadata": {},
+   "source": [
+    "Let's check what the representation actually captured. `collect_ctx_features_per_frame` runs the context encoder directly on each unmasked clip and pools the per-timestep tokens into one vector per frame."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "4e03a044",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "device = next(model.parameters()).device\n",
+    "model.eval()\n",
+    "\n",
+    "@torch.no_grad()\n",
+    "def collect_ctx_features_per_frame(ctx_enc, dataloader, device=\"cpu\"):\n",
+    "    \"\"\"Run the frozen context encoder over a dataset in batches, pooling\n",
+    "    per-timestep tokens into one feature vector per frame.\"\"\"\n",
+    "    ctx_enc.eval()\n",
+    "    t_grid, s_grid = ctx_enc.t_grid, ctx_enc.s_grid\n",
+    "    S = s_grid * s_grid\n",
+    "\n",
+    "    Z, pos, vel = [], [], []\n",
+    "    for batch in dataloader:\n",
+    "        if len(batch) == 4:\n",
+    "            _, videos, positions, velocities = batch\n",
+    "        else:\n",
+    "            videos, positions, velocities = batch\n",
+    "        B = videos.size(0)\n",
+    "        videos = videos.to(device)\n",
+    "\n",
+    "        tokens = ctx_enc(videos)                    # (B, T*S, D)\n",
+    "        tokens = tokens.view(B, t_grid, S, -1)\n",
+    "        z_per_t = tokens.mean(dim=2)                 # pool over space -> (B, T, D)\n",
+    "\n",
+    "        Z.append(z_per_t.cpu().numpy())\n",
+    "        pos.append(torch.stack([positions[:, t * ctx_enc.t_patch] for t in range(t_grid)], dim=1).numpy())\n",
+    "        vel.append(torch.stack([velocities[:, t * ctx_enc.t_patch] for t in range(t_grid)], dim=1).numpy())\n",
+    "\n",
+    "    return np.concatenate(Z, axis=0), np.concatenate(pos, axis=0), np.concatenate(vel, axis=0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a139a1c9",
+   "metadata": {},
+   "source": [
+    "Here, you'll define a helper to fit one Ridge regression per timestep on a validation set, then scoring it on a held-out test set the probe has never seen either. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "2816daf8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sklearn.linear_model import Ridge\n",
+    "\n",
+    "def fit_and_score_probes(model, val_ds, test_ds, device, batch_size=32, alpha=1.0, verbose=True):\n",
+    "    \"\"\"Fit a per-timestep Ridge probe on validation features, score it on\n",
+    "    held-out test features, for both position and velocity.\"\"\"\n",
+    "    val_dataloader = torch.utils.data.DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
+    "    test_dataloader = torch.utils.data.DataLoader(test_ds, batch_size=batch_size, shuffle=False)\n",
+    "\n",
+    "    Z_val, pos_val, vel_val = collect_ctx_features_per_frame(model.ctx_enc, val_dataloader, device=device)\n",
+    "    Z_test, pos_test, vel_test = collect_ctx_features_per_frame(model.ctx_enc, test_dataloader, device=device)\n",
+    "\n",
+    "    t_grid = model.ctx_enc.t_grid\n",
+    "    probes_pos, probes_vel = [], []\n",
+    "    r2_pos, r2_vel = [], []\n",
+    "    for t in range(t_grid):\n",
+    "        p_pos = Ridge(alpha=alpha).fit(Z_val[:, t, :], pos_val[:, t, :])\n",
+    "        p_vel = Ridge(alpha=alpha).fit(Z_val[:, t, :], vel_val[:, t, :])\n",
+    "        probes_pos.append(p_pos); probes_vel.append(p_vel)\n",
+    "\n",
+    "        s_pos = p_pos.score(Z_test[:, t, :], pos_test[:, t, :])\n",
+    "        s_vel = p_vel.score(Z_test[:, t, :], vel_test[:, t, :])\n",
+    "        r2_pos.append(s_pos); r2_vel.append(s_vel)\n",
+    "\n",
+    "        if verbose:\n",
+    "            print(f\"Frame {t * model.ctx_enc.t_patch:2d}: pos R²={s_pos:.3f}, vel R²={s_vel:.3f}\")\n",
+    "\n",
+    "    return probes_pos, probes_vel, r2_pos, r2_vel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "75f84238",
+   "metadata": {},
+   "source": [
+    "The score is R², the fraction of variance in the true position or velocity that the probe's predictions account for: 1.0 means perfect prediction, 0.0 means no better than always guessing the average value, and it can go negative if the probe does worse than that baseline. \n",
+    "\n",
+    "If position and velocity come out linearly decodable this way, from a representation trained with no labels at all, that's the actual claim this notebook has been building toward: that a JEPA-style encoder can recover the state of a physical system directly from pixels, without any supervision."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "a8b23a94",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Pretraining probes, clean clips ---\n",
+      "Frame  0: pos R²=0.965, vel R²=0.649\n",
+      "Frame  2: pos R²=0.973, vel R²=0.754\n",
+      "Frame  4: pos R²=0.976, vel R²=0.775\n",
+      "Frame  6: pos R²=0.978, vel R²=0.817\n",
+      "Frame  8: pos R²=0.983, vel R²=0.779\n",
+      "Frame 10: pos R²=0.982, vel R²=0.836\n",
+      "Frame 12: pos R²=0.979, vel R²=0.805\n",
+      "Frame 14: pos R²=0.980, vel R²=0.819\n",
+      "Frame 16: pos R²=0.981, vel R²=0.808\n",
+      "Frame 18: pos R²=0.980, vel R²=0.788\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"--- Pretraining probes, clean clips ---\")\n",
+    "probes_pos, probes_vel, r2_pos, r2_vel = fit_and_score_probes(model, val_ds, test_ds, device)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4561142",
+   "metadata": {},
+   "source": [
+    "Position R² sits at 0.96–0.98 across every single frame, remarkably stable, while velocity, always the harder quantity to recover since it requires integrating information across time rather than reading off a single instant, still reaches 0.77–0.85 for most of the clip. This is a representation that was never given a single labeled example during pretraining; decoding it this well with a linear probe is the actual evidence that self-supervised masked prediction organized position and velocity into the representation on its own."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c646ae5e",
+   "metadata": {},
+   "source": [
+    "### Visualizing Probe Predictions\n",
+    "\n",
+    "It's also worth seeing what the probes actually predict, frame by frame, and how far off they are."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "713c1b16",
+   "metadata": {},
+   "source": [
+    "The helper `prepare_pretraining_predictions` picks a handful of random test clips, encodes them, and applies the per-timestep probes to produce predicted positions and velocities alongside the ground truth."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "aeaeaa68",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def prepare_pretraining_predictions(model, dataset, probes_pos, probes_vel, device, num_examples=3):\n",
+    "    \"\"\"Pick random examples, run the frozen context encoder, and apply the\n",
+    "    per-timestep probes -- assembling arrays for plot_predictions_with_velocity.\n",
+    "    \"\"\"\n",
+    "    t_grid, s_grid = model.ctx_enc.t_grid, model.ctx_enc.s_grid\n",
+    "    S = s_grid * s_grid\n",
+    "    indices = np.random.choice(len(dataset), size=num_examples, replace=False)\n",
+    "\n",
+    "    videos_np, positions_np, velocities_np = [], [], []\n",
+    "    pred_positions, pred_velocities = [], []\n",
+    "\n",
+    "    with torch.no_grad():\n",
+    "        for i in indices:\n",
+    "            if dataset[0].__len__() == 4:\n",
+    "                _, video, positions, velocities = dataset[i]\n",
+    "            else:\n",
+    "                video, positions, velocities = dataset[i]\n",
+    "            video_b = video.unsqueeze(0).to(device)\n",
+    "\n",
+    "            tokens = model.ctx_enc(video_b)\n",
+    "            tokens = tokens.view(t_grid, S, -1)\n",
+    "            z_per_t = tokens.mean(dim=1).cpu().numpy()\n",
+    "\n",
+    "            videos_np.append(video.numpy())\n",
+    "            positions_np.append(positions.numpy())\n",
+    "            velocities_np.append(velocities.numpy())\n",
+    "            pred_positions.append([probes_pos[t].predict(z_per_t[t:t+1])[0] for t in range(t_grid)])\n",
+    "            pred_velocities.append([probes_vel[t].predict(z_per_t[t:t+1])[0] for t in range(t_grid)])\n",
+    "\n",
+    "    videos_np, positions_np, velocities_np = map(np.array, (videos_np, positions_np, velocities_np))\n",
+    "    pred_positions, pred_velocities = map(np.array, (pred_positions, pred_velocities))\n",
+    "    target_frame_indices = [t * model.ctx_enc.t_patch for t in range(t_grid)]\n",
+    "\n",
+    "    return videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cba726c6",
+   "metadata": {},
+   "source": [
+    "The helper `plot_predictions_with_velocity` then renders each clip's frames with both the ground-truth and predicted bead position and velocity drawn on top."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "830e36f5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_predictions_with_velocity(videos_np, positions_np, velocities_np,\n",
+    "                                    target_frame_indices,\n",
+    "                                    pred_positions, pred_velocities,\n",
+    "                                    context_frame_idx=None,\n",
+    "                                    title_prefix=\"\"):\n",
+    "    \"\"\"\n",
+    "    context_frame_idx: if None, no context column is drawn (masked case).\n",
+    "    \"\"\"\n",
+    "    num_examples, n_steps = pred_positions.shape[:2]\n",
+    "    has_context = context_frame_idx is not None\n",
+    "    total_cols = (1 if has_context else 0) + n_steps\n",
+    "    fig, axes = plt.subplots(num_examples, total_cols, figsize=(3 * total_cols, 3 * num_examples))\n",
+    "    axes = np.atleast_2d(axes).reshape(num_examples, total_cols)\n",
+    "\n",
+    "    for row in range(num_examples):\n",
+    "        col = 0\n",
+    "        axes[row, 0].set_ylabel(f\"Ex {row + 1}\", fontsize=11, fontweight=\"bold\")\n",
+    "\n",
+    "        if has_context:\n",
+    "            ax_ctx = axes[row, col]\n",
+    "            ax_ctx.imshow(videos_np[row, 0, context_frame_idx], cmap=\"gray\", vmin=0, vmax=1)\n",
+    "            gt_pos0 = positions_np[row, context_frame_idx]\n",
+    "            gt_vel0 = velocities_np[row, context_frame_idx]\n",
+    "            ax_ctx.scatter(gt_pos0[1], gt_pos0[0], color=\"tab:green\", edgecolors=\"black\", s=80, label=\"GT\")\n",
+    "            ax_ctx.quiver(gt_pos0[1], gt_pos0[0], gt_vel0[1], gt_vel0[0],\n",
+    "                          angles='xy', scale_units='xy', scale=0.5, color='tab:green', width=0.015, headwidth=3)\n",
+    "            if row == 0:\n",
+    "                ax_ctx.set_title(f\"Context (t={context_frame_idx})\", fontsize=12, fontweight=\"bold\")\n",
+    "            ax_ctx.axis(\"off\")\n",
+    "            col += 1\n",
+    "\n",
+    "        for step, frame_idx in enumerate(target_frame_indices):\n",
+    "            ax = axes[row, col]\n",
+    "            ax.imshow(videos_np[row, 0, frame_idx], cmap=\"gray\", vmin=0, vmax=1)\n",
+    "\n",
+    "            gt_pos, gt_vel = positions_np[row, frame_idx], velocities_np[row, frame_idx]\n",
+    "            ax.scatter(gt_pos[1], gt_pos[0], color=\"tab:green\", edgecolors=\"black\", s=80)\n",
+    "            ax.quiver(gt_pos[1], gt_pos[0], gt_vel[1], gt_vel[0],\n",
+    "                      angles='xy', scale_units='xy', scale=0.5, color='tab:green', width=0.015, headwidth=3)\n",
+    "\n",
+    "            pp, pv = pred_positions[row, step], pred_velocities[row, step]\n",
+    "            ax.scatter(pp[1], pp[0], color=\"tab:red\", marker=\"x\", s=90, linewidths=2, label=\"Predicted\")\n",
+    "            ax.quiver(pp[1], pp[0], pv[1], pv[0],\n",
+    "                      angles='xy', scale_units='xy', scale=0.5, color='tab:red', width=0.015, headwidth=3)\n",
+    "\n",
+    "            if row == 0:\n",
+    "                ax.set_title(f\"{title_prefix}(t={frame_idx})\", fontsize=12, fontweight=\"bold\")\n",
+    "            ax.axis(\"off\")\n",
+    "            col += 1\n",
+    "\n",
+    "    axes[0, 0].legend(loc=\"upper left\", bbox_to_anchor=(0, 1.3), ncol=2, frameon=True)\n",
+    "    plt.tight_layout()\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c5136288",
+   "metadata": {},
+   "source": [
+    "Below you'll take a few test clips, encode them with the frozen context encoder, read out position and velocity at each timestep with the fitted probes, and overlay ground-truth and predicted values on the frames."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "6ff32060",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
+    "    prepare_pretraining_predictions(model, test_ds, probes_pos, probes_vel, device, num_examples=3)\n",
+    "\n",
+    "plot_predictions_with_velocity(\n",
+    "    videos_np, positions_np, velocities_np,\n",
+    "    target_frame_indices=target_frame_indices,\n",
+    "    pred_positions=pred_positions, pred_velocities=pred_velocities,\n",
+    "    context_frame_idx=None,\n",
+    "    title_prefix=\"Probe pred \",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe1ada13",
+   "metadata": {},
+   "source": [
+    "### Curriculum Learning: Adding Distractors\n",
+    "\n",
+    "So far you've trained only on clean clips. To bring in distractors without destabilizing what the model has already learned, you'll use curriculum learning: rather than exposing a model to the full difficulty of a task from the start, training begins on an easier version of the problem, and harder examples are introduced only once the model has settled into a stable representation.\n",
+    "\n",
+    "Here that means starting from the model already pretrained on clean clips and continuing its training on clips with distractors, rather than training on distractors from scratch. In practice, this means loading a distractor version of the same dataset (`p_distractors=1.0`) and calling `model.fit` again on that same `model` instance."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "e91c21c6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃   ┃ Name          ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│ 0 │ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 1 │ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 2 │ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│ 3 │ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 4 │ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 5 │ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 6 │ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "
\n"
+      ],
+      "text/plain": [
+       "┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName         \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m6\u001b[0m\u001b[2m \u001b[0m│ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
Trainable params: 1.4 M                                                                                            \n",
+       "Non-trainable params: 1.2 M                                                                                        \n",
+       "Total params: 2.6 M                                                                                                \n",
+       "Total estimated model params size (MB): 10                                                                         \n",
+       "Modules in train mode: 161                                                                                         \n",
+       "Modules in eval mode: 0                                                                                            \n",
+       "Total FLOPs: 0                                                                                                     \n",
+       "
\n"
+      ],
+      "text/plain": [
+       "\u001b[1mTrainable params\u001b[0m: 1.4 M                                                                                            \n",
+       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
+       "\u001b[1mTotal params\u001b[0m: 2.6 M                                                                                                \n",
+       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 10                                                                         \n",
+       "\u001b[1mModules in train mode\u001b[0m: 161                                                                                         \n",
+       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
+       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "30ea946ce0464ac0b87b73ad0f278377",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "train_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_train.pt\", p_distractors=1.0, seed=0)\n",
+    "val_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_val.pt\", p_distractors=1.0, seed=0)\n",
+    "test_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_test.pt\", p_distractors=1.0, seed=0)\n",
+    "\n",
+    "summary_cl = model.fit(train_ds_w, max_epochs=10, batch_size=16, accelerator=\"auto\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "043893f6",
+   "metadata": {},
+   "source": [
+    "Let's check the losses..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "74ed2c95",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_loss_curves(summary_cl, keys=[\"short\", \"long\"], titles=[\"Short-term loss\", \"Long-term loss\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f7254344",
+   "metadata": {},
+   "source": [
+    "... the R² score..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "e829b6d5",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Pretraining probes, with distractors ---\n",
+      "Frame  0: pos R²=0.850, vel R²=0.361\n",
+      "Frame  2: pos R²=0.883, vel R²=0.463\n",
+      "Frame  4: pos R²=0.896, vel R²=0.569\n",
+      "Frame  6: pos R²=0.915, vel R²=0.617\n",
+      "Frame  8: pos R²=0.918, vel R²=0.533\n",
+      "Frame 10: pos R²=0.911, vel R²=0.618\n",
+      "Frame 12: pos R²=0.900, vel R²=0.658\n",
+      "Frame 14: pos R²=0.895, vel R²=0.654\n",
+      "Frame 16: pos R²=0.903, vel R²=0.571\n",
+      "Frame 18: pos R²=0.894, vel R²=0.546\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"--- Pretraining probes, with distractors ---\")\n",
+    "probes_pos, probes_vel, r2_pos, r2_vel = fit_and_score_probes(model, val_ds_w, test_ds_w, device)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e2de393",
+   "metadata": {},
+   "source": [
+    "... and visualize a few examples."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "4e869c79",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
+    "    prepare_pretraining_predictions(model, test_ds_w, probes_pos, probes_vel, device, num_examples=3)\n",
+    "\n",
+    "plot_predictions_with_velocity(\n",
+    "    videos_np, positions_np, velocities_np,\n",
+    "    target_frame_indices=target_frame_indices,\n",
+    "    pred_positions=pred_positions, pred_velocities=pred_velocities,\n",
+    "    context_frame_idx=None,\n",
+    "    title_prefix=\"Probe pred \",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8a268d16",
+   "metadata": {},
+   "source": [
+    "## Rollout\n",
+    "\n",
+    "Pretraining leaves you with an encoder that turns individual frames into representations carrying position and velocity information, useful, but only a snapshot description of a single instant. Rollout, the second stage of training, teaches a predictor to evolve those representations forward in latent space over multiple steps, so the model can imagine several timesteps ahead rather than just recover the present.\n",
+    "\n",
+    "The context encoder is frozen at this stage. It already produces good per-frame representations, so Rollout only trains a new module, `RolloutPredictor`, to model how those representations change over time."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "20a9a2e0",
+   "metadata": {},
+   "source": [
+    "### The Rollout Predictor\n",
+    "\n",
+    "`RolloutPredictor` is a transformer over the sequence of per-frame latents, structured to make prediction autoregressive: it uses block-causal attention, so each timestep's tokens can attend to their own and all earlier timesteps, but never later ones. A prediction for timestep t+1 never has access to information from t+1 onward. This is a different masking scheme from the `Predictor` used in pretraining, which hides a subset of *spatial* tokens within a single, fixed clip; here masking is *temporal* and causal, restricting what the model can see going forward in time rather than which patches are visible at one instant.\n",
+    "\n",
+    "Its `rollout` method applies this autoregressively: given a single starting latent, it predicts the next timestep, appends that prediction to the sequence, and repeats, extending the latent trajectory one step at a time for as many steps as requested."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "b8a802f0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class RolloutPredictor(nn.Module):\n",
+    "    \"\"\"Block-causal predictor, NO action/state conditioning -- pure passive\n",
+    "    dynamics: given latents for timesteps 0..t, predict timestep t+1.\n",
+    "    \"\"\"\n",
+    "    \n",
+    "    def __init__(self, t_grid, s_grid, enc_dim=128, dim=128, depth=4, heads=4):\n",
+    "        super().__init__()\n",
+    "        self.t_grid = t_grid\n",
+    "        self.s_grid = s_grid\n",
+    "        self.in_proj = nn.Linear(enc_dim, dim)\n",
+    "        self.out_proj = nn.Linear(dim, enc_dim)\n",
+    "        self.register_buffer(\"pos\", pos_embed_3d(t_grid, s_grid, s_grid, dim))\n",
+    "        self.blocks = nn.ModuleList([Block(dim, heads) for _ in range(depth)])\n",
+    "        self.norm = nn.LayerNorm(dim, eps=1e-6)\n",
+    "\n",
+    "    @staticmethod\n",
+    "    def _block_causal_mask(T, width, device):\n",
+    "        t = torch.arange(T, device=device).repeat_interleave(width)\n",
+    "        return t[:, None] < t[None, :]\n",
+    "\n",
+    "    def forward(self, z):\n",
+    "        B, T, S, _ = z.shape\n",
+    "        x = self.in_proj(z) + self.pos[None, :T*S].view(1, T, S, -1)\n",
+    "        x = x.reshape(B, T * S, -1)\n",
+    "        mask = self._block_causal_mask(T, S, z.device)\n",
+    "        for blk in self.blocks:\n",
+    "            x = blk(x, mask)\n",
+    "        x = self.norm(x).view(B, T, S, -1)\n",
+    "        return self.out_proj(x)\n",
+    "\n",
+    "    def rollout(self, z0, n_steps):\n",
+    "        z_seq = z0[:, None]   # (B, 1, S, enc_dim)\n",
+    "        out = []\n",
+    "        for _ in range(n_steps):\n",
+    "            pred = self.forward(z_seq)[:, -1]\n",
+    "            z_seq = torch.cat([z_seq, pred[:, None]], dim=1)\n",
+    "            out.append(pred)\n",
+    "        return torch.stack(out, dim=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9cc2741b",
+   "metadata": {},
+   "source": [
+    "### The Rollout Model\n",
+    "\n",
+    "`RolloutModel` ties the rollout predictor to training, mirroring the role `PretrainingModel` played in the first stage. The context encoder, already trained and now frozen, is used only to produce latents; the only trainable module is `rollout_predictor`.\n",
+    "\n",
+    "Each temporal group of frames is encoded separately, one encoder call per group, restricted to that group's own frames, rather than encoding the whole clip in a single pass. This guarantees no attention leakage across time at the encoding stage itself, before the causal predictor is even applied.\n",
+    "\n",
+    "The loss combines two terms, matching V-JEPA2-AC's approach. `loss_tf` is a teacher-forced loss: given true latents at all timesteps up to T-2, predict the next one at every position simultaneously. `loss_roll` is a short autoregressive rollout: starting only from the first latent, the model predicts several steps forward on its own, each prediction built on prior predictions rather than ground truth, and compares the result to the true latent k steps ahead. Training on both keeps the model accurate at single-step prediction while also exposing it to the compounding error it will face at evaluation time, when only autoregressive rollout is available."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "a63e52aa",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import copy\n",
+    "\n",
+    "class RolloutModel(dl.Application):\n",
+    "    def __init__(self, frozen_ctx_enc, dim=128, depth=4, heads=4,\n",
+    "                 rollout_k=2, rollout_w=1.0, optimizer=None, **kwargs):\n",
+    "        self.encoder = copy.deepcopy(frozen_ctx_enc)\n",
+    "        for p in self.encoder.parameters():\n",
+    "            p.requires_grad_(False)\n",
+    "\n",
+    "        self.rollout_predictor = RolloutPredictor(\n",
+    "            t_grid=self.encoder.t_grid, s_grid=self.encoder.s_grid,\n",
+    "            enc_dim=self.encoder.dim, dim=dim, depth=depth, heads=heads\n",
+    "        )\n",
+    "\n",
+    "        self.rollout_k = rollout_k\n",
+    "        self.rollout_w = rollout_w\n",
+    "\n",
+    "        super().__init__(**kwargs)\n",
+    "        self.optimizer = optimizer or dl.Adam(lr=3e-4)\n",
+    "\n",
+    "        @self.optimizer.params\n",
+    "        def params(self):\n",
+    "            return self.rollout_predictor.parameters()\n",
+    "\n",
+    "    def _shared_step(self, batch, stage):\n",
+    "        if len(batch) == 4:\n",
+    "             _, videos, _, _ = batch\n",
+    "        else:\n",
+    "            videos, _, _ = batch\n",
+    "        self.encoder.eval()\n",
+    "        B = videos.size(0)\n",
+    "        T, S = self.encoder.t_grid, self.encoder.s_grid ** 2\n",
+    "        t_patch = self.encoder.t_patch\n",
+    "\n",
+    "        # Encode each temporal group SEPARATELY, each time restricted to only\n",
+    "        # its own frames -- no attention access to future frames at all.\n",
+    "        z_list = []\n",
+    "        with torch.no_grad():\n",
+    "            for t in range(T):\n",
+    "                frame_slice = videos[:, :, t * t_patch : (t + 1) * t_patch]  # (B, C, t_patch, H, W)\n",
+    "                tokens_t = self.encoder(frame_slice, t_offset=t)\n",
+    "                z_list.append(tokens_t.view(B, S, -1))\n",
+    "        z = torch.stack(z_list, dim=1)   # (B, T, S, D)\n",
+    "\n",
+    "        preds = self.rollout_predictor(z[:, :-1])\n",
+    "        tgt = z[:, 1:]\n",
+    "        loss_tf = (preds - tgt).abs().mean()\n",
+    "\n",
+    "        k = min(self.rollout_k, T - 1)\n",
+    "        rolled = self.rollout_predictor.rollout(z[:, 0], k)\n",
+    "        loss_roll = (rolled[:, -1] - z[:, k]).abs().mean()\n",
+    "\n",
+    "        loss = loss_tf + self.rollout_w * loss_roll\n",
+    "        self.log(f\"{stage}_tf\", loss_tf, on_step=True, on_epoch=True, prog_bar=True)\n",
+    "        self.log(f\"{stage}_roll\", loss_roll, on_step=True, on_epoch=True, prog_bar=True)\n",
+    "        return loss\n",
+    "\n",
+    "    def training_step(self, batch, batch_idx):\n",
+    "        return self._shared_step(batch, \"train\")\n",
+    "\n",
+    "    def validation_step(self, batch, batch_idx):\n",
+    "        return self._shared_step(batch, \"val\")\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44799e75",
+   "metadata": {},
+   "source": [
+    "Let's train. Only `rollout_predictor`'s parameters are updated, the encoder stays frozen throughout, and unlike pretraining, no curriculum is needed here: the encoder already learned to represent distractor clips during its own curriculum stage, so the rollout predictor can train directly on `train_ds_w` from the start."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "2c299d30",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
┏━━━┳━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃   ┃ Name              ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│ 0 │ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 1 │ rollout_predictor │ RolloutPredictor │  826 K │ train │     0 │\n",
+       "│ 2 │ train_metrics     │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 3 │ val_metrics       │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 4 │ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 5 │ optimizer         │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "
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+      ],
+      "text/plain": [
+       "┏━━━┳━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName             \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ rollout_predictor │ RolloutPredictor │  826 K │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ train_metrics     │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ val_metrics       │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ optimizer         │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
Trainable params: 826 K                                                                                            \n",
+       "Non-trainable params: 1.2 M                                                                                        \n",
+       "Total params: 2.0 M                                                                                                \n",
+       "Total estimated model params size (MB): 8                                                                          \n",
+       "Modules in train mode: 103                                                                                         \n",
+       "Modules in eval mode: 0                                                                                            \n",
+       "Total FLOPs: 0                                                                                                     \n",
+       "
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+      ],
+      "text/plain": [
+       "\u001b[1mTrainable params\u001b[0m: 826 K                                                                                            \n",
+       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
+       "\u001b[1mTotal params\u001b[0m: 2.0 M                                                                                                \n",
+       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 8                                                                          \n",
+       "\u001b[1mModules in train mode\u001b[0m: 103                                                                                         \n",
+       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
+       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "488ade0b7c1d491b8832c8c8bbbd3d8a",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "ename": "SystemExit",
+     "evalue": "1",
+     "output_type": "error",
+     "traceback": [
+      "An exception has occurred, use %tb to see the full traceback.\n",
+      "\u001b[31mSystemExit\u001b[39m\u001b[31m:\u001b[39m 1\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/IPython/core/interactiveshell.py:3709: UserWarning: To exit: use 'exit', 'quit', or Ctrl-D.\n",
+      "  warn(\"To exit: use 'exit', 'quit', or Ctrl-D.\", stacklevel=1)\n"
+     ]
+    }
+   ],
+   "source": [
+    "rollout_model = RolloutModel(frozen_ctx_enc=model.ctx_enc, optimizer=dl.Adam(lr=3e-4))\n",
+    "summary_ro = rollout_model.fit(train_ds_w, max_epochs=100, batch_size=32, accelerator=\"auto\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "40d2081a",
+   "metadata": {},
+   "source": [
+    "Let's plot the losses..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b93b69de",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plot_loss_curves(summary_ro, keys=[\"tf\", \"roll\"], titles=[\"Teacher-forcing loss\", \"Rollout loss\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c7420592",
+   "metadata": {},
+   "source": [
+    "### Evaluating Rollout Predictions\n",
+    "\n",
+    "To check whether the model's imagined future actually tracks the physical state of the bead, we need to compare the rollout predictor's latent predictions against the true position and velocity at each future step, the same linear-probing approach used for pretraining, but applied to predicted rather than directly encoded latents."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "732129fe",
+   "metadata": {},
+   "source": [
+    "`extract_rollout_latents_and_targets` encodes only the first frame group, then lets `rollout_predictor.rollout` generate the next `n_steps` latents autoregressively, with no further access to the actual video. Each predicted latent is paired with the ground-truth position and velocity at its corresponding frame. Unlike the pretraining probes, which pooled each frame's tokens into a single feature vector, these features keep the full set of spatial tokens flattened together, since spatial detail may matter more once the model is predicting rather than just encoding."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c59f42fb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def extract_rollout_latents_and_targets(rollout_model, dataloader, n_steps=5):\n",
+    "    \"\"\"Encodes only the first temporal group (frames 0..t_patch-1), then rolls \n",
+    "    forward purely in latent space via rollout_predictor, so the model never \n",
+    "    has direct access to future frames.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    rollout_model.eval()\n",
+    "    rollout_model.encoder.eval()\n",
+    "\n",
+    "    encoder = rollout_model.encoder\n",
+    "    t_patch = encoder.t_patch\n",
+    "    T, S, D = encoder.t_grid, encoder.s_grid ** 2, encoder.dim\n",
+    "\n",
+    "    all_flat = []          # (n_samples, n_steps, S*D) -- no pooling, keep full spatial info\n",
+    "    all_positions = []     # (n_samples, n_steps, 2) -- true position at each rollout step's frame\n",
+    "    all_velocities = []\n",
+    "\n",
+    "    with torch.no_grad():\n",
+    "        for batch in dataloader:\n",
+    "            if len(batch) == 4:\n",
+    "                _, videos, positions, velocities = batch\n",
+    "            else:\n",
+    "                videos, positions, velocities = batch\n",
+    "            B = videos.size(0)\n",
+    "\n",
+    "            # Encode only the first temporal group -- everything after this\n",
+    "            # point is pure latent-space rollout, no further encoder calls.\n",
+    "            frame_slice = videos[:, :, :t_patch]\n",
+    "            z0 = encoder(frame_slice, t_offset=0)   # (B, S, D)\n",
+    "\n",
+    "            rolled = rollout_model.rollout_predictor.rollout(z0, n_steps)   # (B, n_steps, S, D)\n",
+    "            flat = rolled.reshape(B, n_steps, S * D)\n",
+    "\n",
+    "            # Ground truth at each rollout step's corresponding frame\n",
+    "            step_positions = torch.stack(\n",
+    "                [positions[:, (k + 1) * t_patch] for k in range(n_steps)], dim=1\n",
+    "            )  # (B, n_steps, 2)\n",
+    "            step_velocities = torch.stack(\n",
+    "                [velocities[:, (k + 1) * t_patch] for k in range(n_steps)], dim=1\n",
+    "            )\n",
+    "\n",
+    "            all_flat.append(flat.cpu().numpy())\n",
+    "            all_positions.append(step_positions.cpu().numpy())\n",
+    "            all_velocities.append(step_velocities.cpu().numpy())\n",
+    "\n",
+    "    return (np.concatenate(all_flat, axis=0),\n",
+    "            np.concatenate(all_positions, axis=0),\n",
+    "            np.concatenate(all_velocities, axis=0))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7faea68d",
+   "metadata": {},
+   "source": [
+    "`fit_and_score_rollout_probes` mirrors `fit_and_score_probes` from pretraining, fit on validation, scored on held-out test, but one probe per rollout step instead of per frame, using the unpooled latents from `extract_rollout_latents_and_targets`. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ff6c5b57",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def fit_and_score_rollout_probes(rollout_model, val_ds, test_ds, n_steps=None, batch_size=32, alpha=3.0, verbose=True):\n",
+    "    \"\"\"Fit a per-rollout-step Ridge probe on validation latents, score it on\n",
+    "    held-out test latents, for both position and velocity.\"\"\"\n",
+    "    val_dataloader = torch.utils.data.DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
+    "    test_dataloader = torch.utils.data.DataLoader(test_ds, batch_size=batch_size, shuffle=False)\n",
+    "\n",
+    "    if n_steps is None:\n",
+    "        n_steps = rollout_model.encoder.t_grid - 1   # cover the whole clip\n",
+    "\n",
+    "    X_val, Y_val, Z_val = extract_rollout_latents_and_targets(rollout_model, val_dataloader, n_steps=n_steps)\n",
+    "    X_test, Y_test, Z_test = extract_rollout_latents_and_targets(rollout_model, test_dataloader, n_steps=n_steps)\n",
+    "\n",
+    "    t_patch = rollout_model.encoder.t_patch\n",
+    "    probes_pos, probes_vel = [], []\n",
+    "    r2_pos, r2_vel = [], []\n",
+    "    for step in range(X_val.shape[1]):\n",
+    "        p_pos = Ridge(alpha=alpha).fit(X_val[:, step, :], Y_val[:, step, :])\n",
+    "        p_vel = Ridge(alpha=alpha).fit(X_val[:, step, :], Z_val[:, step, :])\n",
+    "        probes_pos.append(p_pos); probes_vel.append(p_vel)\n",
+    "\n",
+    "        s_pos = p_pos.score(X_test[:, step, :], Y_test[:, step, :])\n",
+    "        s_vel = p_vel.score(X_test[:, step, :], Z_test[:, step, :])\n",
+    "        r2_pos.append(s_pos); r2_vel.append(s_vel)\n",
+    "\n",
+    "        if verbose:\n",
+    "            true_frame_idx = (step + 1) * t_patch\n",
+    "            print(f\"Rollout Step {step+1} (frame {true_frame_idx}) -> Test R²: \"\n",
+    "                  f\"{s_pos:.3f} (Position), {s_vel:.3f} (Velocity)\")\n",
+    "\n",
+    "    return probes_pos, probes_vel, r2_pos, r2_vel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9a9d345",
+   "metadata": {},
+   "source": [
+    "R² at step k measures how much position and velocity information survives k steps of autoregressive rollout, so a declining trend across steps is the expected signature of compounding error, not necessarily a failure."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b968667b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "print(\"--- Strict Rollout Evaluation (Fit on Val, Score on Test, unpooled features) ---\")\n",
+    "trained_probes_pos, trained_probes_vel, r2_pos_roll, r2_vel_roll = fit_and_score_rollout_probes(rollout_model, val_ds_w, test_ds_w)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0ca8c67b",
+   "metadata": {},
+   "source": [
+    "### Visualizing Rollout Predictions\n",
+    "\n",
+    "As with pretraining, `prepare_rollout_predictions` picks a few random test clips, rolls the encoded first frame group forward autoregressively, and reads out position and velocity at each step with the fitted rollout probes, assembling the same shape of arrays that `plot_predictions_with_velocity` expects, the same plotting helper from pretraining, reused as-is."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a1fe972e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def prepare_rollout_predictions(rollout_model, dataset, probes_pos, probes_vel, device, num_examples=3, n_steps=None):\n",
+    "    \"\"\"Pick random examples, roll out the frozen encoder's latents\n",
+    "    autoregressively, and apply the per-step probes -- assembling arrays\n",
+    "    for plot_predictions_with_velocity.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    encoder = rollout_model.encoder\n",
+    "    t_patch = encoder.t_patch\n",
+    "    S = encoder.s_grid ** 2\n",
+    "\n",
+    "    if n_steps is None:\n",
+    "        n_steps = encoder.t_grid - 1   # cover the whole clip\n",
+    "\n",
+    "    indices = np.random.choice(len(dataset), size=num_examples, replace=False)\n",
+    "\n",
+    "    videos_np, positions_np, velocities_np = [], [], []\n",
+    "    pred_positions, pred_velocities = [], []\n",
+    "\n",
+    "    with torch.no_grad():\n",
+    "        for i in indices:\n",
+    "            if dataset[0].__len__() == 4:\n",
+    "                _, video, positions, velocities = dataset[i]\n",
+    "            else:\n",
+    "                video, positions, velocities = dataset[i]\n",
+    "            video_b = video.unsqueeze(0).to(device)\n",
+    "\n",
+    "            z0 = encoder(video_b[:, :, :t_patch], t_offset=0)          # (1, S, D)\n",
+    "            rolled = rollout_model.rollout_predictor.rollout(z0, n_steps)   # (1, n_steps, S, D)\n",
+    "            flat = rolled.reshape(n_steps, -1).cpu().numpy()            # (n_steps, S*D)\n",
+    "\n",
+    "            videos_np.append(video.numpy())\n",
+    "            positions_np.append(positions.numpy())\n",
+    "            velocities_np.append(velocities.numpy())\n",
+    "            pred_positions.append([probes_pos[s].predict(flat[s:s+1])[0] for s in range(n_steps)])\n",
+    "            pred_velocities.append([probes_vel[s].predict(flat[s:s+1])[0] for s in range(n_steps)])\n",
+    "\n",
+    "    videos_np, positions_np, velocities_np = map(np.array, (videos_np, positions_np, velocities_np))\n",
+    "    pred_positions, pred_velocities = map(np.array, (pred_positions, pred_velocities))\n",
+    "\n",
+    "    target_frame_indices = [(s + 1) * t_patch for s in range(n_steps)]\n",
+    "    context_frame_idx = t_patch - 1\n",
+    "\n",
+    "    return videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities, context_frame_idx"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c57dc727",
+   "metadata": {},
+   "source": [
+    "Let's see what the rollout predictor actually imagines, plotted against ground truth."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a941ffbc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "videos_np, positions_np, velocities_np, target_frame_indices, pred_pos, pred_vel, context_frame_idx = \\\n",
+    "    prepare_rollout_predictions(rollout_model, test_ds_w, trained_probes_pos, trained_probes_vel, device,\n",
+    "                                 num_examples=3)\n",
+    "\n",
+    "plot_predictions_with_velocity(\n",
+    "    videos_np, positions_np, velocities_np,\n",
+    "    target_frame_indices=target_frame_indices,\n",
+    "    pred_positions=pred_pos, pred_velocities=pred_vel,\n",
+    "    context_frame_idx=context_frame_idx,\n",
+    "    title_prefix=\"Rollout \",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "45e0efd6",
+   "metadata": {},
+   "source": [
+    "## Further Readings\n",
+    "\n",
+    "LeCun, Y. (2022) A Path Towards Autonomous Machine Intelligence Version 0.9.2, *Open Review*, 62(1): 1–62. https://openreview.net/forum?id=BZ5a1r-kVsf\n",
+    "\n",
+    "Assran, M., *et al.* (2025). V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning. *arXiv*, 2506.09985.\n",
+    "\n",
+    "Ennadir, S., Zólyomi, L., and Smirnov, O. (2026). Understanding Early Collapse in Predictive World-Model Pretraining. In *Proceedings of the\n",
+    "ICLR 2026 the 2nd Workshop on World Models: Understanding, Modelling and Scaling*. https://openreview.net/forum?id=SdOYmP67a2"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "deeptrack_dev (3.12.8)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Companion/world_model/jepa_world_model.ipynb b/Companion/world_model/jepa_world_model.ipynb
deleted file mode 100644
index d3803b371..000000000
--- a/Companion/world_model/jepa_world_model.ipynb
+++ /dev/null
@@ -1,3089 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "1c41d949",
-   "metadata": {},
-   "source": [
-    "# Measuring Particle Diffusion with a JEPA world model\n",
-    "\n",
-    "
\n",
-    "\"Open\n",
-    "If using Colab/Kaggle: You need to uncomment the code in the cell below this one.\n",
-    "
"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "42aabbb3",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# !pip install deeptrack deeplay torch torchvision matplotlib scikit-learn  # Uncomment if using Colab/Kaggle."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1adfb1f1",
-   "metadata": {},
-   "source": [
-    "Joint Embedding Predictive Architectures (JEPAs) allow an AI system to learn how the world works purely by observing it, creating an internal \"world model\" without requiring human labels.\n",
-    "\n",
-    "In this notebook, you will use a JEPA world model to analyze a stochastic physical system: the Brownian diffusion of a particle. You will see how predicting in an abstract latent space—rather than predicting raw pixels—lets a neural network represent the statistics of an inherently unpredictable process, instead of chasing an exact future it has no way of knowing. By the end, you will test whether the model's representation captures something physically meaningful, by training a small linear probe to extract the particle's diffusion coefficient ($D$) straight from its abstract representation—a quantity the network was never directly trained to predict."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "db87d875",
-   "metadata": {},
-   "source": [
-    "
\n",
-    "Note: This companion example extends several concepts introduced throughout the book, specifically, encoder-decoder architectures (Chapter 4) and particle diffusion (Chapter 11). Unlike several examples in the book, the network is trained not to reproduce its input but to predict its own future latent representations, learning an implicit model of the system's dynamics directly from simulated video.\n",
-    "\n",
-    "**Deep Learning Crash Course**  \n",
-    "Giovanni Volpe, Benjamin Midtvedt, Jesús Pineda, Henrik Klein Moberg, Harshith Bachimanchi, Joana B. Pereira, Carlo Manzo  \n",
-    "No Starch Press, San Francisco (CA), 2026  \n",
-    "ISBN-13: 9781718503922  \n",
-    "\n",
-    "[https://nostarch.com/deep-learning-crash-course](https://nostarch.com/deep-learning-crash-course)\n",
-    "\n",
-    "You can find the other notebooks on the [Deep Learning Crash Course GitHub page](https://github.com/DeepTrackAI/DeepLearningCrashCourse).\n",
-    "
"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "53fb6d56",
-   "metadata": {},
-   "source": [
-    "## Understanding JEPA World Models\n",
-    "Many artificial intelligence problems require an understanding of how a surrounding environment evolves. For instance, a robot navigating a room needs to anticipate collisions, a self-driving car needs to predict pedestrian movements, and an automated microscope needs to track how moving cells or particles spread over time.\n",
-    "\n",
-    "To make sense of the world, humans and animals rely on an internal World Model—a mental simulator that uses past observations to predict future outcomes. In machine learning, building an effective world model generally involves balancing two competing realities:\n",
-    "\n",
-    "1. Unpredictable Specifics: High-frequency, chaotic, or stochastic details where the exact future state is fundamentally uncertain (e.g., the exact, jittery trajectory of a single diffusing particle).\n",
-    "\n",
-    "2. Predictable Statistics: Structural invariants or global properties that govern how that uncertainty behaves over time (e.g., the environmental diffusion coefficient, $D$).\n",
-    "\n",
-    "Traditional predictive machine learning models typically try to predict the future down to the exact pixel. Given a video sequence, a generative network (like a standard Video Autoencoder or GAN) attempts to reconstruct subsequent frames pixel-by-pixel. However, in stochastic environments, predicting every single pixel is fundamentally a losing game. Because the exact path of a random particle cannot be known in advance, pixel-space models suffer from the \"blurry image\" problem—they mathematically average all possible futures, resulting in a faded, low-utility smudge.\n",
-    "\n",
-    "Joint Embedding Predictive Architectures (JEPAs) solve this dilemma by changing where the prediction happens. Instead of training a network to generate future raw pixels, a JEPA passes the data through an encoder and performs its predictions entirely within an abstract representation space (latent space).\n",
-    "\n",
-    "Crucially, this architecture does not magically look \"through\" the randomness to find a hidden, clean physical signal. In a system like diffusion, the randomness **is** the physical signal. Instead, the JEPA learns to represent the macroscopic statistics of the uncertainty.  By optimizing to predict future latent states without memorizing unpredictable pixel-level specifics, the model naturally captures how the system spreads globally, allowing us to accurately extract underlying properties like $D$—matching the realistic performance boundaries of a truly chaotic system."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "210a80b2",
-   "metadata": {},
-   "source": [
-    "### The Generative Dead End: Why Pixel Prediction Fails\n",
-    "Historically, the most intuitive way to build an AI world model from video data was to use generative modeling. Given a sequence of past video frames, a neural network is optimized to output the exact raw pixels of the subsequent frames.\n",
-    "\n",
-    "While visually striking when successful, Yann LeCun argues that generative pixel-level prediction is a fundamental engineering bottleneck—and an unfeasible strategy for learning physics—for two major reasons:\n",
-    "\n",
-    "- The Nuisance Variable Problem: A single pixel value can change drastically due to irrelevant factors like a shifting shadow, a camera sensor's grain, or background leaves rustling in the wind. Generative models waste immense computational capacity trying to reconstruct these high-frequency, non-essential \"nuisance variables.\"\n",
-    "\n",
-    "- The Multimodal Uncertainty Trap: In a stochastic or chaotic environment, the exact future cannot be perfectly known. If a particle is undergoing random thermal collisions, it has infinite possible paths. When a pixel-level model tries to handle multiple possible futures simultaneously, the mathematical average of those futures results in a blurred, low-utility average image—a faded smudge."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "682eec1f",
-   "metadata": {},
-   "source": [
-    "### The JEPA Paradigm: Moving to Representation Space\n",
-    "Joint Embedding Predictive Architectures (JEPAs) circumvent the flaws of generative modeling by changing where the prediction takes place. Instead of predicting the future in high-dimensional pixel space, a JEPA predicts the future in a lower-dimensional, abstract representation space (latent space).\n",
-    "\n",
-    "The JEPA framework relies on a highly synchronized multi-network system:\n",
-    "\n",
-    "- The Context Encoder: Takes a history of frames (e.g., a 10-frame window) and flattens them into an abstract latent state vector, $z_0$, summarizing everything important about the system's current state.\n",
-    "\n",
-    "- The Target Encoder: Processes the actual future frames and extracts their true abstract latent representation, $z_1$. Crucially, this encoder does not backpropagate gradients directly; its weights are updated as a slow Exponential Moving Average (EMA) of the Context Encoder to serve as a stable, moving anchor.\n",
-    "\n",
-    "- The Latent Predictor: Receives the present latent state $z_0$ and a time horizon conditioning parameter ($\\delta$), and is tasked with guessing the future abstract state $\\hat{z}_1$.\n",
-    "\n",
-    "Because a JEPA is tasked with predicting abstract features rather than exact pixel locations, it naturally learns to discard individual pixel-level unpredictabilities. Instead, it captures the macroscopic statistics of the system's uncertainty. It learns to represent how space and uncertainty scale over time relative to environmental constants (like the diffusion coefficient, $D$).By bypassing the need to generate images, the network is free to focus entirely on learning the mathematical structure of the physical environment, creating an elegant, robust window into self-supervised physical common sense."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b4448972",
-   "metadata": {},
-   "source": [
-    "### The JEPA Optimization Objective: Loss and the Collapse Problem\n",
-    "\n",
-    "In traditional generative world models, the loss function is simple: it is usually a Mean Squared Error (MSE) calculated between the predicted pixels and the true future pixels. The raw pixel grid acts as a natural anchor that prevents the model from doing anything lazy.\n",
-    "\n",
-    "In a JEPA, however, there is **no pixel decoder**. The loss is calculated entirely within the abstract latent space:\n",
-    "$$\n",
-    "L_{\\text{pred}} = \\|\\hat{z}_1 - z_1\\|^2\n",
-    "$$\n",
-    "\n",
-    "Where $\\hat{z}_1$ is the predicted future representation and $z_1$ is the true future representation produced by the target encoder. This design poses a massive mathematical danger known as **Representation Collapse**.\n",
-    "\n",
-    "### The Danger of Trivial Representations\n",
-    "Because both the context encoder and the target encoder are neural networks that we control, the model can discover a massive \"shortcut\" to drive the prediction error to zero: **it can learn to output a constant vector for every single frame.** If the encoders map every single image sequence—regardless of whether the particle is moving fast, slow, left, or right—to the exact same vector (e.g., $z = [0, 0, \\dots, 0]$), then the predictor can simply output zero. The prediction error becomes exactly zero, but the representations are completely useless, carrying zero information about the physics of the environment.\n",
-    "\n",
-    "To build a meaningful world model, we must force the latent representations to be highly informative while minimizing prediction error. JEPA achieves this by introducing explicit **anti-collapse regularization** adapted from self-supervised frameworks like **VICReg** (Variance-Invariance-Covariance Regularization)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "54332dbf",
-   "metadata": {},
-   "source": [
-    "### The Three Pillars of the JEPA Loss Function\n",
-    "\n",
-    "To prevent collapse and force the model to capture the true underlying physics, the total loss function is broken down into three distinct mathematical objectives: **Invariance (Prediction)**, **Variance**, and **Covariance**.\n",
-    "\n",
-    "$$\\mathcal{L}_{\\text{total}} = \\alpha \\mathcal{L}_{\\text{pred}} + \\beta \\mathcal{L}_{\\text{var}} + \\gamma \\mathcal{L}_{\\text{cov}}$$\n",
-    "\n",
-    "#### 1. The Invariance Loss ($\\mathcal{L}_{\\text{pred}}$)\n",
-    "This is the core predictive world-model objective. It minimizes the Mean Squared Error between the predicted future latent state $\\hat{z}_1$ and the actual target latent state $z_1$:\n",
-    "\n",
-    "$$\\mathcal{L}_{\\text{pred}} = \\frac{1}{B}\\sum_{i=1}^{B} \\|\\hat{z}_{1,i} - z_{1,i}\\|^2$$\n",
-    "\n",
-    "It forces the predictor to understand temporal dynamics. To minimize this, the model must calculate how a physical history transforms across an elapsed time horizon $\\delta$.\n",
-    "\n",
-    "#### 2. The Variance Regularizer ($\\mathcal{L}_{\\text{var}}$)\n",
-    "To prevent the encoders from collapsing into a single static point, the variance regularizer forces the latent vectors across a training batch to vary. It calculates the standard deviation $\\sigma$ of each latent dimension across the batch and penalizes it if it drops below a target threshold (typically $1.0$):\n",
-    "\n",
-    "$$\\mathcal{L}_{\\text{var}} = \\frac{1}{d}\\sum_{j=1}^{d} \\max\\left(0, 1 - \\sigma(z_{\\cdot, j})\\right)$$\n",
-    "\n",
-    "It acts as an expansive force. It explicitly forbids the encoders from squeezing all physical images into a single point, ensuring that different physical behaviors are mapped to distinct, unique locations in latent space.\n",
-    "\n",
-    "#### 3. The Covariance Regularizer ($\\mathcal{L}_{\\text{cov}}$)\n",
-    "Even with high variance, a model can cheat by making all latent variables track the exact same signal (e.g., if dimension 1 tracks particle position, dimensions 2 through 16 might redundantly copy dimension 1). The covariance loss penalizes the off-diagonal elements of the latent covariance matrix:\n",
-    "\n",
-    "$$\\mathcal{L}_{\\text{cov}} = \\frac{1}{d}\\sum_{j \\neq k} \\left(\\text{Cov}(z)_{j,k}\\right)^2$$\n",
-    "\n",
-    "It acts as an information decoherer. It forces the different dimensions of your latent space to be linearly independent of one another. This maximizes the \"capacity\" of the embedding space, pushing the model to cleanly separate different orthogonal physical features (like tracking the particle's spatial $x,y$ position in some dimensions, and isolating the global diffusion rate $D$ in others)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6c5bc4d2",
-   "metadata": {},
-   "source": [
-    "## Simulating particle-diffusion videos\n",
-    "\n",
-    "You'll simulate short video clips of a Brownian particle in a box, where the diffusion coefficient $D$ varies from\n",
-    "clip to clip. The world model will never be told $D$ directly — it has to infer it implicitly from how \"jittery\"\n",
-    "the particle's motion looks across frames. This is exactly the kind of latent physical parameter a JEPA-style model\n",
-    "should be able to recover from dynamics alone."
-   ]
-  },
-  {
-   "cell_type": "raw",
-   "id": "f7a7e826",
-   "metadata": {
-    "vscode": {
-     "languageId": "raw"
-    }
-   },
-   "source": [
-    "You'll separate the **true physics simulation** (the Brownian\n",
-    "motion integration) from **rendering** (DeepTrack2's optics pipeline). This is convenient pedagogically: we always\n",
-    "have access to ground truth `positions`, which we'll use later only to *evaluate* what the world model has learned,\n",
-    "never during self-supervised training."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "c125997d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "IMAGE_SIZE = 64        # image size in pixels, corresponds to the box size \n",
-    "N_FRAMES = 20          # frames per clip\n",
-    "DELTA_T = 1.0          # time between frames (arbitrary units)\n",
-    "\n",
-    "def reflect(pos, lo, hi):\n",
-    "    \"\"\"Reflect a scalar position back into [lo, hi] if it overshoots.\"\"\"\n",
-    "    span = hi - lo\n",
-    "    pos = pos - lo\n",
-    "    pos = np.abs(pos)                                # reflect off lo\n",
-    "    pos = pos % (2 * span)\n",
-    "    pos = np.where(pos > span, 2 * span - pos, pos)  # reflect off hi\n",
-    "    return pos + lo\n",
-    "\n",
-    "def simulate_trajectory(D, n_frames=N_FRAMES, image_size=IMAGE_SIZE,\n",
-    "                         delta_t=DELTA_T, margin=4):\n",
-    "    \"\"\"Simulate a single Brownian trajectory with reflective boundaries.\n",
-    "\n",
-    "    Returns:\n",
-    "        positions: (n_frames, 2) true (x, y) positions in pixel units\n",
-    "    \"\"\"\n",
-    "    pos = np.array([image_size // 2, image_size // 2])  # start in the center\n",
-    "    # pos = np.random.uniform(margin, image_size - margin, size=2)\n",
-    "    positions = [pos.copy()]\n",
-    "    for _ in range(n_frames - 1):\n",
-    "        step = np.sqrt(2 * D * delta_t) * np.random.randn(2)\n",
-    "        pos = pos + step\n",
-    "        pos[0] = reflect(pos[0], margin, image_size - margin)\n",
-    "        pos[1] = reflect(pos[1], margin, image_size - margin)\n",
-    "        positions.append(pos.copy())\n",
-    "    return np.array(positions)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "db40d752",
-   "metadata": {},
-   "source": [
-    "## Optical Rendering through a Fluorescence Microscope"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "1b22485e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import deeptrack as dt\n",
-    "\n",
-    "def render_trajectory(positions, image_size=IMAGE_SIZE):\n",
-    "    \"\"\"Render a sequence of (x, y) positions into a video of a fluorescent particle.\n",
-    "\n",
-    "    Returns:\n",
-    "        frames: (n_frames, image_size, image_size) float32 array in [0, 1]\n",
-    "    \"\"\"\n",
-    "    current_position = {\"value\": positions[0]}\n",
-    "\n",
-    "    optics = dt.Fluorescence(\n",
-    "        NA=0.8,\n",
-    "        wavelength=560e-9,\n",
-    "        resolution=1e-7,\n",
-    "        magnification=1,\n",
-    "        output_region=(0, 0, image_size, image_size),\n",
-    "    )\n",
-    "    particle = dt.PointParticle(\n",
-    "        position=lambda: current_position[\"value\"],\n",
-    "        position_unit=\"pixel\",\n",
-    "        intensity=200,\n",
-    "    )\n",
-    "    pipeline = optics(particle)\n",
-    "\n",
-    "    frames = []\n",
-    "    for p in positions:\n",
-    "        current_position[\"value\"] = p\n",
-    "        frame = pipeline.update()()\n",
-    "        frames.append(np.asarray(frame).squeeze())\n",
-    "    frames = np.stack(frames).astype(\"float32\")\n",
-    "    frames = frames / (frames.max() + 1e-8)\n",
-    "    return frames"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "5e3b7036",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def make_particle_clip(D, n_frames=N_FRAMES, image_size=IMAGE_SIZE, delta_t=DELTA_T):\n",
-    "    \"\"\"Simulate and render one video clip of a single Brownian particle.\n",
-    "\n",
-    "    Returns:\n",
-    "        frames: (n_frames, image_size, image_size) float32 array in [0, 1]\n",
-    "        positions: (n_frames, 2) true (x, y) positions in pixel units\n",
-    "    \"\"\"\n",
-    "    positions = simulate_trajectory(D, n_frames, image_size, delta_t)\n",
-    "    frames = render_trajectory(positions, image_size)\n",
-    "    return frames, positions"
-   ]
-  },
-  {
-   "cell_type": "raw",
-   "id": "4a36d8ac",
-   "metadata": {
-    "vscode": {
-     "languageId": "raw"
-    }
-   },
-   "source": [
-    "IMAGE_SIZE = 64\n",
-    "N_FRAMES = 24          # frames per clip\n",
-    "DELTA_T = 1.0          # time between frames (arbitrary units)\n",
-    "D_RANGE = (0.1, 10.0)  # diffusion coefficient range, varied per clip\n",
-    "WINDOW = 10  \n",
-    "\n",
-    "def reflect(pos, lo, hi):\n",
-    "    \"\"\"Reflect a scalar position back into [lo, hi] if it overshoots.\"\"\"\n",
-    "    span = hi - lo\n",
-    "    pos = pos - lo\n",
-    "    pos = np.abs(pos)                      # reflect off lo\n",
-    "    pos = pos % (2 * span)\n",
-    "    pos = np.where(pos > span, 2 * span - pos, pos)  # reflect off hi\n",
-    "    return pos + lo\n",
-    "\n",
-    "def make_particle_clip(D, n_frames=N_FRAMES, image_size=IMAGE_SIZE, delta_t=DELTA_T):\n",
-    "    \"\"\"Simulate one video clip of a single Brownian particle with diffusion coefficient D.\n",
-    "\n",
-    "    Returns:\n",
-    "        frames: (n_frames, image_size, image_size) float32 array in [0, 1]\n",
-    "        positions: (n_frames, 2) true (x, y) positions in pixel units\n",
-    "    \"\"\"\n",
-    "\n",
-    "    margin = 4\n",
-    "    pos = np.random.uniform(margin, image_size - margin, size=2)\n",
-    "    current_position = {\"value\": pos}\n",
-    "\n",
-    "    optics = dt.Fluorescence(\n",
-    "        NA=0.8,\n",
-    "        wavelength=560e-9,\n",
-    "        resolution=1e-7,\n",
-    "        magnification=1,\n",
-    "        output_region=(0, 0, image_size, image_size),\n",
-    "    )\n",
-    "\n",
-    "    particle = dt.PointParticle(\n",
-    "        position=lambda: current_position[\"value\"],\n",
-    "        position_unit=\"pixel\",\n",
-    "        intensity=200,\n",
-    "    )\n",
-    "\n",
-    "    pipeline = optics(particle)\n",
-    "\n",
-    "    # Pre-compute the true Brownian trajectory ourselves (Euler-Maruyama),\n",
-    "    # then re-render the particle at each position. This keeps the physics\n",
-    "    # explicit and lets us keep ground-truth positions for the probing step.\n",
-    "    # pos = np.array([image_size / 2, image_size / 2], dtype=np.float64)\n",
-    "    positions = [pos.copy()]\n",
-    "    for _ in range(n_frames - 1):\n",
-    "        step = np.sqrt(2 * D * delta_t) * np.random.randn(2)\n",
-    "        pos = pos + step\n",
-    "        pos[0] = reflect(pos[0], 4, image_size - 4)\n",
-    "        pos[1] = reflect(pos[1], 4, image_size - 4)\n",
-    "        positions.append(pos.copy())\n",
-    "    positions = np.array(positions)\n",
-    "\n",
-    "    frames = []\n",
-    "    for p in positions:\n",
-    "        current_position[\"value\"] = p\n",
-    "        frame = pipeline.update()()\n",
-    "        frames.append(np.asarray(frame).squeeze())\n",
-    "    frames = np.stack(frames).astype(\"float32\")\n",
-    "    frames = frames / (frames.max() + 1e-8)\n",
-    "    return frames, positions\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "18cf80d7",
-   "metadata": {},
-   "source": [
-    "### Visualize an Example Clip"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "d3933ac1",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
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-       ""
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "from matplotlib import pyplot as plt\n",
-    "from matplotlib import animation\n",
-    "from IPython.display import HTML\n",
-    "\n",
-    "# Quick sanity check\n",
-    "D_demo = 10.0\n",
-    "frames_demo, pos_demo = make_particle_clip(D_demo)\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize=(4, 4))\n",
-    "im = ax.imshow(frames_demo[0], cmap=\"gray\", vmin=frames_demo.min(), vmax=frames_demo.max())\n",
-    "title = ax.set_title(f\"D={D_demo}, t=0\")\n",
-    "ax.axis(\"off\")\n",
-    "\n",
-    "def update(i):\n",
-    "    im.set_data(frames_demo[i])\n",
-    "    title.set_text(f\"D={D_demo}, t={i}\")\n",
-    "    return [im, title]\n",
-    "\n",
-    "anim = animation.FuncAnimation(\n",
-    "    fig, update, frames=len(frames_demo), interval=150, blit=False\n",
-    ")\n",
-    "plt.close(fig)  # prevent a duplicate static plot from also rendering\n",
-    "\n",
-    "HTML(anim.to_jshtml())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4cf74a02",
-   "metadata": {},
-   "source": [
-    "## Data Pipeline: Constructing the Context and Target Windows\n",
-    "\n",
-    "To train the JEPA world model, you'll need a dataset that streams video clips of diffusing particles.  The `DiffusionClipDataset()` handles this by dynamically generating video clips on the fly and slicing them into specific temporal windows. For every index sampled, the dataset performs the following operations:\n",
-    "\n",
-    "- Simulates a Full Video: It draws a random environmental diffusion coefficient ($D$) from our specified range and generates a continuous trajectory of N_FRAMES.\n",
-    "\n",
-    "- Establishes the Present Anchor: It randomly selects a frame index $t_0$ to represent the \"present moment.\" To ensure there are enough past frames to fill our context window, $t_0$ is constrained to look back at least `window` frames.\n",
-    "\n",
-    "- Samples a Random Future Horizon: It randomly samples a time gap ($\\delta$) ranging from $1$ to the maximum remaining frames in the clip. This sets our future target frame at $t_1 = t_0 + \\delta$.\n",
-    "\n",
-    "- Assembles the Tensors:\n",
-    "\n",
-    "    - x0 (Context Window): A sequence of 10 consecutive frames leading up to and including the present moment ($[t_0 - 9, \\dots, t_0]$).\n",
-    "    - x1 (Target Window): A sequence of 10 consecutive frames leading up to and including the future moment ($[t_1 - 9, \\dots, t_1]$).\n",
-    "    - Conditioning & Ground Truths: It extracts the elapsed time gap delta_t ($\\Delta t$), the true environmental rate D_true ($D$), and the precise 2D spatial positions (pos0, pos1) of the particle at both timestamps for downstream verification."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "29ae5714",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import torch\n",
-    "\n",
-    "WINDOW = 10 # window size for sampling clips\n",
-    "D_RANGE = (0.1, 10.0)  # range of diffusion coefficients to sample from\n",
-    "\n",
-    "class DiffusionClipDataset(torch.utils.data.Dataset):\n",
-    "    def __init__(self, n_clips=2000, n_frames=N_FRAMES, image_size=IMAGE_SIZE,\n",
-    "                 d_range=D_RANGE, window=WINDOW):\n",
-    "        self.n_clips = n_clips\n",
-    "        self.n_frames = n_frames\n",
-    "        self.image_size = image_size\n",
-    "        self.d_range = d_range\n",
-    "        self.window = window\n",
-    "\n",
-    "    def __len__(self):\n",
-    "        return self.n_clips\n",
-    "\n",
-    "    def __getitem__(self, idx):\n",
-    "        D = np.random.uniform(*self.d_range)\n",
-    "        frames, positions = make_particle_clip(D, self.n_frames, self.image_size)\n",
-    "\n",
-    "        w = self.window\n",
-    "        t0 = np.random.randint(w - 1, self.n_frames - w )\n",
-    "        delta = np.random.randint(w, self.n_frames - t0)\n",
-    "        t1 = t0 + delta\n",
-    "\n",
-    "        x0 = torch.from_numpy(frames[t0 - w + 1 : t0 + 1]).float()  # (w, H, W)\n",
-    "        x1 = torch.from_numpy(frames[t1 - w + 1 : t1 + 1]).float()  # (w, H, W)\n",
-    "\n",
-    "        delta_t = torch.tensor([delta], dtype=torch.float32)\n",
-    "        D_true = torch.tensor([D], dtype=torch.float32)\n",
-    "        pos0 = torch.from_numpy(positions[t0]).float()\n",
-    "        pos1 = torch.from_numpy(positions[t1]).float()\n",
-    "\n",
-    "        return x0, x1, delta_t, D_true, pos0, pos1\n",
-    "\n",
-    "train_ds = DiffusionClipDataset(n_clips=2000)\n",
-    "val_ds = DiffusionClipDataset(n_clips=400)\n",
-    "\n",
-    "train_loader = torch.utils.data.DataLoader(train_ds, batch_size=32, shuffle=True)\n",
-    "val_loader = torch.utils.data.DataLoader(val_ds, batch_size=32, shuffle=False)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ff89d73b",
-   "metadata": {},
-   "source": [
-    "## Understanding World Models\n",
-    "\n",
-    "We will build a **Joint-Embedding Predictive Architecture (JEPA)**:\n",
-    "- an **encoder** $E_\\theta$ that maps a video frame to a latent state $z_t = E_\\theta(x_t)$\n",
-    "- a **target encoder** $E_{\\bar\\theta}$ (an EMA copy of $E_\\theta$, no gradient) that produces the *prediction target*\n",
-    "- a **predictor** $P_\\phi$ that predicts $\\hat z_{t+\\Delta t} = P_\\phi(z_t, \\Delta t)$\n",
-    "- training signal: $\\hat z_{t+\\Delta t} \\approx E_{\\bar\\theta}(x_{t+\\Delta t})$, **not** pixel reconstruction\n",
-    "\n",
-    "The key pedagogical point: we never ask the model to reconstruct pixels. Diffusion videos are mostly noise/texture —\n",
-    "not worth modeling. We ask the model to predict *its own representation* of the future. We will see this is harder to\n",
-    "get right (it can collapse to a trivial constant) and we'll fix that with an EMA target + a variance regularizer\n",
-    "(VICReg-style), in the spirit of I-JEPA / V-JEPA.\n",
-    "\n",
-    "### Roadmap\n",
-    "1. Simulate particle-diffusion videos with **DeepTrack2** (vary the diffusion coefficient $D$)\n",
-    "2. Build encoder / target-encoder / predictor\n",
-    "3. Train self-supervised with a latent-prediction loss + anti-collapse regularization\n",
-    "4. **Probe**: train a tiny linear head latent → true $D$, true position — this is the moment we check whether the\n",
-    "   world model \"discovered\" physics\n",
-    "5. Visualize latent trajectories vs. true trajectories\n",
-    "6. **Ablation**: remove the EMA target / regularizer and watch the representation collapse\n",
-    "7. (Optional, advanced) Differentiable-simulator comparison: optimize $D$ directly through DeepTrack2's\n",
-    "   gradient-preserving pipeline and compare to what the learned world model infers"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c111c0ee",
-   "metadata": {},
-   "source": [
-    "## 3. The world model: encoder, EMA target encoder, predictor\n",
-    "\n",
-    "We build everything with **Deeplay**, so each block is a swappable, composable module. The encoder is a small CNN;\n",
-    "the predictor is an MLP that takes $(z_t, \\Delta t)$ and outputs $\\hat z_{t+\\Delta t}$.\n",
-    "\n",
-    "Two design choices worth flagging:\n",
-    "- **EMA target encoder**: the target representation $E_{\\bar\\theta}(x_{t+\\Delta t})$ is produced by a *momentum copy*\n",
-    "  of the encoder, updated as $\\bar\\theta \\leftarrow \\tau \\bar\\theta + (1-\\tau)\\theta$, with **no gradient** flowing\n",
-    "  through it. This is the standard trick (BYOL/I-JEPA/V-JEPA) to prevent the trivial collapse \"encoder outputs a\n",
-    "  constant, predictor learns the constant, loss = 0\".\n",
-    "- **Variance regularization** (VICReg-style): we additionally penalize the embeddings if their per-dimension\n",
-    "  variance across the batch collapses toward 0. This is a second, complementary defense against collapse, and lets\n",
-    "  us demonstrate what happens when we strip each one out (Section 6).\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "fcdd01ba",
-   "metadata": {},
-   "source": [
-    "## Framing the Architecture: Why We Condition on Time ($\\Delta t$)\n",
-    "\n",
-    "When applying Joint Embedding Predictive Architectures to video data (such as Meta's V-JEPA), it is common practice to use fixed-size context and target windows. For example, a model might take a fixed block of frames and learn to predict a subsequent, fixed block of frames. Because the time gap between the context and the target is always identical, the predictor network does not need to know when it is predicting; it only needs to learn a static temporal mapping.\n",
-    "\n",
-    "However, because our goal is to recover the underlying physics of diffusion, we introduce a deliberate modification to the standard literature setup: **we explicitly condition our Latent Predictor on a variable time horizon ($\\Delta t$).**\n",
-    "\n",
-    "Instead of predicting a single fixed future block, our model is given a 10-frame context window and asked to predict anywhere from 1 to 14 frames into the future, with the exact horizon sampled randomly for every training example.\n",
-    "\n",
-    "### The Pedagogical Value of Variable Horizons\n",
-    "\n",
-    "We make this architectural departure for two reasons:\n",
-    "\n",
-    "1. **Discouraging a \"Memorized Displacement\" Shortcut:** In pure Brownian motion, the environmental diffusion coefficient ($D$) is not a static displacement; it is the proportionality constant that dictates how the uncertainty scales over time ($\\sigma^2 \\sim 2D\\Delta t$). If the time gap were always fixed, the model could satisfy the prediction objective by memorizing a one-off displacement scale for that specific horizon, without ever needing a notion of rate. By varying $\\Delta t$, the model is instead asked to be consistent across many different horizons simultaneously—a design intended to encourage it to internalize a generalizable rate, rather than a single fixed-horizon shortcut.\n",
-    "2. **Visualizing the Arrow of Diffusion:** Conditioning on $\\Delta t$ lets us evaluate the model's performance as a function of elapsed time. This makes it possible to directly plot how latent prediction error grows as the horizon expands—a quantifiable window into how a world model handles accumulating stochastic uncertainty."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "924e8d3b",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import deeplay as dl\n",
-    "from typing import Optional\n",
-    "from torch import nn\n",
-    "import torch.nn.functional as F\n",
-    "\n",
-    "\n",
-    "LATENT_DIM = 64\n",
-    "\n",
-    "class WorldModel(dl.Application):\n",
-    "    def __init__(self, latent_dim=LATENT_DIM, ema_tau=0.99, lam=1.0, mu=1.0, nu=0.01, use_ema=True,\n",
-    "                 optimizer=None, **kwargs):\n",
-    "\n",
-    "        self.encoder = dl.ConvolutionalEncoder2d(\n",
-    "            in_channels=WINDOW,\n",
-    "            hidden_channels=[32, 64],\n",
-    "            out_channels=128,\n",
-    "            postprocess=dl.Layer(nn.AdaptiveAvgPool2d, 1),\n",
-    "        )\n",
-    "        self.encoder.strided(stride=2, apply_to_first_layer=True, apply_to_last_layer=True)\n",
-    "        self.encoder_proj = nn.Sequential(\n",
-    "            nn.Linear(128, latent_dim),\n",
-    "            nn.BatchNorm1d(latent_dim),\n",
-    "        )\n",
-    "\n",
-    "        self.predictor = dl.MultiLayerPerceptron(\n",
-    "            in_features=latent_dim + 1,\n",
-    "            hidden_features=[128, 128],\n",
-    "            out_features=latent_dim,\n",
-    "        )\n",
-    "        self.predictor[\"blocks\", :-1].all.normalized(nn.BatchNorm1d)\n",
-    "        self.predictor[\"blocks\", :-1].configure(order=[\"layer\", \"normalization\", \"activation\"])\n",
-    "\n",
-    "\n",
-    "        self.use_ema = use_ema\n",
-    "        self.ema_tau = ema_tau\n",
-    "        self.lam = lam\n",
-    "        self.mu = mu\n",
-    "        self.nu = nu\n",
-    "\n",
-    "        if self.use_ema:\n",
-    "            self.target_encoder = dl.ConvolutionalEncoder2d(\n",
-    "                in_channels=WINDOW,\n",
-    "                hidden_channels=[32, 64],\n",
-    "                out_channels=128,\n",
-    "                postprocess=dl.Layer(nn.AdaptiveAvgPool2d, 1),\n",
-    "            )\n",
-    "            self.target_encoder.strided(stride=2, apply_to_first_layer=True, apply_to_last_layer=True)\n",
-    "            self.target_proj = nn.Sequential(\n",
-    "                nn.Linear(128, latent_dim),\n",
-    "                nn.BatchNorm1d(latent_dim),\n",
-    "            )\n",
-    "        else:\n",
-    "            self.target_encoder = self.encoder\n",
-    "            self.target_proj = self.encoder_proj\n",
-    "\n",
-    "        super().__init__(**kwargs)\n",
-    "\n",
-    "        self.optimizer = optimizer or dl.Adam(lr=1e-4)\n",
-    "\n",
-    "        @self.optimizer.params\n",
-    "        def params(self):\n",
-    "            return self.parameters()\n",
-    "\n",
-    "        self._target_synced = False\n",
-    "\n",
-    "    def encode(self, x):\n",
-    "        z = self.encoder_proj(self.encoder(x).flatten(1))\n",
-    "        return F.normalize(z, dim=-1)\n",
-    "\n",
-    "    def encode_target(self, x):\n",
-    "        z = self.target_proj(self.target_encoder(x).flatten(1))\n",
-    "        return F.normalize(z, dim=-1)\n",
-    "\n",
-    "    def forward(self, x0, x1, delta_t):\n",
-    "        z0 = self.encode(x0)\n",
-    "        z1_pred = self.predictor(torch.cat([z0, delta_t / N_FRAMES], dim=-1))\n",
-    "        z1_pred = F.normalize(z1_pred, dim=-1)   # predictor output must match target's scale\n",
-    "        if self.use_ema:\n",
-    "            with torch.no_grad():\n",
-    "                z1_target = self.encode_target(x1)\n",
-    "        else:\n",
-    "            z1_target = self.encode_target(x1)\n",
-    "        return z0, z1_pred, z1_target\n",
-    "    \n",
-    "    def variance_loss(self, z, gamma=None):\n",
-    "        if gamma is None:\n",
-    "            gamma = 1.0 / (z.shape[-1] ** 0.5)   # ~0.125 for latent_dim=64\n",
-    "        std = z.std(dim=0) + 1e-4\n",
-    "        return F.relu(gamma - std).mean()\n",
-    "\n",
-    "    # def covariance_loss(self, z):\n",
-    "    #     z = z - z.mean(dim=0)\n",
-    "    #     n, d = z.shape\n",
-    "    #     cov = (z.T @ z) / (n - 1)\n",
-    "    #     off_diag = cov.flatten()[:-1].view(d - 1, d + 1)[:, 1:].flatten()\n",
-    "    #     return (off_diag ** 2).sum() / d\n",
-    "    \n",
-    "    def covariance_loss(self, z):\n",
-    "        z = z - z.mean(dim=0)\n",
-    "        cov = (z.T @ z) / (z.shape[0] - 1)\n",
-    "        off_diag = cov - torch.diag(torch.diagonal(cov))\n",
-    "        return (off_diag ** 2).sum() / z.shape[1]\n",
-    "\n",
-    "    def compute_loss(self, z0, z1_pred, z1_target):\n",
-    "        pred_loss = F.mse_loss(z1_pred, z1_target)\n",
-    "        loss = {\"pred\": self.lam * pred_loss}\n",
-    "        if self.mu > 0:\n",
-    "            reg_loss = self.variance_loss(z0) + self.variance_loss(z1_pred)\n",
-    "            loss[\"reg\"] = self.mu * reg_loss\n",
-    "        if self.nu > 0:\n",
-    "            cov_loss = self.covariance_loss(z0) + self.covariance_loss(z1_pred)\n",
-    "            loss[\"cov\"] = self.nu * cov_loss\n",
-    "        return loss\n",
-    "\n",
-    "    def _shared_step(self, batch, stage):\n",
-    "        x0, x1, delta_t, D_true, pos0, pos1 = batch\n",
-    "        z0, z1_pred, z1_target = self(x0, x1, delta_t)\n",
-    "        loss = self.compute_loss(z0, z1_pred, z1_target)\n",
-    "        for name, v in loss.items():\n",
-    "            self.log(f\"{stage}_{name}\", v, on_step=True, on_epoch=True,\n",
-    "                      prog_bar=True, logger=True)\n",
-    "        return sum(loss.values())\n",
-    "\n",
-    "    def training_step(self, batch, batch_idx):\n",
-    "        return self._shared_step(batch, \"train\")\n",
-    "\n",
-    "    def validation_step(self, batch, batch_idx):\n",
-    "        return self._shared_step(batch, \"val\")\n",
-    "\n",
-    "    def on_train_batch_end(self, outputs, batch, batch_idx):\n",
-    "        if self.use_ema:\n",
-    "            self.update_target()\n",
-    "\n",
-    "    # @torch.no_grad()\n",
-    "    # def update_target(self):\n",
-    "    #     if not self._target_synced:\n",
-    "    #         self.target_encoder.load_state_dict(self.encoder.state_dict())\n",
-    "\n",
-    "    @torch.no_grad()\n",
-    "    def update_target(self):\n",
-    "        if not self._target_synced:\n",
-    "            self.target_encoder.load_state_dict(self.encoder.state_dict())\n",
-    "            self.target_proj.load_state_dict(self.encoder_proj.state_dict())\n",
-    "            for p in list(self.target_encoder.parameters()) + list(self.target_proj.parameters()):\n",
-    "                p.requires_grad_(False)\n",
-    "            self._target_synced = True\n",
-    "            return\n",
-    "        for p, p_t in zip(self.encoder.parameters(), self.target_encoder.parameters()):\n",
-    "            p_t.data.mul_(self.ema_tau).add_(p.data, alpha=1 - self.ema_tau)\n",
-    "        for p, p_t in zip(self.encoder_proj.parameters(), self.target_proj.parameters()):\n",
-    "            p_t.data.mul_(self.ema_tau).add_(p.data, alpha=1 - self.ema_tau)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "id": "12a0bd11",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from lightning.pytorch.callbacks import Callback\n",
-    "from sklearn.linear_model import Ridge\n",
-    "from sklearn.model_selection import train_test_split\n",
-    "from sklearn.metrics import r2_score\n",
-    "\n",
-    "class ProbeMonitorCallback(Callback):\n",
-    "    def __init__(self, check_every_n_epochs=1, n_clips=300):\n",
-    "        self.check_every_n_epochs = check_every_n_epochs\n",
-    "        self.n_clips = n_clips\n",
-    "        self.history = []\n",
-    "\n",
-    "    @torch.no_grad()\n",
-    "    def _collect_probe_data(self, model):\n",
-    "        model.eval()\n",
-    "        Z, Z2, DT, DS, POS = [], [], [], [], []\n",
-    "        ds = DiffusionClipDataset(n_clips=self.n_clips)\n",
-    "        loader = torch.utils.data.DataLoader(ds, batch_size=32, shuffle=False)\n",
-    "        for x0, x1, delta_t, D_true, pos0, pos1 in loader:\n",
-    "            x0, x1 = x0.to(model.device), x1.to(model.device)\n",
-    "            z0 = model.encode(x0)\n",
-    "            z1 = model.encode(x1)\n",
-    "            Z.append(z0.cpu()); Z2.append(z1.cpu())\n",
-    "            DT.append(delta_t); DS.append(D_true); POS.append(pos0)\n",
-    "        return torch.cat(Z), torch.cat(Z2), torch.cat(DT), torch.cat(DS), torch.cat(POS)\n",
-    "\n",
-    "    def on_train_epoch_end(self, trainer, pl_module):\n",
-    "        epoch = trainer.current_epoch\n",
-    "        if (epoch + 1) % self.check_every_n_epochs != 0:\n",
-    "            return\n",
-    "\n",
-    "        Z0, Z1, DT_, D_, POS0 = self._collect_probe_data(pl_module)\n",
-    "        feat_D = torch.cat([Z0, Z1, DT_], dim=1).numpy()\n",
-    "        target_D = D_.numpy().ravel()\n",
-    "\n",
-    "        Xtr, Xte, ytr, yte = train_test_split(feat_D, target_D, test_size=0.25, random_state=0)\n",
-    "        probe = Ridge(alpha=1.0).fit(Xtr, ytr)\n",
-    "        r2 = r2_score(yte, probe.predict(Xte))\n",
-    "\n",
-    "        self.history.append((epoch, r2))\n",
-    "        pl_module.log(\"probe_D_r2\", r2, prog_bar=True, on_step=False, on_epoch=True)\n",
-    "        print(f\"  [epoch {epoch}] D probe R^2 = {r2:.3f}\")\n",
-    "\n",
-    "        pl_module.train()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5a15788b",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:76: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default\n"
-     ]
-    },
-    {
-     "data": {
-      "text/html": [
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┏━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
-       "┃   ┃ Name           ┃ Type                   ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
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-       "│ 0 │ encoder        │ ConvolutionalEncoder2d │ 95.3 K │ train │     0 │\n",
-       "│ 1 │ encoder_proj   │ Sequential             │  8.4 K │ train │     0 │\n",
-       "│ 2 │ predictor      │ MultiLayerPerceptron   │ 33.7 K │ train │     0 │\n",
-       "│ 3 │ target_encoder │ ConvolutionalEncoder2d │ 95.3 K │ train │     0 │\n",
-       "│ 4 │ target_proj    │ Sequential             │  8.4 K │ train │     0 │\n",
-       "│ 5 │ train_metrics  │ MetricCollection       │      0 │ train │     0 │\n",
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-       "│ 8 │ optimizer      │ Adam                   │      0 │ train │     0 │\n",
-       "└───┴────────────────┴────────────────────────┴────────┴───────┴───────┘\n",
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-       "┡━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ encoder        │ ConvolutionalEncoder2d │ 95.3 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ encoder_proj   │ Sequential             │  8.4 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ predictor      │ MultiLayerPerceptron   │ 33.7 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ target_encoder │ ConvolutionalEncoder2d │ 95.3 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ target_proj    │ Sequential             │  8.4 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ train_metrics  │ MetricCollection       │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m6\u001b[0m\u001b[2m \u001b[0m│ val_metrics    │ MetricCollection       │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m7\u001b[0m\u001b[2m \u001b[0m│ test_metrics   │ MetricCollection       │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m8\u001b[0m\u001b[2m \u001b[0m│ optimizer      │ Adam                   │      0 │ train │     0 │\n",
-       "└───┴────────────────┴────────────────────────┴────────┴───────┴───────┘\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
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-     "data": {
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-       "
Trainable params: 241 K                                                                                            \n",
-       "Non-trainable params: 0                                                                                            \n",
-       "Total params: 241 K                                                                                                \n",
-       "Total estimated model params size (MB): 0                                                                          \n",
-       "Modules in train mode: 47                                                                                          \n",
-       "Modules in eval mode: 0                                                                                            \n",
-       "Total FLOPs: 0                                                                                                     \n",
-       "
\n"
-      ],
-      "text/plain": [
-       "\u001b[1mTrainable params\u001b[0m: 241 K                                                                                            \n",
-       "\u001b[1mNon-trainable params\u001b[0m: 0                                                                                            \n",
-       "\u001b[1mTotal params\u001b[0m: 241 K                                                                                                \n",
-       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 0                                                                          \n",
-       "\u001b[1mModules in train mode\u001b[0m: 47                                                                                          \n",
-       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
-       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
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-     "metadata": {},
-     "output_type": "display_data"
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-    {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "27747b3be8144f7084ed9b4e722f0c81",
-       "version_major": 2,
-       "version_minor": 0
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-      "text/plain": [
-       "Output()"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
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-     "data": {
-      "text/html": [
-       "
/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/\n",
-       "_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and \n",
-       "treespec.is_leaf()` instead.\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/\n",
-       "_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and \n",
-       "treespec.is_leaf()` instead.\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
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-       "
/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/co\n",
-       "nnectors/data_connector.py:434: The 'val_dataloader' does not have many workers which may be a bottleneck. Consider\n",
-       "increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/co\n",
-       "nnectors/data_connector.py:434: The 'val_dataloader' does not have many workers which may be a bottleneck. Consider\n",
-       "increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
-      ]
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-     "metadata": {},
-     "output_type": "display_data"
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-     "data": {
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/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/co\n",
-       "nnectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. \n",
-       "Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve \n",
-       "performance.\n",
-       "
\n"
-      ],
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-       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/co\n",
-       "nnectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. \n",
-       "Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve \n",
-       "performance.\n"
-      ]
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-     "output_type": "display_data"
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-       "
  [epoch 0] D probe R^2 = 0.334\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "  [epoch 0] D probe R^2 = 0.334\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
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-       "
  [epoch 1] D probe R^2 = 0.516\n",
-       "
\n"
-      ],
-      "text/plain": [
-       "  [epoch 1] D probe R^2 = 0.516\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "probe_monitor = ProbeMonitorCallback(check_every_n_epochs=1, n_clips=300)\n",
-    "\n",
-    "model = WorldModel(optimizer=dl.Adam(lr=1e-3)).create()\n",
-    "history = model.fit(train_ds, val_data=val_ds, max_epochs=15, batch_size=32, accelerator = \"auto\", callbacks=[probe_monitor])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8f9b1333",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "epochs, r2s = zip(*probe_monitor.history)\n",
-    "plt.plot(epochs, r2s, marker=\"o\")\n",
-    "plt.xlabel(\"epoch\"); plt.ylabel(\"D probe R²\")\n",
-    "plt.title(\"Probe R² over training\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5a64741e",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "markdown",
-   "id": "50d5e387",
-   "metadata": {},
-   "source": [
-    "## 4. Loss: latent prediction + anti-collapse regularizer\n",
-    "\n",
-    "$$ \\mathcal{L} = \\underbrace{\\|\\hat z_{t+\\Delta t} - \\text{sg}(z_{t+\\Delta t})\\|^2}_{\\text{prediction loss}} \\;+\\; \\lambda \\underbrace{\\sum_d \\max(0,\\, \\gamma - \\text{std}(z_{\\cdot, d}))}_{\\text{variance regularizer (VICReg-style)}} $$\n",
-    "\n",
-    "`sg` = stop-gradient (handled here by the target encoder having `requires_grad=False` and being updated only via EMA).\n",
-    "The variance term pushes each latent dimension to keep some spread *within the batch*, so it can't collapse to a\n",
-    "single point for every input.\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c4e78483",
-   "metadata": {},
-   "source": [
-    "## 6. Probing: did the world model discover physics?\n",
-    "\n",
-    "We freeze the encoder and fit a small linear/MLP probe from $z_t$ alone to:\n",
-    "- the true diffusion coefficient $D$ (a *global* property of the clip)\n",
-    "- the true particle position (a property of the single frame)\n",
-    "\n",
-    "If the encoder's latent space is rich enough to predict $D$ well, the self-supervised prediction objective has\n",
-    "forced the model to represent something about the *dynamics regime* of the clip — not just the current pixel\n",
-    "pattern. This is the chapter's main \"aha\" moment.\n",
-    "\n",
-    "Note: $D$ is a property of the *whole clip*, not a single frame, so to probe it fairly we feed the probe a short\n",
-    "window of frames (or, more simply here, two latents $z_t, z_{t+\\Delta t}$ and let it use their difference).\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "336727af",
-   "metadata": {},
-   "source": [
-    "# diagnosstic 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "ff4e8986",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "## Diagnostic: is D actually recoverable from raw pixel displacements?\n",
-    "#\n",
-    "# This bypasses the model entirely. We simulate many clips at different D,\n",
-    "# compute the raw pixel displacement statistics directly from the rendered\n",
-    "# frames (via simple centroid tracking, NOT from the ground-truth `positions`\n",
-    "# array -- we want to know what's visible in the IMAGES, since that's all the\n",
-    "# encoder ever sees), and check whether D is recoverable from that signal.\n",
-    "#\n",
-    "# If this comes back with a weak/no relationship, the bottleneck is the\n",
-    "# rendering/resolution regime, not the world-model architecture, and no\n",
-    "# amount of context_k or loss tuning will fix it -- you'd need to change the\n",
-    "# image_size, the D range, or the optics (PSF size, magnification, etc.).\n",
-    "\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "\n",
-    "def centroid_from_frame(frame, threshold_rel=0.3):\n",
-    "    \"\"\"Cheap centroid estimate directly from pixel intensities (mimics what\n",
-    "    any reasonable encoder could in principle extract from a single frame).\"\"\"\n",
-    "    thresh = frame.max() * threshold_rel\n",
-    "    mask = frame > thresh\n",
-    "    if mask.sum() == 0:\n",
-    "        mask = frame > 0\n",
-    "    ys, xs = np.nonzero(mask)\n",
-    "    weights = frame[ys, xs]\n",
-    "    if weights.sum() == 0:\n",
-    "        return np.array([np.nan, np.nan])\n",
-    "    cy = np.average(ys, weights=weights)\n",
-    "    cx = np.average(xs, weights=weights)\n",
-    "    return np.array([cx, cy])\n",
-    "\n",
-    "\n",
-    "def measure_pixel_displacement_vs_D(n_clips=200, k=14, n_frames=N_FRAMES):\n",
-    "    Ds, true_disps, pix_disps = [], [], []\n",
-    "\n",
-    "    for _ in range(n_clips):\n",
-    "        D = np.random.uniform(*D_RANGE)\n",
-    "        frames, positions = make_particle_clip(D, n_frames=n_frames)\n",
-    "\n",
-    "        t0s = np.random.randint(0, n_frames - k, size=3)\n",
-    "        for t0 in t0s:\n",
-    "            true_disp = np.linalg.norm(positions[t0 + k] - positions[t0])\n",
-    "\n",
-    "            c0 = centroid_from_frame(frames[t0])\n",
-    "            c1 = centroid_from_frame(frames[t0 + k])\n",
-    "            if np.any(np.isnan(c0)) or np.any(np.isnan(c1)):\n",
-    "                continue\n",
-    "            pix_disp = np.linalg.norm(c1 - c0)\n",
-    "\n",
-    "            Ds.append(D)\n",
-    "            true_disps.append(true_disp)\n",
-    "            pix_disps.append(pix_disp)\n",
-    "\n",
-    "    return np.array(Ds), np.array(true_disps), np.array(pix_disps)\n",
-    "\n",
-    "\n",
-    "Ds, true_disps, pix_disps = measure_pixel_displacement_vs_D(n_clips=200, k=14)\n",
-    "\n",
-    "print(f\"n samples: {len(Ds)}\")\n",
-    "print(f\"correlation(D, true_disp)  = {np.corrcoef(Ds, true_disps)[0, 1]:.3f}  \"\n",
-    "      f\"(sanity check -- should be strongly positive by construction)\")\n",
-    "print(f\"correlation(D, pix_disp)   = {np.corrcoef(Ds, pix_disps)[0, 1]:.3f}  \"\n",
-    "      f\"(THIS is what matters -- can pixels alone reveal D?)\")\n",
-    "print(f\"correlation(true_disp, pix_disp) = {np.corrcoef(true_disps, pix_disps)[0, 1]:.3f}  \"\n",
-    "      f\"(how faithfully does rendering preserve the true displacement?)\")\n",
-    "\n",
-    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
-    "\n",
-    "axes[0].scatter(Ds, true_disps, s=8, alpha=0.4)\n",
-    "axes[0].set_xlabel(\"D\"); axes[0].set_ylabel(\"true displacement (k frames)\")\n",
-    "axes[0].set_title(\"Ground truth: D vs true displacement\")\n",
-    "\n",
-    "axes[1].scatter(Ds, pix_disps, s=8, alpha=0.4, color=\"orange\")\n",
-    "axes[1].set_xlabel(\"D\"); axes[1].set_ylabel(\"pixel-centroid displacement (k frames)\")\n",
-    "axes[1].set_title(\"From RENDERED PIXELS: D vs measured displacement\")\n",
-    "\n",
-    "axes[2].scatter(true_disps, pix_disps, s=8, alpha=0.4, color=\"green\")\n",
-    "lims = [0, max(true_disps.max(), pix_disps.max())]\n",
-    "axes[2].plot(lims, lims, \"r--\", alpha=0.5)\n",
-    "axes[2].set_xlabel(\"true displacement\"); axes[2].set_ylabel(\"pixel-centroid displacement\")\n",
-    "axes[2].set_title(\"Rendering fidelity check\")\n",
-    "\n",
-    "plt.tight_layout()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e32e6b7e",
-   "metadata": {},
-   "source": [
-    "# diagnostic"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "baa9a949",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "train_pred = history.history[\"train_pred_epoch\"][\"value\"]\n",
-    "train_reg = history.history.get(\"train_reg_loss_val\")\n",
-    "\n",
-    "plt.figure(figsize=(6, 4))\n",
-    "plt.plot(train_pred, label=\"pred_loss\")\n",
-    "if train_reg is not None:\n",
-    "    plt.plot(train_reg, label=\"reg_loss\")\n",
-    "plt.xlabel(\"epoch\"); plt.ylabel(\"loss\"); plt.legend()\n",
-    "plt.title(\"Training loss breakdown\")\n",
-    "plt.show()\n",
-    "\n",
-    "print(f\"pred_loss: first={train_pred[0]:.4f}  last={train_pred[-1]:.4f}\")\n",
-    "print(f\"  -> dropped to {100 * train_pred[-1] / train_pred[0]:.1f}% of initial value\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "6c791ea9",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import torch\n",
-    "\n",
-    "@torch.no_grad()\n",
-    "def check_latent_variance(model, n_clips=300):\n",
-    "    model.eval()\n",
-    "    ds = DiffusionClipDataset(n_clips=n_clips)\n",
-    "    loader = torch.utils.data.DataLoader(ds, batch_size=32, shuffle=False)\n",
-    "    Zs = []\n",
-    "    for x0, x1, delta_t, D_true, pos0, pos1 in loader:\n",
-    "        x0 = x0.to(model.device)\n",
-    "        Zs.append(model.encode(x0).cpu())\n",
-    "    Z = torch.cat(Zs)\n",
-    "    return Z, Z.std(dim=0)\n",
-    "\n",
-    "Z0_check, per_dim_std = check_latent_variance(model)\n",
-    "print(f\"Per-dim std -- mean: {per_dim_std.mean():.4f}, min: {per_dim_std.min():.4f}, max: {per_dim_std.max():.4f}\")\n",
-    "\n",
-    "gamma = 1.0  # whatever you set in variance_loss\n",
-    "near_floor = (per_dim_std - gamma).abs() < 0.1\n",
-    "print(f\"Dims near the regularizer floor: {near_floor.sum().item()} / {len(per_dim_std)}\")\n",
-    "\n",
-    "# Confirm it's not just stochastic noise in eval mode\n",
-    "x0_sample, *_ = next(iter(torch.utils.data.DataLoader(DiffusionClipDataset(n_clips=4), batch_size=4)))\n",
-    "x0_sample = x0_sample.to(model.device)\n",
-    "z_a, z_b = model.encode(x0_sample), model.encode(x0_sample)\n",
-    "print(f\"Repeat-forward diff (should be ~0): {(z_a - z_b).abs().max().item():.6f}\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "899a11b5",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from sklearn.decomposition import PCA\n",
-    "pca = PCA().fit(Z0_check.numpy())\n",
-    "print(np.cumsum(pca.explained_variance_ratio_)[:10])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "71b3e56f",
-   "metadata": {},
-   "source": [
-    "# test"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "c8491ab5",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "D probe  R^2 = 0.564\n",
-      "position probe  R^2 = 0.003\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "@torch.no_grad()\n",
-    "def collect_probe_data(model, n_clips=600):\n",
-    "    model.eval()\n",
-    "    Z, Z2, DT, DS, POS = [], [], [], [], []\n",
-    "    ds = DiffusionClipDataset(n_clips=n_clips)\n",
-    "    loader = torch.utils.data.DataLoader(ds, batch_size=32, shuffle=False)\n",
-    "    for x0, x1, delta_t, D_true, pos0, pos1 in loader:\n",
-    "        x0, x1 = x0.to(model.device), x1.to(model.device)\n",
-    "        z0 = model.encode(x0)\n",
-    "        z1 = model.encode(x1)\n",
-    "        Z.append(z0.cpu()); Z2.append(z1.cpu())\n",
-    "        DT.append(delta_t); DS.append(D_true); POS.append(pos0)\n",
-    "    return (torch.cat(Z), torch.cat(Z2), torch.cat(DT), torch.cat(DS), torch.cat(POS))\n",
-    "\n",
-    "\n",
-    "Z0, Z1, DT_, D_, POS0 = collect_probe_data(model)\n",
-    "\n",
-    "# Feature for the D-probe: concatenate z0, z1, and delta_t (so the probe can use\n",
-    "# \"how much did the latent move, given how much time passed\" -- exactly the\n",
-    "# quantity that defines a diffusion coefficient).\n",
-    "feat_D = torch.cat([Z0, Z1, DT_], dim=1).numpy()\n",
-    "target_D = D_.numpy().ravel()\n",
-    "\n",
-    "feat_pos = Z0.numpy()\n",
-    "target_pos = POS0.numpy()\n",
-    "\n",
-    "from sklearn.linear_model import Ridge\n",
-    "from sklearn.model_selection import train_test_split\n",
-    "from sklearn.metrics import r2_score\n",
-    "\n",
-    "Xtr, Xte, ytr, yte = train_test_split(feat_D, target_D, test_size=0.25, random_state=0)\n",
-    "probe_D = Ridge(alpha=1.0).fit(Xtr, ytr)\n",
-    "pred_D = probe_D.predict(Xte)\n",
-    "print(f\"D probe  R^2 = {r2_score(yte, pred_D):.3f}\")\n",
-    "\n",
-    "Xtr2, Xte2, ytr2, yte2 = train_test_split(feat_pos, target_pos, test_size=0.25, random_state=0)\n",
-    "probe_pos = Ridge(alpha=1.0).fit(Xtr2, ytr2)\n",
-    "pred_pos = probe_pos.predict(Xte2)\n",
-    "print(f\"position probe  R^2 = {r2_score(yte2, pred_pos):.3f}\")\n",
-    "\n",
-    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
-    "axes[0].scatter(yte, pred_D, s=10, alpha=0.5)\n",
-    "axes[0].plot([yte.min(), yte.max()], [yte.min(), yte.max()], \"r--\")\n",
-    "axes[0].set_xlabel(\"true D\"); axes[0].set_ylabel(\"predicted D\"); axes[0].set_title(\"D probe\")\n",
-    "\n",
-    "axes[1].scatter(yte2[:, 0], pred_pos[:, 0], s=10, alpha=0.5, label=\"x\")\n",
-    "axes[1].scatter(yte2[:, 1], pred_pos[:, 1], s=10, alpha=0.5, label=\"y\")\n",
-    "axes[1].plot([0, IMAGE_SIZE], [0, IMAGE_SIZE], \"r--\")\n",
-    "axes[1].set_xlabel(\"true position\"); axes[1].set_ylabel(\"predicted position\")\n",
-    "axes[1].legend(); axes[1].set_title(\"position probe\")\n",
-    "plt.tight_layout(); plt.show()\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8830f506",
-   "metadata": {},
-   "source": [
-    "## 7. Visualizing latent trajectories\n",
-    "\n",
-    "A qualitative check: encode every frame of a single clip and look at the latent trajectory (via PCA), next to the\n",
-    "true (x, y) trajectory. A good world model's latent trajectory should \"look like\" a (possibly distorted/rotated)\n",
-    "version of the true motion — smooth, continuous, and varying systematically with $D$.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "d518d0d1",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from sklearn.decomposition import PCA\n",
-    "\n",
-    "@torch.no_grad()\n",
-    "# def encode_full_clip(model, D):\n",
-    "#     frames, positions = make_particle_clip(D)\n",
-    "#     x = torch.from_numpy(frames).unsqueeze(1).to(model.device)  # (T, 1, H, W)\n",
-    "#     z = model.encode(x).cpu().numpy()   # <-- was model.encoder(x)\n",
-    "#     return z, positions\n",
-    "def encode_full_clip(model, D, w=WINDOW):\n",
-    "    frames, positions = make_particle_clip(D)\n",
-    "    windows = np.stack([frames[i - w + 1 : i + 1] for i in range(w - 1, len(frames))])\n",
-    "    x = torch.from_numpy(windows).float().to(model.device)\n",
-    "    z = model.encode(x).cpu().numpy()\n",
-    "    return z, positions[w - 1:]\n",
-    "\n",
-    "\n",
-    "model.eval()\n",
-    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
-    "for ax, D_val in zip(axes, [0.1, 0.8, 1.8]):\n",
-    "    z, positions = encode_full_clip(model, D_val)\n",
-    "    z_pca = PCA(n_components=2).fit_transform(z)\n",
-    "    ax.plot(positions[:, 0], positions[:, 1], \"o-\", label=\"true (x, y)\", alpha=0.6)\n",
-    "    ax2 = ax.twinx().twiny()\n",
-    "    ax2.plot(z_pca[:, 0], z_pca[:, 1], \"x--\", color=\"orange\", label=\"latent (PCA)\", alpha=0.8)\n",
-    "    ax.set_title(f\"D = {D_val}\")\n",
-    "plt.tight_layout(); plt.show()\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "98793cbb",
-   "metadata": {},
-   "source": [
-    "## 8. Ablation: what happens without the anti-collapse defenses?\n",
-    "\n",
-    "We retrain two broken variants:\n",
-    "- **No EMA target** (predictor and target encoder share weights and gradients — a classic recipe for collapse)\n",
-    "- **No variance regularizer** ($\\lambda = 0$)\n",
-    "\n",
-    "Watch the prediction loss: it can go to (near) zero *for the wrong reason* — the encoder learns to output a\n",
-    "near-constant vector, which is trivially easy to \"predict\". The probe R² is the tell: collapse gives low prediction\n",
-    "loss but a useless representation (probe R² near zero).\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "7950d7cf",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class WorldModelNoEMA(WorldModel):\n",
-    "    \"\"\"Target encoder IS the online encoder (no separate weights, no stop-gradient).\"\"\"\n",
-    "    def forward(self, x0, x1, delta_t):\n",
-    "        z0 = self.encoder(x0)\n",
-    "        z1_pred = self.predictor(z0, delta_t)\n",
-    "        z1_target = self.encoder(x1)  # gradient flows here too -- no stop-gradient!\n",
-    "        return z0, z1_pred, z1_target\n",
-    "\n",
-    "    @torch.no_grad()\n",
-    "    def update_target(self):\n",
-    "        pass  # nothing to update; there is no separate target encoder\n",
-    "\n",
-    "\n",
-    "def quick_eval_probe(model, n_clips=400):\n",
-    "    Z0, Z1, DT_, D_, POS0 = collect_probe_data(model, n_clips=n_clips)\n",
-    "    feat_D = torch.cat([Z0, Z1, DT_], dim=1).numpy()\n",
-    "    Xtr, Xte, ytr, yte = train_test_split(feat_D, D_.numpy().ravel(), test_size=0.25, random_state=0)\n",
-    "    probe = Ridge(alpha=1.0).fit(Xtr, ytr)\n",
-    "    return r2_score(yte, probe.predict(Xte))\n",
-    "\n",
-    "\n",
-    "# Variant A: no EMA target (collapse-prone)\n",
-    "model_no_ema = WorldModelNoEMA().to(device)\n",
-    "hist_no_ema = train_world_model(model_no_ema, train_loader, val_loader, n_epochs=10, lam=1.0)\n",
-    "r2_no_ema = quick_eval_probe(model_no_ema)\n",
-    "print(f\"No-EMA variant: final pred_loss={hist_no_ema['pred_loss'][-1]:.4f}, probe R^2={r2_no_ema:.3f}\")\n",
-    "\n",
-    "# Variant B: no variance regularizer (lam=0), EMA kept\n",
-    "model_no_reg = WorldModel().to(device)\n",
-    "hist_no_reg = train_world_model(model_no_reg, train_loader, val_loader, n_epochs=10, lam=0.0)\n",
-    "r2_no_reg = quick_eval_probe(model_no_reg)\n",
-    "print(f\"No-regularizer variant: final pred_loss={hist_no_reg['pred_loss'][-1]:.4f}, probe R^2={r2_no_reg:.3f}\")\n",
-    "\n",
-    "print(f\"Full model probe R^2 was: {r2_score(yte, pred_D):.3f}\")\n",
-    "print(\"Compare: low pred_loss + low probe R^2 == collapse, not a good world model.\")\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9ccc5cd8",
-   "metadata": {},
-   "source": [
-    "## 9. (Optional, advanced) Analysis-by-synthesis through the differentiable simulator\n",
-    "\n",
-    "DeepTrack2's pipeline is gradient-preserving. As a contrast to the *learned* world model, we can directly optimize a\n",
-    "diffusion coefficient by backpropagating an image-reconstruction loss through the simulator itself (\"analysis by\n",
-    "synthesis\" / differentiable rendering), and compare the result to what our learned model's probe infers from the\n",
-    "same clip. This connects the chapter back to your earlier \"classical differentiable simulation\" material and shows\n",
-    "two different routes to the same physical insight: a model that *learned* to infer $D$ implicitly, vs. optimization\n",
-    "that infers $D$ explicitly via a differentiable forward model.\n",
-    "\n",
-    "We leave this as an extension for the reader / next revision of the notebook — it requires exposing $D$ as a\n",
-    "`torch.nn.Parameter` inside the simulation step rather than a plain numpy float, which depends on how your local\n",
-    "DeepTrack2/Deeplay version exposes differentiable parameters in `pipeline.update()`.\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bd779ae9",
-   "metadata": {},
-   "source": [
-    "## 10. Summary & what to try next\n",
-    "\n",
-    "- We trained a JEPA-style world model that predicts **latent** futures, not pixels, on simulated diffusion videos.\n",
-    "- The EMA target + variance regularizer were both necessary to avoid collapse — the ablation made this concrete.\n",
-    "- A simple linear probe shows the latent space encodes the diffusion coefficient $D$ and the particle's position,\n",
-    "  even though neither was ever a training target.\n",
-    "\n",
-    "**Extensions worth trying:**\n",
-    "- Multiple particles per clip → forces a decision between a single global latent vs. per-particle \"slots\" (a natural\n",
-    "  segue into object-centric / slot-based world models)\n",
-    "- Add DeepTrack2's optical aberrations/noise to make the rendering more realistic, and see whether the probe R² for\n",
-    "  $D$ degrades — a nice lesson on how much \"physics signal\" survives realistic imaging noise\n",
-    "- Replace the CNN encoder with a small ViT (swap-in, thanks to Deeplay's modularity) and compare probe quality\n",
-    "- Try predicting multiple $\\Delta t$ steps ahead recurrently, and see how prediction error grows with horizon —\n",
-    "  this is the classic compounding-error problem in world models\n"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "deeptrack_dev (3.12.8)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.8"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}

From bcfcf9e722c17993db113d3616a413ba4041ea64 Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Mon, 24 Aug 2026 00:31:05 +0200
Subject: [PATCH 4/9] jepa2

---
 Companion/cc_jepa/jepa.ipynb | 8826 ++++++++++++++++------------------
 1 file changed, 4276 insertions(+), 4550 deletions(-)

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
index 069f6ddd9..be4350ae6 100644
--- a/Companion/cc_jepa/jepa.ipynb
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -194,7 +194,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "7f80d1e0",
    "metadata": {},
    "outputs": [],
@@ -459,42 +459,42 @@
        "\n",
        "\n",
        "
\n",
-       "  \n",
+       "  \n",
        "  
\n",
-       "    \n",
+       "           oninput=\"anim4e905bb64e4e4e74b1406709a2cd8f36.set_frame(parseInt(this.value));\">\n",
        "    
\n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
        "    
\n",
-       "    
\n",
-       "      \n",
-       "      \n",
-       "      Once\n",
+       "      \n",
-       "      \n",
-       "      Loop\n",
+       "      \n",
-       "      \n",
+       "      \n",
        "    
\n",
        "  
\n",
        "
\n",
@@ -504,201 +504,174 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_img456dc6af641c40aa8fc45e5909b94eb3\";\n",
-       "    var slider_id = \"_anim_slider456dc6af641c40aa8fc45e5909b94eb3\";\n",
-       "    var loop_select_id = \"_anim_loop_select456dc6af641c40aa8fc45e5909b94eb3\";\n",
+       "    var img_id = \"_anim_img4e905bb64e4e4e74b1406709a2cd8f36\";\n",
+       "    var slider_id = \"_anim_slider4e905bb64e4e4e74b1406709a2cd8f36\";\n",
+       "    var loop_select_id = \"_anim_loop_select4e905bb64e4e4e74b1406709a2cd8f36\";\n",
        "    var frames = new Array(20);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA4QAAAHCCAYAAAC30AdjAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
        "bGliIHZlcnNpb24zLjEwLjgsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvwVt1zgAAAAlwSFlzAAAP\\\n",
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-       "EAAAoFICIQAAQKUEQgAAgEoJhAAAAJUSCAEAAColEAIAAFRKIAQAAKiUQAgAAFApgRAAAKBSAiEA\\\n",
-       "AEClBEIAAIBKCYQAAACVEggBAAAqJRACAABUSiAEAABo6vT/AD3yItsdkmmAAAAAAElFTkSuQmCC\\\n",
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        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        anim456dc6af641c40aa8fc45e5909b94eb3 = new Animation(frames, img_id, slider_id, 149.0,\n",
+       "        anim4e905bb64e4e4e74b1406709a2cd8f36 = new Animation(frames, img_id, slider_id, 149.0,\n",
        "                                 loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
@@ -5038,7 +5035,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Datasets already exist. Skipping dataset generation.\n"
+      "saved 10000 clips to datasets/bouncing bead with distractors/particles_train.pt\n",
+      "saved 2000 clips to datasets/bouncing bead with distractors/particles_val.pt\n",
+      "saved 1000 clips to datasets/bouncing bead with distractors/particles_test.pt\n"
      ]
     }
    ],
@@ -5221,7 +5220,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
        "
"
       ]
@@ -5592,7 +5591,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "9dda25001c404d65bf176dcc55b92c20",
+       "model_id": "2a1c6fb842574e27bcd556929b974887",
        "version_major": 2,
        "version_minor": 0
       },
@@ -5620,6 +5619,23 @@
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "ename": "SystemExit",
+     "evalue": "1",
+     "output_type": "error",
+     "traceback": [
+      "An exception has occurred, use %tb to see the full traceback.\n",
+      "\u001b[31mSystemExit\u001b[39m\u001b[31m:\u001b[39m 1\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/IPython/core/interactiveshell.py:3709: UserWarning: To exit: use 'exit', 'quit', or Ctrl-D.\n",
+      "  warn(\"To exit: use 'exit', 'quit', or Ctrl-D.\", stacklevel=1)\n"
+     ]
     }
    ],
    "source": [
@@ -5637,7 +5653,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "id": "f692f783",
    "metadata": {},
    "outputs": [],
@@ -5674,24 +5690,13 @@
     "\n",
     "Both curves show a similar shape: a sharp early drop, a rise, then a slow decline. The initial drop isn't genuine learning, it's representation collapse: early in training, the untrained predictor's gradients can pull the encoder toward mapping every input to nearly the same constant representation, which is trivially easy to \"predict\" and drives the loss down fast for the wrong reason. As the EMA-updated target stabilizes and the representation starts differentiating again, escaping that collapse, the loss rises, before beginning a slower, genuine decline as the model actually learns to solve the masked-prediction task (Ennadir, Zólyomi, and Smirnov, 2026)."
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "id": "10ddc233",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10ddc233",
+   "metadata": {},
+   "outputs": [],
    "source": [
     "plot_loss_curves(summary, keys=[\"short\", \"long\"], titles=[\"Short-term loss\", \"Long-term loss\"])"
    ]
@@ -5720,7 +5725,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": null,
    "id": "4e03a044",
    "metadata": {},
    "outputs": [],
@@ -5766,7 +5771,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "2816daf8",
    "metadata": {},
    "outputs": [],
@@ -5812,28 +5817,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "id": "a8b23a94",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "--- Pretraining probes, clean clips ---\n",
-      "Frame  0: pos R²=0.965, vel R²=0.649\n",
-      "Frame  2: pos R²=0.973, vel R²=0.754\n",
-      "Frame  4: pos R²=0.976, vel R²=0.775\n",
-      "Frame  6: pos R²=0.978, vel R²=0.817\n",
-      "Frame  8: pos R²=0.983, vel R²=0.779\n",
-      "Frame 10: pos R²=0.982, vel R²=0.836\n",
-      "Frame 12: pos R²=0.979, vel R²=0.805\n",
-      "Frame 14: pos R²=0.980, vel R²=0.819\n",
-      "Frame 16: pos R²=0.981, vel R²=0.808\n",
-      "Frame 18: pos R²=0.980, vel R²=0.788\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "print(\"--- Pretraining probes, clean clips ---\")\n",
     "probes_pos, probes_vel, r2_pos, r2_vel = fit_and_score_probes(model, val_ds, test_ds, device)"
@@ -5867,7 +5854,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": null,
    "id": "aeaeaa68",
    "metadata": {},
    "outputs": [],
@@ -5918,7 +5905,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": null,
    "id": "830e36f5",
    "metadata": {},
    "outputs": [],
@@ -5988,21 +5975,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": null,
    "id": "6ff32060",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "
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-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
     "    prepare_pretraining_predictions(model, test_ds, probes_pos, probes_vel, device, num_examples=3)\n",
@@ -6030,108 +6006,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": null,
    "id": "e91c21c6",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
-     ]
-    },
-    {
-     "data": {
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-       "┃   ┃ Name          ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
-       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│ 0 │ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│ 1 │ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│ 2 │ predictor     │ Predictor        │  216 K │ train │     0 │\n",
-       "│ 3 │ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 4 │ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 5 │ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 6 │ optimizer     │ Adam             │      0 │ train │     0 │\n",
-       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n",
-       "
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-       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName         \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
-       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ predictor     │ Predictor        │  216 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m6\u001b[0m\u001b[2m \u001b[0m│ optimizer     │ Adam             │      0 │ train │     0 │\n",
-       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
Trainable params: 1.4 M                                                                                            \n",
-       "Non-trainable params: 1.2 M                                                                                        \n",
-       "Total params: 2.6 M                                                                                                \n",
-       "Total estimated model params size (MB): 10                                                                         \n",
-       "Modules in train mode: 161                                                                                         \n",
-       "Modules in eval mode: 0                                                                                            \n",
-       "Total FLOPs: 0                                                                                                     \n",
-       "
\n"
-      ],
-      "text/plain": [
-       "\u001b[1mTrainable params\u001b[0m: 1.4 M                                                                                            \n",
-       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
-       "\u001b[1mTotal params\u001b[0m: 2.6 M                                                                                                \n",
-       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 10                                                                         \n",
-       "\u001b[1mModules in train mode\u001b[0m: 161                                                                                         \n",
-       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
-       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "30ea946ce0464ac0b87b73ad0f278377",
-       "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "Output()"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/html": [
-       "
\n"
-      ],
-      "text/plain": []
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "train_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_train.pt\", p_distractors=1.0, seed=0)\n",
     "val_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_val.pt\", p_distractors=1.0, seed=0)\n",
@@ -6150,21 +6028,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": null,
    "id": "74ed2c95",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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vv67S5z7dErlKl9p9/vnnS5o0aWLGRrGxsWYp3rLL7Wrf6zK8DRs2LPHx8SmJiIgw46dVq1ZZj9Gx1KWXXmqe0zGYHvt///d/Jfv3769SXwKOxk3/Y+tADAAAAACcLc2G0OkumsmhGR4AUBlqggAAAABwGDrV9ESW2hhaRwwAToWaIAAAAAAchtYP+/jjj01NC62rtXjxYvnyyy9NEVZdRQ0AToUgCAAAAACHoSuXaIFVLayqq6lZiqWyfDyAqqAmCAAAAAAAcAnUBAEAAAAAAC6BIAgAAAAAAHAJ1ASpQHFxsezbt08CAwPFzc2t9n8qAAA4uJKSEsnJyZHo6Ghxd+eey+kw9gAAoHbGHgRBKqABkNjY2HP8EQAAgKSkJGnQoAEdcRqMPQAAqJ2xB0GQCmgGiKXzgoKCqulHAQCA69AVG/SGguWailNj7AEAQO2MPQiCVMAyBUYDIARBAAA4e0wrPbN+YuwBAEDNjj2YpAsAAAAAAFwCQRAAAAAAAOASmA4DAA6mqKhICgsLbd0MwMrLy0s8PDzoEQBwEYxF4MjjDoIgAOBAcnNzJTk52SwBBtjT3Futwl6nTh1bNwUAUMMYi8DRxx0EQQDAge66aADE399f6tWrR8FJ2AUNyKWnp5vfzRYtWpARAgBOjLEInGHcQRAEAByEToHRf/g1AOLn52fr5gBW+ju5e/du8zvKtBgAcF6MReAM4w4KowKAg2HJUdgbficBwLXw7z4c+fePIAgAAAAAAHAJBEEAAOfkueeek7y8vDN+3b59++Siiy6qkfb885//rNXPpnckMjMzxZksWLBAOnXqJM5o4sSJ0rhxY/H19ZXu3bvLihUrqvS6qVOnmp/1wIEDy+2//fbbzf6y22WXXVZDrQcA2MtYxFbXyuoc69iTSy65RL7//vsafx+CILUoN/9Ybb4dACen9UGOFByr0a0qq9A8//zzFQ48jh079b950dHRsmjRIrFHlrZX9tnguKZNmyajRo2SMWPGyJo1a6Rjx44yYMAASUtLO+XrdO7xo48+WulgWYMe+/fvt25ffvml2IO8wiJbNwGAE2MsAkdEYdRaUFRcIo9+vV5+2bhffnu4tzQKC6iNtwXg5I4WFkmb0bNq9D3+emGA+HtXfqm49957zVf9w1ALU2lgo379+rJ9+3bzR+WWLVtk6NChkpCQIAUFBRIbGysffPCBOUb/qNS7J5YMCr17/tJLL5k7AFr1e/To0XLHHXdU+t7btm0zd+B1qb7i4mK59tpr5d///rd5Tv8Ivfrqq2XHjh3mvb755hsJDQ01Ve2ffPJJ+fXXX81xffr0kTfeeEO8vb3Nudzd3a1t17sRZT/bb7/9JhEREafts1WrVsmDDz5o2qWZBv/973+lZ8+e5jNpX2jb9LN27txZPvroI1m2bJn84x//MG3T4It+f99991V6/pUrV8oTTzwh2dnZ5jX/+te/5KabbrL251133WXaqs+99dZbEh8fb143ZcoUef311833+nN4//33JSYmxjx+9dVX5bPPPjOfX4vuzps3z+zX9tx///3yxx9/mO8/+eQT6dKliziyN998U+6++27r79akSZNkxowZ8uGHH5rfjYpoX+rPToNiGrirKOvHx8fH/K7Zi4Vb0+WFn/6UuPpBMnHo+bZuDgAn5epjkRNVdq39+OOPzXVWC3pu2rTJXDO++uoradq0qTlWA/Off/651K1b1wTm9VhtW1Wcamzzv//9z1z39Hs9Th937drVjFPmzp1r9nt6eprrvI5ZKqLFR5999lkzNtD+a9mypbz33numrZaxk/ZxRkaG9OjRw1xXdSyhfa8/Gx2vabBs5MiR8n//93/mnJs3bzaZLDomUjrWsPwcFy9ebNqvWTr9+/c356tuZILUAg93Nzl4uEDyjxXLlyuSauMtAaBWWC5M+ofhunXrTJBg9erV5o9KvSCqcePGmcDAhg0bzABFUzgro4MCnZqgF3K9QJ8qm2TChAly1VVXyfr162Xjxo3m7r7F8uXLzYDjr7/+Mm3Si7XSwYgGEbSN2l4NkmiQwqJs2yv6bKejg4Prr7/eDGb08+rA44YbbjABER3QNGnSxLRVn9MLvBo7dqzJMND30IHR4MGDKz2/DtLuueceM1DSPp09e7Y88sgjsnfvXvN8VlaWtG7d2pxfB3hDhgyRnJwcc97HHnvM9Ks+d+GFF5pgidLAxrfffmsGHdqXeoz+HJT2w/Dhw81+Hbw8/fTT4sj056M/Y0tgSOngTR8vXbq00te98MIL5uc/YsSIU6ZE6zGtWrUyQawDBw6csi35+fkmkFV2q05Bvp6yI/2wCYYUHCuu1nMDgD2x5VikrFNda5WOP15++WUzDtDrjt6AUNpOvQ6vXbvWvK/lml5Vpxrb6BhBgx26X7Mf27Zta67puu/PP/8032twQ4MhldGgTkBAgGmbnqd9+/byzDPPlBtzzZo1ywQ2Dh48aH1vHTfoNVE/r76H3qjSGz/an3rjSgMo2k+63Xjjjdbzafvnz59v+lPPe6rr89kiE6SWDOne0AxEvl6VJKP6txRvT+JPAM6Nn5eHuTtS0+9xpjQrITAw0Pr4iy++MHdGdFqJbuHh4ZW+Vu/UqLi4OHNnIiUlRRo0aFDhsb179zaDDQ0wXHzxxeX+sNWpCWFhYeZ7vSuhF2A1Z84cc9G1/JGvGQFaH0IzKypq+5nSu0z6R7XexVG9evWSyMhIM2i44IILzMBAByTadkvNCL1j8+KLL5o7JX379jWvqcySJUtk586dcvnll5/0vno3SftMP5/S99O7YTqo0kGOvp8l80PvuOgf9npX6OeffzZ3X4KDg81zemfHonnz5qZmhqUf//Of/4gj07tU+pn1Z1KWPrYMlE+kwSENKOnPsDLatxr80iCXDt40O0d/Rjpwq2zpPg1+aWZJTenYIETC6/hIRm6+rNh1UHq1qPz/OwA4W64+FilL/3Cv7FpruY7qdcLy/fjx4833GpAo214NuOu5qupUY5t+/frJbbfdZrJj9bqkWRxNmzY1gYg777zTjEGuvPJKM3apjGbF6E0WDdRYbihoXS2Lm2++uVzb3377bXMd1HZpYEZpYEqvk7pPj9WfwS233GI9R9mfx6BBg0y/66ZZOnpd1f6qTvwlXkv6xUVIZJCPHDhcILP+TKmttwXgxDRlU9NDa3I7myXI6tSpU+4PSL0Y/vLLLyair5kRp6qxUTYVU/94PNXdF82w0PRNvctgyQo50/Oc+PnKtr26WN5DL+D6h7QGFaZPn27SUXVgpOmgehcoKirKDBp00FQZTSfVuzh6HsuWmJhogiene//T7TvXn4cz0iwaHTxOnjz5lANmzd655pprzN0xLZqqgSW9K6fZIZV56qmnzKDSsiUlVW+mqLu7m/SNq2e+n7M5tVrPDQAWrj4WOZUT2322Y5NzeV8NXLzyyitmSssVV1xhCnwHBwebftBsUb0B0KFDBzN16FRjDw3YWMYdmmWrfVmV97fXsQdBkFri6eEug7o2NN9/vnxPbb0tANQ4jejrH3EVOXTokHleszL0zoFlWkp10MwJvYM/bNgwee2110yK5elotsinn35q2qIXVZ0be+mll57VZ6uIBmS0PolOU7FkbugdJL2TsWvXLjMo0zsmOpjYunWryWLRLA69M6R3bjQIcqrPoam1eh69k2KhAxL9PEo/k97pUpq2qvNp9b31Ts/MmTPNY0vqsN4d0sGF/vGujy2fU6fcWO5aORsNZOhnTk0tHxTQxxXV89C7TzonW++gWe5K6e/Pjz/+aL7X5yuid9n0vU41qNQ7dkFBQeW26tavdWnGy9wtqVUqcgwAjspWY5GyTnWtPRW9kaHBCh0T6L/VWqPqTFQ2ttHv9Tqltbx02q1OOdGxQXp6uhw+fNgco9NzNKtDAxuV0eC+ZrIeOXLEPNavOpXGQuuuadt17KC1ziyZufpVbyIofU+9AaQ1PnSs5O/vX66AuGZq1iamw9SiwV1jZcK8bbJs50HZkZ4rzepV/x1HAKhtOr1DL2p6QdPpF2VpWqjWwtALng4+9IJ4pnNdK6MXXT23zmPVwENVCmdpPQ0dEJx/fmmhSC1+eqol5sp+tqoURtW26EVe5xDra/VuhrZTgx9ff/21uftkuauhc2z1bozOq7XMx9XnLLVCKqJTVTRrRAczen69s9OwYUPrcnKWuzu64om+h6b/6sCvXbt25v0sU3C0WJtlYKKZDjpg0wCL/mGv837LBlmcifaxFqTV1GPLMrf6u6OPH3jggZOO11Roy1QqC/15aYaIFp3VfqxIcnKyqQmi2T221Kt5uHh7uEvSwaOyLS1XWkae/VQvALBnthqLlHWqa+2paCar1tXQmxYhISFmiq9+rarKxjYalNApL1qnQ6/vWpRVgxRJSUnmxouOIfQYLd5+4jTbsnRajdax0kxWSzaH7tPMVKWZrToNWAMdmvVqGVdp9o3WyNIsSQ3uaF0xyxTbH374wdQM0SCMTsXRLFhL0dTa4FbCrYGTaHEyHUhqNLG678zc9clKmbM5Te7q1USeuapNtZ4bgHPT1E3NAtCsgcoqeMN1nVjh3ta/mzV5LT3XJXK12KveCezWrZsplqcV+jUl2JJZpPO5tWZHRXTetfaxJfCkd7+0todOz9JsEh2IPv744yZQogEUyxzt06mp/hr+4QpTk+yJy+LkvkuaVdt5AbgmxiI1Q68ZetNC/zTXgM7Ro0fl3XffFXt3++23m7HHqW4o1ebvYVWvpUyHqWVDuzcyX79Zkyx5hc6ZbgwAgL3Sgmta4FWXPdSBm04n0vRlS7FUrbFiWbKvKjR7Ryvb67QiLTinReE020RXKahqAKQmxbcuzV6aS10QALBbGoA/77zzpE2bNuY6pAXTUXPIBKlATd69Kioukd6vzZe9mUflv4M6ynXnnb7SMAC48t0Xnct6YlEsTcHUZWJrk66gUlG9Dl0BxM/Pz2Hfy9UyQexVTfWXjjd6vjJP3N1EVj3TX0IDKl8GEQBOh7FI7Y1FNEhvWfGtLM1mfPjhhx32vewhE4SaILXMw93N1AZ5Y/ZW+XxZIkEQADiNVatW2UUfVaXmiCO+F5xbTIiftI4Kks37s2X+ljS5oTM3XwDAEcYilmxFZ3sve8B0GBsY1DXWBENW7TkkCSk5tmgCAAdGKSfYG34n7Zt1SswWlsoFUD34dx+O/PtHEMQGIoJ8pf/xZeu+YLlcAFVkWWLNshwqYC8sv5OnWwYQtmFZKvf3rRlScKyYHwOAs8ZYBM4w7mA6jI0MvaChzPwzRaav3StPXB4n/t78KACcmi5vpku/6RJkXl5eZkkxwNZ0iVn9ndTfTf0dhf3pEBMs4XV8JCM3X5bvOiAXtahn6yYBcFCMReAM4w5GKzbSs1m4NAz1l8SDR+Tn9fvl5q6xtmoKAAeha7NHRUWZQlB79uyxdXMAKw3INWzY0PyOwv64u7tJ37h68tWqZJm7OY0gCICzxlgEzjDuIAhiwwHJkO4N5ZVft8jnKxIJggCoEm9vb2nRogVTYmB3v5dkJtn/lBgTBNmSKmOubkPACsBZYywCRx93EASxoRs7N5A3fkuQ9UmZsmlvlrSLCbZlcwA4CP1H35WWyAVw7i5qES7enu6SdPCobEvLlZaRgXQrgLPGWASOjAnlNqTzcwe0rW++/2JFoi2bAgAAnJjWHruwWZj5fs5mVokBALgugiA2NrR7I/P1h7V7JTf/mK2bAwAAnHyVGK0LAgCAqyIIYmMXNA2VpvUC5HBBkfywbq+tmwMAAJxUv7gI83VN4iE5kJtv6+YAAGATBEFsTCvaDunW0Hz/xfJEKSkpsXWTAACAE4oO8ZM2UUGiQ435Cem2bg4AADZBEMROCqRqsbI/92XL+uQsWzcHAAA4qX6tS7NB5m2hLggAwDXZRRBk4sSJ0rhxY7PaQffu3WXFihWVHjt9+nTp0qWLhISESEBAgHTq1EmmTJlyUnZFRdvrr78u9ijE31uuah9lvv9i+R5bNwcAADh5XZDft2ZIwbFiWzcHAADXC4JMmzZNRo0aJWPGjJE1a9ZIx44dZcCAAZKWVnHRrtDQUHn66adl6dKlsmHDBrnjjjvMNmvWLOsx+/fvL7d9+OGHJghyww03iL0a0r10SsxP6/dL1tFCWzcHAAA4oQ4xwVIv0McUY1++64CtmwMAgOsFQd588025++67TSCjTZs2MmnSJPH39zeBi4pccsklct1110nr1q2lWbNm8tBDD0mHDh1k8eLF1mPq169fbvvhhx+kT58+0rRpU7FXnRvVlZaRdeRoYZF8v5YCqQAAoPq5u7tJ31alU2JYJQYA4IpsGgQpKCiQ1atXS3x8/N8Ncnc3jzXT43S0iOjcuXMlISFBevfuXeExqampMmPGDBkxYoTYM81UsSyXS4FUAABQ03VB5mxOpSA7AMDl2DQIkpGRIUVFRRIZWTo/1UIfp6SkVPq6rKwsqVOnjnh7e8uVV14p48ePl/79+1d47CeffCKBgYFy/fXXV3q+/Px8yc7OLrfZwsDzYsTXy10SUnNk9Z5DNmkDAABwbr1ahJuC7MmHjsrW1FxbNwcAANeaDnM2NKixbt06Wblypbz00kumpsiCBQsqPFan1QwdOtQUXa3M2LFjJTg42LrFxsaKLQT7eck1HaOt2SAAAADVzd/bU3o2C7NmgwAA4EpsGgQJDw8XDw8PM2WlLH2stTwqo1NmmjdvblaGeeSRR+TGG280gYwTLVq0yEyVueuuu07Zjqeeespkl1i2pKQksZUhx6fE/Lxxvxw6XGCzdgAAAOfV9/gqMfO2VFyIHgAAZ2XTIIhOZ+ncubOp62FRXFxsHvfo0aPK59HX6JSWE33wwQfm/LrizKn4+PhIUFBQuc1WOjYIlrbRQWbZum/XJNusHQAAwHn1iyutC7Im8ZAcyD15DAUAgLOy+XQYncoyefJkU7tj8+bNct9998nhw4fNajFq2LBhJlPDQjM+Zs+eLTt37jTHv/HGGzJlyhS59dZby51X63p8/fXXp80CsccCqZblcr9YkUjBMgAAUO2iQ/ykTVSQlJSIzE9Ip4cBAC7D09YNGDRokKSnp8vo0aNNMVSd4jJz5kxrsdTExEQz/cVCAyT333+/JCcni5+fn8TFxclnn31mzlPW1KlTTQDhlltuEUdzbacYeXnGZtmZfliW7TwoPY7P2wUAAKgu8a0j5K/92TJ3c6rc2LkBHQsAcAluJRopwElZJFogVeuD2GpqzL++22iKo17dMVrG33IePyEAgEOxh2upI7FFf61PypRrJ/4hAd4esmZ0f/Hx9KiV9wUAwJbXUptPh0HFhnQrnRIzc9N+yWCuLgAAqGbtY4KlXqCPHC4okuU7D9K/AACXQBDETrWLCZaOsSFSWFQi36ymQCoAAKhe7u5u1gKpOiUGAABXQBDEjg09ng2i02KKi5m1BAAAqldfSxBkSxrF2AEALoEgiB27qmOUBPp6SuLBI/LHjgxbNwcAADiZXi3CxdvTXZIPHZWtqbm2bg4AADWOIIgd8/f2lOvPi7FmgwAAAFT3WKPn8VXo5jAlBgDgAgiC2Lkh3RuZr7/9lSpp2Xm2bg4AAHAy/VpHmq/UBQEAuAKCIHauVf1A6dKorhQVl8hXq5Js3RwAAOBk+rUurQuyNimTFekAAE6PIIgDGNK9tEDqlyuSTDAEAACgukQF+0nb6CApKRGZvyWNjgUAODWCIA7givZREuLvJXszj8rvW9Nt3RwAAOC0U2IIggAAnBtBEAfg6+UhN5zfwHz/+fI9tm4OAABwMv2OL5W7aFu65B8rsnVzAACoMQRBHGxKzLwtabIv86itmwMAAJxI+5hgqRfoI4cLimT5zoO2bg4AADWGIIiDaFavjlzQNFS0JMi0lRRIBQAA1cfd3c2aDcIqMQAAZ0YQxIEMPb5c7tSViXKsqNjWzQEAAE5YF2TO5jQp0SqpAAA4IYIgDmRA2/oSFuAtqdn5ZloMAABAdenVPFx8PN1NIfaE1Bw6FgDglAiCOBBvT3e5sYulQGqirZsDAACciJ+3h/RsHm6+Z5UYAICzIgjiYIZ0Ky2Q+vu2dEk6eMTWzQEAAE6kX+vSuiBzNqfauikAANQIgiAOplFYgFzUIlx0qu6XK8gGAQAA1afv8eKo65IyJSM3n64FADgdgiAOaOjx5XK/WpUshRRIBQAA1SQq2E/aRgeZmy3zqT8GAHBCBEEctHp7vUAfc4dm9l+kqwIAgOodZyjqggAAnBFBEAfk5eEug7vGmu8/X77H1s0BAABOJP54XZBF29Il/1iRrZsDAEC1IgjioAZ1jRU3N5E/th+QXRmHbd0cAADgJNpFB0tEoI8cLiiSZTsP2ro5AABUK4IgDqpBXX+5pGU98z0FUgEAQHVxd3ezrhIzl1ViAABOhiCIAxvavZH5+vWqJNJVAQBAtekX93ddkBKtkgoAgJMgCOLALmlVT6KCfeXQkUKZuSnF1s0BAMAhTJw4URo3biy+vr7SvXt3WbFiRZVeN3XqVHFzc5OBAwdWesy9995rjhk3bpw4sp7Nw8XH0132Zh6VhNQcWzcHAIBqQxDEgXmaAqmly+V+vjzR1s0BAMDuTZs2TUaNGiVjxoyRNWvWSMeOHWXAgAGSlpZ2ytft3r1bHn30UbnooosqPea7776TZcuWSXR0tDg6P28PEwhRrBIDAHAmBEGcoECqh7ubrNh1ULZxpwYAgFN688035e6775Y77rhD2rRpI5MmTRJ/f3/58MMPK31NUVGRDB06VJ5//nlp2rRphcfs3btXRo4cKZ9//rl4eXk5xU/BUhdkDnVBAABOhCCIg6sf7Cv94koHKV+sIBsEAIDKFBQUyOrVqyU+Pt66z93d3TxeunRppa974YUXJCIiQkaMGFHh88XFxXLbbbfJY489Jm3btnW6uiDrkjIlIzff1s0BAKBaEARxAkO6l06J+XZ1suQVFtm6OQAA2KWMjAyT1REZWfrHvYU+TkmpuLbW4sWL5YMPPpDJkydXet5XX31VPD095cEHH6xyW/Lz8yU7O7vcZo83WtrFBInWRZ235dTThQAAcBQEQZxA7xb1pEFdP8nOOyY/b9hv6+YAAOAUcnJyTIaHBkDCw0vrY5xIM0veeust+fjjj01B1KoaO3asBAcHW7fY2Fix71ViUm3dFAAAqgVBECfg7u4mt3QrzQb5YvkeWzcHAAC7pIEMDw8PSU0t/we9Pq5fv/5Jx+/YscMURL366qtNpodun376qfz444/me31+0aJFpqhqw4YNrcfs2bNHHnnkEbMCTWWeeuopycrKsm5JSUlij+JblwZBFm3LINsUAOAUCII4iZu6NBBPdzdZk5gpm/fbX0otAAC25u3tLZ07d5a5c+eWq+ehj3v06HHS8XFxcbJx40ZZt26ddbvmmmukT58+5nvN3tBMkQ0bNpQ7RleH0fogs2bNqrQtPj4+EhQUVG6zRzodJjLIR44UFMnyXQdt3RwAAM6Z57mfAvYgItBXBrStLzM27pcvlifKiwPb2bpJAADYHV0ed/jw4dKlSxfp1q2bjBs3Tg4fPmxWi1HDhg2TmJgYM13F19dX2rUrfz0NCQkxXy37w8LCzFaWrg6jmSWtWrUSR6dTfPrGRciXK5LMlJiLW9azdZMAADgnZII4YYHU79bulcP5x2zdHAAA7M6gQYPkP//5j4wePVo6depkMjdmzpxpLZaamJgo+/dTX6viuiBpUqJVUgEAcGBuJVzNTqIV2rVImc7Rtdf01IoUF5dIvzcXyq6Mw/LK9e1l8PE6IQAA1DZHvZbaij3319GCIun0wm+Sf6xYfn3oImkdZV/tAwDgTK6lNs8EmThxoikcpimn3bt3lxUrVlR67PTp0036qqaiBgQEmDs4U6ZMOem4zZs3mzm72gF6XNeuXc2dHdcokFpaXf6LFc7/eQEAQM3z8/aQXs1LV8dhlRgAgKOzaRBk2rRpZm7umDFjZM2aNdKxY0cZMGCAqbJekdDQUHn66adl6dKlpgiZzt/VrWzhMa3U3qtXL1PMbMGCBea4Z5991gRZXMGNnWPF28NdNiRnycbkLFs3BwAAOIF+x1eJmbO54jEaAACOwqbTYTTzQ7M0JkyYYK3QrpXWR44cKU8++WSVznH++efLlVdeKS+++KJ5PHjwYFOQrKIMEWdISa2Kh6aulR/W7TNZIWOv72Dr5gAAXJCjX0trm733V2p2nnR/ea64uYms+Fe81Av0sXWTAABwrOkwBQUFsnr1aomPj/+7Me7u5rFmepyOxm50SbuEhATp3bu3NYgyY8YMadmypckoiYiIMIGW77//XlzJkOO1QDQQkpNXaOvmAAAABxcZ5CvtY4JFb53NTyAbBADguGwWBMnIyJCioiJrNXYLfZySklLp6zSqU6dOHfH29jYZIOPHj5f+/fub53QaTW5urrzyyity2WWXyW+//SbXXXedXH/99bJw4cJKz5mfn2+iRmU3R9atSag0j6gjRwqK5Pt1+2zdHAAA4AR0qVxFXRAAgCOzeWHUMxUYGGiWs1u5cqW89NJLpqaI1v6wZIKoa6+9Vh5++GFTOFWn1Vx11VUyadKkSs85duxYkzZj2XRKjiNzc3OzZoN8vmwPy9kBAIBzFn+8LsiibRmSV1hEjwIAHJLNgiDh4eHi4eEhqamp5fbr4/r161f6Op0y07x5cxPgeOSRR+TGG280QQzLOT09PaVNmzblXtO6detTrg7z1FNPmQwTy5aUlCSO7obzG4iPp7tsScmRtUmZtm4OAABwcO1igiQyyMdkmi7becDWzQEAwLGCIDqdpXPnzqauh4VmcujjHj16VPk8+hqdzmI5pxZa1TohZW3dulUaNWpU6Tl8fHxM4ZSym6ML9veSqzpEm++/WM5yuQAA4NwzTfvGlWaDzGWVGACAg7LpdBidyjJ58mT55JNPZPPmzXLffffJ4cOHzbK3atiwYSZLw0IzPmbPni07d+40x7/xxhtmFZhbb73Vesxjjz1mlt7V827fvt2sPPPTTz/J/fffL65mSPfSKTE/rd8nWUcokAoAAM5NfOu/64LYcIFBAADOmqfY0KBBgyQ9PV1Gjx5tiqHqFJeZM2dai6XqFBad/mKhARINZiQnJ4ufn5/ExcXJZ599Zs5joYVQtf6HBkwefPBBadWqlXz77bfSq1cvcTXnNwyRuPqBZkrM9LXJckfPJrZuEgAAcGA9m4eLr5e77MvKk837c6RNtONnzwIAXItbCWH8s15f2BFMWbpbnv3hT7NazOyHe5tUVgAAapozXUtrgyP1112frJQ5m9Pk0UtbygN9W9i6OQAAnNG11OFWh8GZGXhejPh7e8j2tFxZufsQ3QcAAM6JpS6IBkIAAHA0BEGcXKCvl1zTsbRA6ufL99i6OQAAwMH1O14XZH1ypqTnlBanBwDAURAEcQFDu5eujPPrxhQ5eLjA1s0BAAAOLDLIV9rHBIvWRZ2/hWwQAIBjIQjiAto3CDaDlYKiYvl2dbKtmwMAAJwkG2TO5lRbNwUAgDNCEMRFDD2+XO4XKxJZ0g4AAJyT+NaldUEWbcuQvMIiehMA4DAIgriIqztGSx0fT9mVcViW7jhg6+YAAAAH1jY6SOoH+crRwiJZupNxBQDAcRAEcREBPp4y8DxLgdREWzcHAAA4MDc3N+l7fErMPFaJAQA4EIIgLmRIt9ICqbP+TKGaOwAAOCf94kqDIHM3pzLVFgDgMAiCuJA20UFyXsMQOVZcIl+tSrJ1cwAAgAPr2TxcfL3cZV9Wnmzen2Pr5gAAUCUEQVx0udypKxOluLjE1s0BAAAOytfLQ3o1D7dmgwAA4AgIgriYqzpESZCvpyQdPCqLtmfYujkAAMCB9Tu+SsycLWm2bgoAAFVCEMQF79rc0LmB+f7zZXts3RwAAOAEdUHWJ2VKWk6erZsDAMBpEQRxQUO7NzRf525Jk5QsBiwAAODsRAT5SocGweb7+WSDAAAcAEEQF9Q8IlC6NQ6VouISmbaSAqkAAODs9YsrnRIzl6VyAQAOgCCIixp6QUNrgdRjRcW2bg4AAHBQ/VqXTolZtC1D8gqLbN0cAABOiSCIi7qsXX2p6+8l+7PyZEFCuq2bAwAAHFTb6CCpH+QrRwuLZOnOA7ZuDgAAp0QQxEX5eHrITV1izfdfrEi0dXMAAICDcnNzk77Hs0FYKhcAYO8IgriwW7qVTomZn5AmyYeO2Lo5AADAQcUfD4LM25wmJSUltm4OAACVIgjiwpqEB0jP5mGiYxUKpAIAgLN1YbNw8fVyl31ZefLX/mw6EgBgtwiCuLgh3RqZrxoEKaRAKgAAOAu+Xh7Sq3k98z2rxAAA7BlBEBfXv02khNfxlrScfObxAgCAc54SM3dLGr0IALBbBEFcnLenu9x8vEDq58spkAoAAM5O37jSIMj6pExJy8mjGwEAdokgCEyBVDc3kUXbMmTPgcP0CAAAOGMRQb7SoUGw+X4+2SAAADtFEAQSG+ovvVuUzuP9ckUSPQIAAM5Kv7hI83XOZqbEAADsE0EQGEO6ly6X+/WqJCk4VkyvAACAM9bveF2QxdsyJK+wiB4EANgdgiAw+sVFSGSQjxw4XCCz/kyhVwAAwBlrGx0kUcG+crSwSJbuOEAPAgDsDkEQGJ4e7jKoa2k2yBcUSAUAAGfBzc3NWiB1zuZU+hAAYHcIgsBqcNdYcXcTWbrzgOxIz6VnAADAGYtvXVoXZN6WNCkpKaEHAQB2hSAIrKJD/Kx3b74kGwQAAJyFHs3CxM/LQ/Zn5clf+7PpQwCAXSEIggoLpH6zJpmCZgAA4Iz5enlIz+bh5vu5rBIDALAzBEFQzsUtIyQmxE8yjxTKr5v20zsAAOCMxR9fJWYudUEAAHaGIAjK8XB3M7VB1OfLEukdAABwxizTa9cnZ0ladh49CACwGwRBcJJBXWNNMGTVnkOyNTWHHgIAAGckIshXOjYIthZIBQDAXhAEQYUDl/7HK7uzXC4AADgb/Y6PJeZQFwQAYEcIguCUBVK/XZMsRwuK6CUAAHBG+h2vC/LH9gyKrQMA7IZdBEEmTpwojRs3Fl9fX+nevbusWLGi0mOnT58uXbp0kZCQEAkICJBOnTrJlClTyh1z++23i5ubW7ntsssuq4VP4jx6NQ+XhqH+kpN3TH7asM/WzQEAAA6mTVSQRAX7ytHCIlm644CtmwMAgH0EQaZNmyajRo2SMWPGyJo1a6Rjx44yYMAASUureP5oaGioPP3007J06VLZsGGD3HHHHWabNWtWueM06LF//37r9uWXX9bSJ3IO7u5ucku30myQz5dTIBUA4DzO5OZLWVOnTjU3VgYOHFhu/3PPPSdxcXHm5kzdunUlPj5eli9fLq5O+8pSIHUOq8QAAOyEzYMgb775ptx9990mkNGmTRuZNGmS+Pv7y4cffljh8Zdccolcd9110rp1a2nWrJk89NBD0qFDB1m8eHG543x8fKR+/frWTQclODM3dWkgXh5usj4pUzbtzaL7AAAO70xvvljs3r1bHn30UbnoootOeq5ly5YyYcIE2bhxoxmPaIDl0ksvlfT0dHF18cfrgmhx1JKSEls3BwAA2wZBCgoKZPXq1eaOiYW7u7t5rJkep6MX07lz50pCQoL07t273HMLFiyQiIgIadWqldx3331y4EDlaZj5+fmSnZ1dboNIeB0fGdC2vumKL1aQDQIAcHxnevNFFRUVydChQ+X555+Xpk2bnvT8kCFDzNhFn2vbtq15Dx1LaMaqq+vRLEz8vDxkf1ae/LmP8RUAwMWDIBkZGWZgERlZepfAQh+npKRU+rqsrCypU6eOeHt7y5VXXinjx4+X/v37l5sK8+mnn5oAyauvvioLFy6Uyy+/3LxXRcaOHSvBwcHWLTY2tho/pWMb2r2R+frD2r2Sm3/M1s0BAKDWb7688MIL5sbKiBEjqvQe77//vhlPaJaJq9+A8fXykF4tws33c1klBgBgB2w+HeZsBAYGyrp162TlypXy0ksvmbRWzfywGDx4sFxzzTXSvn17M2/3559/NseWPaasp556ygRWLFtSUlItfhr7dkHTUGlaL0AOFxTJ5N932ro5AADU6s0Xnd7ywQcfyOTJk095bh1r6A0arTPy3//+V2bPni3h4aV//Lv6DZj446vEzN2SauumAABg2yCIDg48PDwkNbX8RVEfax2Pyuhdm+bNm5uVYR555BG58cYbzWCiMpqequ+1ffv2Cp/X+iFBQUHlNvxd1Oyei0pTf9+au00mzq+4DwEAcDY5OTly2223mQDIqQIaqk+fPuYGzZIlS0xG6s0333zKOiOudAOmz/HiqBuSsyQtO8/WzQEAuDibBkF0Okvnzp3NtBWL4uJi87hHjx5VPo++RtNKK5OcnGxqgkRFRZ1zm13RoK6x8nB8S/P967MS5D+zEihuBgBwOGd682XHjh2mIOrVV18tnp6eZtPptj/++KP5Xp+30JVh9AbNBRdcYDJH9Hn9WhlXugETEegrHWNDrAVSAQBw6ekwOpVF77B88sknsnnzZlPE9PDhw6ZgmRo2bJi5W2KhGR+aYrpz505z/BtvvCFTpkyRW2+91Tyfm5srjz32mCxbtswMXDSgcu2115qBiVZ/x9llgzwU30KeujzOPJ4wf7v8e8ZmAiEAAIdypjdfdNlbXfFFMzwsm063tWR9nGoKy+lu0LiaftalcgmCAABsy9PG7y+DBg0yS8iNHj3azMfVKS4zZ860ztdNTEw0018sNEBy//33m+wOPz8/M0D57LPPzHmU3uHRauwaVMnMzJTo6GizTN2LL75o7rrg7P3fxc1MgbMxP/4pHyzeJXmFRfLite3E3d2NbgUAOAS9+TJ8+HDp0qWLdOvWTcaNG3fSzZeYmBhz00Xre7Rr167c60NCSjMaLPv1tVqfTIMjmnGqdUcmTpwoe/fulZtuuskGn9A+9WsdIW/O3iqLt6eb8YOOJwAAcMkgiHrggQfMVpETi5n++9//NltlNDAya9asam8jSg2/sLFZ6u6J6Rvk8+WJkldYLK/e0F48PWyeVAQAQLXffDkdvfmyZcsWc/NFAyBhYWHStWtXWbRokVkuF6XaRAVJdLCv7MvKkyU7MqRvXPnitAAA1Ba3kpKSklp7Nwehy9RppXYtVObMc3TPxQ/r9sqor9ZLUXGJXNkhSsYN6iReBEIAAMdxLT0zrtBfz3y/UT5blihDujeUl69rb+vmAABc9FrK7XuclWs7xcjEIeeJl4ebzNiwX+77bI3kHyuiNwEAQIX6tS7N/pi3OY26YgAAmyEIgrN2Wbsoef+2LuLj6S5zNqfKXZ+skqMFBEIAAMDJejQNE39vD0nJzpM/92XTRQAAmyAIgnPSJy5CPrq9q6kTsmhbhtz+0QrJzT9GrwIAgHK0GGqv5uHm+7msEgMAsBGCIDhnFzYPlykjukkdH09Zvuug3PbBcsk6WkjPAgCAk1aJUXO3pNIzAACbIAiCatGlcah8fld3CfbzkrWJmTJk8jI5eLiA3gUAAOUySNWG5CxJzc6jZwAAtY4gCKpNx9gQmXrPBRIW4G3m+g5+f6mk5TDAAQAApSICfc14Qc3bkka3AAAcIwjyySefyIwZM6yPH3/8cQkJCZELL7xQ9uzZU53tg4NpHRUk0/6vh0QG+cjW1FwZ9N4y2Zd51NbNAgA4OMYeziP+eDbI3M1MiQEAOEgQ5OWXXxY/Pz/z/dKlS2XixIny2muvSXh4uDz88MPV3UY4mOYRdeSr/+shMSF+sivjsNz83lJJOnjE1s0CADgwxh7Ot1Tu4u0ZklfIqnIAAAcIgiQlJUnz5s3N999//73ccMMNcs8998jYsWNl0aJF1d1GOKBGYQHy1b09pHGYvyQfOio3TVoqO9Nzbd0sAICDYuzhPFpHBUp0sK/kFRbLkh0Ztm4OAMDFnFUQpE6dOnLgwAHz/W+//Sb9+/c33/v6+srRo0x9QCnNBNGMkBYRdSQlO09ufm+ZJKTk0D0AAMYeLszNzc2aDTKHpXIBAI4QBNGgx1133WW2rVu3yhVXXGH2//nnn9K4cePqbiMcWESQrymWqrVCMnLzZdD7S2XT3ixbNwsA4GAYeziXvseXyp23OU1KSkps3RwAgAs5qyCI1gDp0aOHpKeny7fffithYWFm/+rVq+WWW26p7jbCwYXV8ZGpd19gqsFnHimUWyYvk9V7Dtm6WQAAB8LYw7n0aBom/t4eJlNUV5QDAKC2uJUQfj9Jdna2BAcHS1ZWlgQFBdXaD8PZ5eQVyoiPV8mK3QfNwOeD4V2lR7PSABoAwLlwLaW/TueeT1fJb3+lyj/jW8g/41vWwm8lAMCZVXXscVaZIDNnzpTFixeXuzvTqVMnGTJkiBw6xB1+VCzQ10s+vrOr9GoeLkcKiuT2j1bIwq3pdBcAgLGHC4o/XhdkLnVBAAC16KyCII899piJsqiNGzfKI488YuqC7Nq1S0aNGlXdbYQT8ff2lP8N7yJ94yIk/1ix3P3JKvntzxRbNwsAYOcYezifPnER4uYmsnFvlqRm59m6OQAAF3FWQRANdrRp08Z8rzVBrrrqKnn55ZdNRsivv/5a3W2Ek/H18pBJt3aWK9rXl4KiYrn/8zXy0/p9tm4WAMCOMfZwPvUCfaRjgxDz/bwtabZuDgDARZxVEMTb21uOHDlivp8zZ45ceuml5vvQ0FBrhghwyt8hT3d5e/B5ct15MXKsuEQemrpWvlmdTKcBABh7uJD446vEzN2cauumAABchOfZvKhXr15m2kvPnj1lxYoVMm3aNLNfl8tt0KBBdbcRTsrTw13euKmj+Hq5y5crkuTRr9fL0cIiue2CRrZuGgDAzjD2cE79WkfKf37bKou3Z0heYZHJFgUAwO4yQSZMmCCenp7yzTffyLvvvisxMTFmv06Fueyyy6q7jXBi7u5u8vJ17eX2Cxubx89+v0n+t2inrZsFALAzjD2cU1z9QIkO9pW8wmL5Y3uGrZsDAHABLJFbAZb1q326UvNrsxLk3QU7zONHL20pD/RtYYOWAACqA9dS+quq9AbIlGV75JZuDWXs9e35HxAAUKNjj7OaDqOKiork+++/l82bN5vHbdu2lWuuuUY8PEhjxJlzc3OTxwe0Ej8vD3lz9laTGqtTYx69tJV5DgAAxh7OqV/rCBMEmbclVUpK2nHdBwDUqLMKgmzfvt0sibt3715p1aqV2Td27FiJjY2VGTNmSLNmzaq7nXABGux4sF8LUyPk5V+2yMT5O+RoQbE8e1VrBkQA4OIYezivC5qGib+3h6Rm58umvdnSvkGwrZsEAHBiZ1UT5MEHHzSBjqSkJFmzZo3ZEhMTpUmTJuY54Fzc07uZvHhtW/P9h3/skqe/3yTFxSV0KgC4MMYezkuLoV7UItx8P3cLq8QAAOwwE2ThwoWybNkysySuRVhYmLzyyitmxRjgXN3Wo7H4eHnIE99ukC+WJ5qK8a/d0MGsKAMAcD2MPZx/lZhZf6bK3M1p8s/4lrZuDgDAiZ3VX5Q+Pj6Sk5Nz0v7c3Fzx9vaujnYBcnOXWBk3qJN4uLvJ9DV75aGp66SwqJieAQAXxNjDufVpFSFaAmzj3ixJzc6zdXMAAE7srIIgV111ldxzzz2yfPlys6qHbpoZcu+995riqEB1ubZTjEwccr54ebjJjI375b7PVpusEACAa2Hs4dzqBfpIxwYh5nvNBgEAwK6CIG+//bapCdKjRw/x9fU124UXXijNmzeXcePGVX8r4dIua1dfJg/rIj6e7jJnc5rc/ekqOVpAIAQAXAljD+cX3zrCfJ27mbogAICa41aiaRznUKndskRu69atTRDEldYXRu1asj1D7vp0lRwpKJJuTULlw9u7Sh2fs17lGQDggNdSxh7Oa/P+bLn8rUXmpse60ZeKn7eHrZsEAHDCsUeV/4IcNWrUKZ+fP3++9fs333yzqqcFquzC5uHy6Z3d5I6PVsqKXQfl1v8tl0/u7CbBfl70IgA4IcYeriWufqDEhPjJ3syj8sf2DIlvE2nrJgEAnFCVgyBr166t0nFuWtUKqCFdGofK53d3l2EfrpB1SZkyZPIymTKiu4QGUJAXAJwNYw/XomPIfq0j5NOle2TuljSCIAAA2wZBymZ6ALbUoUGIfHn3BXLbB8vlz33ZMvj9pfLZXd0lItCXHwwAOBHGHq65VK4GQeZtSZWSknbcXAMA2EdhVMDWWkcFydR7ekhkkI9sTc2VQe8tk32ZR23dLAAAcA4uaBoq/t4ekpqdL5v2ZtOXAIBqRxAEDqt5RB356v96mPnDuzIOy83vLZXEA0ds3SwAAHCWfDw95KIW4eb7OawSAwBw1iDIxIkTpXHjxmap3e7du8uKFSsqPXb69OnSpUsXCQkJkYCAAOnUqZNMmTKl0uPvvfdek0rJ0r3OqVFYgHx9bw9pHOYvyYeOmkDIjvRcWzcLAACcw5QYNevPFDlaUEQ/AgCcKwgybdo0U/19zJgxsmbNGunYsaMMGDBA0tLSKjw+NDRUnn76aVm6dKls2LBB7rjjDrPNmjXrpGO/++47WbZsmURHR9fCJ4GtRIf4mYyQFhF1JCU7Twa9t1S2pJBCCwCAI+obFyFeHm6yJSVHLvnPfJm6IlGOFRXbulkAACdh8yCILqd79913m0BGmzZtZNKkSeLv7y8ffvhhhcdfcsklct1110nr1q2lWbNm8tBDD0mHDh1k8eLF5Y7bu3evjBw5Uj7//HPx8mIJVWcXEeQrU++5QNpEBUlGboEMfn+ZbEzOsnWzAADAGQqv4yPvDu1sprtqbZAnp2+UAeN+l5mbUqSkpIT+BAA4bhCkoKBAVq9eLfHx8X83yN3dPNZMj9PRC+HcuXMlISFBevfubd1fXFwst912mzz22GPStm3bGms/7EtYHR+zakyn2BDJPFJols9dveegrZsFAADOUHybSJn36MXy7FVtpK6/l+xIPyz3frZarn93iSzfeYD+BAA4ZhAkIyNDioqKJDKydO6nhT5OSUmp9HVZWVlSp04d8fb2liuvvFLGjx8v/fv3tz7/6quviqenpzz44INVakd+fr5kZ2eX2+CYgv29zHK53ZqESk7+MbntgxWydAeDJQAAHLFI6oheTWTh431kZN/m4uflIWsTM2XQ+8vkzo9XMvUVAOCY02HORmBgoKxbt05WrlwpL730kqkpsmDBAvOcZpa89dZb8vHHH1d5bfmxY8dKcHCwdYuNja3hT4CaVMfHUz65o5upLn+koEhu/2iF/LR+Hym0AAA4oCBfL3nk0lay8LFL5NYLGoqHu5vM25Iml7+1SB75ar0kH2JlOABA1bmV2HBypU6H0fof33zzjQwcONC6f/jw4ZKZmSk//PBDlc5z1113SVJSkimOqqvAaFBEp9VYaLaJPtbgxu7duyvMBNHNQjNB9FjNOAkKCjrnzwnbyCsskge+WCNzNpcW2e3WOFSeuaq1dGgQwo8EAGqYXkv1xgLXUvqruu1Mz5U3ftsqMzbuN4+9PdxlWI9G8o8+zaVugHe1vx8AwLnGHjbNBNHpLJ07dzZ1PcrW89DHPXr0qPJ59DWWIIbWAtFVYzRTxLLp6jBaH6SiFWSUj4+P6aSyGxyfr5eHvDO0szzYt7n4ernLit0H5ZoJf8ioaetkX+ZRWzcPAACchab16sjEoefLD//oKT2ahklBUbH8b/Eu6f3afJk4f7scKThGvwIAKuUpNqZZG5r50aVLF+nWrZvJ5Dh8+LBZLUYNGzZMYmJizJQVpV/1WF0ZRgMfv/zyi0yZMkXeffdd83xYWJjZytLVYerXry+tWrWywSeELXl7usuoS1vJLd0byuuzEmT6mr0yfe1ec/font5N5d6Lm0mAj83/NwAAAGeoY2yIfHF3d/l9W4a8+usW+Wt/trnWf7xkt/wzvoXc3CVWvDwccuY3AKAG2fyvv0GDBkl6erqMHj3aFEPt1KmTzJw501osNTExsdzUFg2Q3H///ZKcnCx+fn4SFxcnn332mTkPUJmoYD958+ZOcvuFjeXfMzbLil0HZfy87TJ1ZZI8emlLubFzrJljDAAAHIfWf7u4ZT25qHm4/LRhn/zntwRJOnhUnv5uk3ywaJc8NqCVXNaufpXrxAEAnJ9Na4LYK+YxOzf9lf/tr1QZ+8tm2X2gtJhaXP1AeebKNtKrRbitmwcAToFrKf1lCwXHiuWL5Xvk7Xnb5eDhAmvGyJOXxUmPZuUzhQEArjn2IAhyDp0Hxx8oTVm2R96eu02yjhaafX3jIuRfV8RJ84hAWzcPABwa11L6y5Zy8gpl8qJd8r9FO81KceqSVvXk8QFx0iaasR0AOCOCILXQeXAOmUcK5O252+XTpbvlWHGJmRYzpFtDM584rI6PrZsHAA6Jayn9ZQ/Sc/Jl/Lxt8sXyRHON11kxAzvFyKj+LSU21N/WzQMAVCOCILXQeXC+Jfde+XWLmSqjAn085R99m5s6IrrSDACg6riWnhn6q2btzjgsb8zeKj+t32ddVnfoBQ3lgT7NueEBAE7CIZbIBextyb33h3WRqfdcIO1igiQn/5gJisS/udAMmiifAwDOYeLEidK4cWPx9fWV7t27y4oVK6r0uqlTp5oCmwMHDrTuKywslCeeeELat28vAQEBEh0dbVa227ev9I9t2IfG4QEy/pbz5KcHeslFLcLNsrof/bFbLn59gYyfu41ldQHAhRAEAU5wQdMw+fEfveSNmzpK/SBfST50VEZ+uVZueHeJrEk8RH8BgAObNm2ajBo1SsaMGSNr1qyRjh07yoABAyQtLe2Ur9u9e7c8+uijctFFF5Xbf+TIEXOeZ5991nydPn26JCQkyDXXXFPDnwRno32DYJkyortMGdHN3PDIzT9mMkR6v7bA1AkrLCqmYwHAyVEYtQKkpMLiaEGRTF60U95dsEOOFpYWVru6Y7Q8PqAVc4kBwAGvpZr50bVrV5kwYYJ5XFxcLLGxsTJy5Eh58sknK3xNUVGR9O7dW+68805ZtGiRZGZmyvfff1/pe6xcuVK6desme/bskYYNGzp0fzmz4uISmbFxv1lWd8/x1eIah/nLowNayRXtosTdnWV1AcCRMB0GqAZ+3h7yYL8WsuCxS+TmLg1MQTWdGtPvzYVmqkx2XumqMgAA+1dQUCCrV6+W+Ph46z53d3fzeOnSpZW+7oUXXpCIiAgZMWJEld5HAxk6bSYkJKTSY/Lz881greyG2qVBDr2xMfvhi+WFa9tKeB1v2X3giDzwxVoZ+M4f8sf2DH4kAOCEmA4DVEFkkK+8dmNH+XlkL7mwWZhZXnfSwh3S5/UF8tmyPXKM9FkAsHsZGRkmqyMyMrLcfn2ckpJS4WsWL14sH3zwgUyePLlK75GXl2dqhNxyyy2nzOgYO3asyfywbJqNAtvw9nSXYT0ay8LH+sjD8S0lwNtDNiRnydD/LZfbPlgum/Zm8aMBACdCEAQ4A22jg+Xzu7rLB8O7SNN6AXLgcIE88/0mufytRTI/IY3iqQDgRHJycuS2224zAZDw8PDTHq9FUm+++WZzLXj33XdPeexTTz1lMkYsW1JSUjW2HGcjwMdTHopvIQsf72NWhvPycJNF2zLkqvGL5cEv10ri8SkzAADH5mnrBgCORlOc+7WOlN4t68mXKxLlv7O3yra0XLnjo5Wm4vzTV7aWuPrM5wYAe6OBDA8PD0lNLV0K3UIf169f/6Tjd+zYYQqiXn311dZ9WkNEeXp6mgKozZo1KxcA0Tog8+bNO21dDx8fH7PB/oTX8ZHnrmkrd/ZsIm/MTpAf1u2TH9fvk1837Zeh3RvJA32bm2MAAI6JTBDgLHl5lKbPLnisj9zTu6l4e7ibO0ZXvLVInpq+QdJy8uhbALAj3t7e0rlzZ5k7d265oIY+7tGjx0nHx8XFycaNG2XdunXWTVd96dOnj/neMoXFEgDZtm2bzJkzR8LCwmr1c6FmNAzzl7cGn2emwuqNj8KiEvl4yW65+LX5Mm7OVrOyDADA8bA6TAWo0I6zoWmyr87cYirNK51TfH+f5jKiVxPx9fKgUwG4FHu9luoSucOHD5f33nvPrOAybtw4+eqrr2TLli2mNsiwYcMkJibG1OyoyO23315udRgNgNx4441medyff/65XL2R0NBQE3hx5P7C35Zsz5BXZm4x9UKUFlId2beF3NKtoakrAgCwLVaHAWxwx2ji0PPlm3t7SMfYEDlcUCSvz0qQvv9ZIN+tTTZL8QEAbGvQoEHyn//8R0aPHi2dOnUyGR0zZ860Bi8SExNl//7SYHZV7N27V3788UdJTk4254uKirJuS5YsqcFPgtp2YfNw+eEfPWXikPPNUroZuQUy5sc/Jf7NhWa6DNd5AHAMZIJUgLsxOFc6EPppwz55bWaC7M08avZ1aBAsz1zZRro1CaWDATg9rqX0lzMrLCqWqSuT5K052yQjN9/saxsdJE9eHicXtahn6+YBgEvKrmJWJUGQc+g84HTyCovkg8W75J35201miLq8XX0zSGoUFkAHAnBaXEvpL1dwOP+YfLh4l7z3+05rjZCezcPk8QFxJisUAFB7CILUQucBVZWeky//nbNVpq5IFJ0Vo8vuDe/R2MwlDvb3oiMBOB2upfSXKzmQmy8T5++Qz5btkYKi0hWEOsWGyC3dYuWqDtFm+V0AQM0iCFILnQecqYSUHHnpl83y+9Z08zjE30se6tdCbr2gkVltBgCcBddS+ssVJR08Iv+dvdXUCDl2vBaYFkq/plOMDO4aa6bGurm52bqZAOCUCILUQucBZ2tBQpq8/Mtm2Zqaax43DQ+Qp65oLfGtIxgcAXAKXEvpL1fPAP12TbJMW5kkuzIOW/e3jgoy2SHXdoqRYD8yQQGgOhEEqYXOA87FsaJimbYqSd78bascOFxg9vVoGiZPX9la2sUE07kAHBrXUvoLIiUlJbJs50GZujJRft2UIgXHSqfK+Hq5yxXto8zyul0a1eUGCABUA4IgtdB5QHXIySuUdxfskP8t3mUGR5ole8P5DeTRS1tJ/WBfOhmAQ+JaSn+hvMwjBfLd2r0ydUWSJKTmWPc3qxcgg7s2lOvPj5GwOj50GwCcJYIg54CBG2wh+dARs6SuziNWfl4eck/vpmajoBoAR8O1lP5C5dkha5MyTbH0n9bvl6OFpavHadH0S9vWl1u6NpQLm4WJuzu1QwDgTBAEOQcM3GBLaxMPyb9nbJbVew6Zx94e7tK+QbB0aVxXujQKlc6N6kpogDc/JAB2jWsp/YWqZYNqIESny2xIzrLujw31k0FdYuWmLrESGURWKABUBUGQc8DADfZwl+iXjSny+qwtsvvAkZOe19RZExBpXFe6Ng6VxmH+zCcGYFe4ltJfODN/7ssyU2W+X7dXcvKOmX0e7m7Sp1WEKaZ6cct64slKcgBQKYIg54CBG+wpGLLnwBFZufugyQxZteeQbE8rXVGmrLAAb5MhYrJFGodKu+hg8fZkyV0AtsO1lP7C2TlaUCS/bCzNDlm5uzQrVNUP8pWbuzQw2SGxof50LwCcgCDIOWDgBnt26HCBNSCyes9BWZ+cZa02b+Hj6S4dG4QczxSpK50bhkqwP0vxAag9XEvpL5y77Wk5JjtEl9s9dKTQ7NMC6r2ah5uVZeJbR3LTAwCOIwhyDhi4wZHkHyuSTXuzZNXu0sDIqt0HrQOlslpE1DFZIl2OZ4w0DGUKDYCaw7WU/kL1Xutn/5VqAiKLt2eUywS9sXMDGdQ1VprWq0OXA3Bp2VVc5dWtRPPtcVadB9gj/V96Z8ZhWb37kHUajT4+Ub1AHxMQKZ1GEypto4PEi7nGAKoJ11L6CzUj8cARmbYqUb5elSxpOfnW/d2ahJraIZe3ixJfLw+6H4DLySYIUvOdBziKA7n51ik0mimycW+WFBaVj3/6erlLp9gQU3BVM0XOb1RXgnyZQgPg7HAtpb9Qs44VFcv8hHSz1O78hDQpPn5ZD/L1lOvPbyCDu8VKXH3GsQBcRzZBkJrvPMBR5RUWmaX4Vu05aDJGVicekswTptDonONWkYEmU0RXoNGvDer6sQoNgCrhWnpm6C+ci/1ZR01myLSVSbI386h1f8fYELmla6xc3TFaAnw86WQATo0gSC10HuAsiotLZEd67vFMEc0YOWhWpTlRZJCPNVNEv7aOCmS5PgAV4lp6ZugvVNf1XGuG6MoyWkPEkvUZ4O0h13SKlkFdG0rHBsHc0ADglAiC1ELnAc4sLSdP1hwPiqzcc0j+3Jslxyy5tsf5e3vIeQ1DpLMGRhrVNd8HMoUGANfSM8bYA9UtIzdfpq9JNsVUy9YGi6sfaFaWGdgphpXjADgVgiC10HmAKzlaUCTrkzNNTZHS5XkPSU7esXLHuLvp4CrIZIro9JkeTcMkIsjXZm0GYDtcS+kv2E/B9BW7DsrUlUnyy8b9kn+s2Oz38XSXK9tHmZVltKiqm86DBQAHRhCkFjoPcPWU221pudYVaHQKTdLBv+chKw93N7mpcwP5R5/mEhvqb7O2Aqh9XEvpL9ifrCOF8t3aZBMQ2ZKSY93ftF6ADO4aKzec30DC6vjYtI0AcLYIgpwDBm7A2UnNzrPWFNHgyKa92Wa/l4eb3Nwl1gRDokP86F7ABXAtpb9g39kh65OzzMoyP67fJ0cKiqzX6/jWkSYzpHVUkNmC/VgpDoBjIAhSC50H4NQ0Q2TcnK2yaFuGeezt4S63dIuV+/s0l0imyQBOjWsp/QXHkJt/TH5av88ERDQwciJdGU6DIW10iy79ympxAOyRQwVBJk6cKK+//rqkpKRIx44dZfz48dKtW7cKj50+fbq8/PLLsn37diksLJQWLVrII488Irfddpv1mOeee06mTp0qSUlJ4u3tLZ07d5aXXnpJunfvXqX2MHADqpfORX5zdoIs23nQPPb2dJdbuzeSey9pKhGB1AwBnBHXUvoLjuevfdky688U+Wt/tmzeny3Jh8pPc7UI9PX8OzByPDjSIrKO+Hh61HqbAcDhgiDTpk2TYcOGyaRJk0yQYty4cfL1119LQkKCREREnHT8ggUL5NChQxIXF2cCHD///LMJgsyYMUMGDBhgjvniiy/Ma5s2bSpHjx6V//73v+acGjipV6/eadvEwA2oGUt2ZMh/Z2+VlbsPmce+Xu4yrEdj+b/eTZmDDDgZrqX0F5yjhsjmlGwTHNGgiAZHtqXmSkFRaXHVsjzd3aR5RJ1yWSP6fWiAt03aDsD1ZDtKEEQDH127dpUJEyaYx8XFxRIbGysjR46UJ598skrnOP/88+XKK6+UF1988ZSdMWfOHOnXr99pz8fADag5+k/O4u0Z8ubsrbI2MdO61O7wCxvLPRc1lboMlgCnwLWU/oJzKjhWLDvSc0uDIvtKAyO6ZR4prPD4+kG+1mk0JkASHSSNQv3FXZeUAwAbjD08xYYKCgpk9erV8tRTT1n3ubu7S3x8vCxdurRKf0zNmzfPZI28+uqrlb7H+++/bzpDp9pUJD8/32xlOw9AzdAl+C5qUU96NQ+XBVvTTWbIhuQseXfBDvl0yW65s1cTuatXUwn2pxAbAAD2Rqe0WoqmXn/+32PylOy80qCIZo0czx7ZfeCI2a/bvC1p1nPozY+4+oHHgyPB5muryEDx82Y6DYCaZ9MgSEZGhhQVFUlkZGS5/fp4y5Ytlb5OIzsxMTEmcOHh4SHvvPOO9O/fv9wxOk1m8ODBcuTIEYmKipLZs2dLeHh4hecbO3asPP/889X0qQBUNRjSp1WEXNKynszdnCb/nbNV/tyXLePnbZeP/9gtIy5qYgIiQb4EQwAAsPdrelSwn9n6tY4sV3R1y/H6IiZjZF+2WZpXV6NZk5hpNgtNDGkSHiBtooOldVSgdUoNtcMAVDebTofZt2+fCWYsWbJEevToYd3/+OOPy8KFC2X58uUVvk6nzOzcuVNyc3Nl7ty5ZhrM999/L5dccon1mMOHD8v+/ftNoGXy5MkmY0TPV1GdkYoyQXRKDqvDALVH/yn67a9UkxmiAyQV5Osp9/RuKrf3bCJ1fGwaswVwhpgOQ38BFTlWVCy7Dxw2Nz427885HhzJkozcggqPD6/jUxoUOT6lpm10kDQOCxBPD3c6GIDj1QTRqSr+/v7yzTffyMCBA637hw8fLpmZmfLDDz9U6Tx33XWXWQlm1qxZlR6jq8jceeed5abeVIaBG2A7xcUlMvPPFBMM2ZaWa/bV9feSe3o3k2E9GkkAwRDAIXAtpb+AM5GWk1caFLHUGdmXJbsyDktxBX+p+Hi6W6fTWAqxxkUFccMEcHHZjlATxLJ8rWZzWIIgmuWhjx944IEqn0dfUzaT42yPAWB7WijtivZRMqBtfZmxcb+Mm7NVdqYflldnbpH/Ldop917cTG69oBHzhgEAcCI67UW3i1v+vZLj0YIiSUgtDYxYptToV51Osz45y2xlNQrzN1kiDer6SUxdP2lQ119iQvwktq6fySihGCsAZfP88lGjRpnMjy5duki3bt3MErk6leWOO+4wz+vyuTplRut2KP2qxzZr1swENX755ReZMmWKvPvuu+Z5fe1LL70k11xzjakFotNhJk6cKHv37pWbbrrJpp8VQNV5uLvJNR2j5cr2UfLj+r3y1pxtpsDaS79slvd+3yn3X9JMhnRvKL5eFFEDAMAZaaHUTrEhZiubMbrn4JFyq9Po9/uz8mTPgSNmq6ygqwZENEBigiTme//jwRI/E4DRsQcA52fzIMigQYMkPT1dRo8eLSkpKdKpUyeZOXOmtVhqYmKiWTHGQoMc999/vyQnJ4ufn5/ExcXJZ599Zs6jtFCqFlX95JNPTAAkLCzMLMG7aNEiadu2rc0+J4CzowOS685rIFd3iJbpa/fK23O3SfKho/LCz3/Je7/vkH/0aS6DusaKjyfBEAAAnJ1mc2gBVd00c9Ti4OEC2ZKSLckHj0ryoSNmrJCceVT2Hjoq+7OOmqV9dXqNbhXx8igt7lpRgEQ3XeqXOiSAc7BpTRB7xTxmwH4VFhXLN6uTZcK87bI386jZFx3sK//o21xu6hxr7vQAsD2upfQXYE9jh5SsPBMY0bGDJUiiAZLkzCOyPzNPjlVUfOSEmzIaCPk7MOIvDY5nlug+DaAwBgFsyyEKo9orBm6A/cs/ViRfrUqWifO2S0p2ntmnd24e7Ndcrj+/gXhRNR6wKa6l9BfgKIqKSyQ12xIkOWKySUqDJaUBk32ZeVJQVHzKc7i5SWmQpExgxARKjmeWRIf4MYUXqGEEQWqh8wDYXl5hkUxdkSgTF+yQ9Jx8a2G0B/u2kGs7RZO6CtgI11L6C3AWWockPTffGhT5O6NEs0lKH+cfO3WQRNUL9LFmkZQNlmjh1pgQf4q+A+eIIEgtdB4A+wqGfLZsj0xauEMycgvMvqbhAfJQfAu5qkM0xc6AWsa1lP4CXIUm1uvY46SpNoeOWIMluqLN6XSMDZEH+jSX+NYR4qapJQDOCEGQc8DADXBcRwqOyZSlpcGQQ0cKzb7mEXXkn/Et5Ip2USyPB9QSrqX0F4C/gyQ6JjkxMFI2YJKTf8zaXa2jgmRk3+ZyWdv6jFuAM0AQ5BwwcAMcX27+MflkyW55//edknW0NBjSKjJQHu7fQi5tw6ACqGlcS+kvAFWXlp0nHy3ZLZ8u2S2Hj2eNtIysY1bBI6MVqBqCIOeAgRvgPHLyCuWjP3bL5EU7JSev9C5Lm6ggebh/S9JNgRrEtZT+AnDmMo8UyIeLd5mAiGXcotN7NRhCrTPg1AiCnAMGboDz0WyQDxbvMgMLzRJR7WOCZVT/lnJJq3rMvQWqGddS+gvAuY1bNCvkf4t3WTNaG4b6y/2XNDOr4LEcL3AygiDngIEb4Nx3WDQrRLNDLEXKOsWGmGDIRS3CCYYA1YRrKf0F4NzpjRutdaZjl4OHSwu/68oy917STG7u0kB8PD3oZuA4giDngIEb4PwO5ObL+4t2yqdL9sjRwtJgSJdGdU0wpEezMIIhwDniWkp/Aajewu9fLE+U937fKek5+WZfZJCP3HtxM7mlW0Px9SIYAmRXcZVXtxItVwwGboCL0oHEewt3yJRleyT/WLHZ171JqFlat3uTMJbWBc4SQRD6C0D1yysskqkrEmXSwp2Skp1n9oXX8ZF7ejeRod0bSYCPJ90Ol5VNEKTmOw+Ac1Vlf2fBDnOXpaCoNBhSx8fTTJU5v1FdOb9hiJzXsK4E+3nZuqmAQ+BaSn8BqDn5x4rkm9XJ8s78HWbJXVXX30vuuqipDOvRSAJ9Ga/A9WQTBKn5zgPgfPZnHZWJ87fLd2v2WpeoK6tFRB3prEERExipK83qBTB1BqgA19IzQ38BOBuFRcVmzDJxwXbZc+CI2ac3bO7o2VjuuLCJBPsTDIHryCYIUvOdB8B5FRWXSEJKjqxJPCRr9hyS1YmHrIOLskL8veS82JDSwEjDutIxNoRUVIBr6Rlj7AHgXBwrKpafNuyT8fO2y870w2ZfoI+nDL+wsYzo1UTqBnjTwXB62QRBar7zALiWjNx8ExBZk5hpvq5PzrTWEbFwdxOJqx90PFskRDo3DJXYUD+yReByuJbSXwBscxPnl437ZcK87ZKQmmP2+Xt7yG09GsndFzU19UMAZ0UQpBY6D4BrKzhWLJv3Z5tskdUaHNlzSPZllRYpK0sHHFpTxDKNpn1MMFXc4fTs+Vo6ceJEef311yUlJUU6duwo48ePl27dup32dVOnTpVbbrlFrr32Wvn++++t+6dPny6TJk2S1atXy8GDB2Xt2rXSqVMnp+kvAI6nuLhEfvsrRd6eu13+2p9t9vl6uZviqf/Xu6lEBPnauolAtSMIUgudBwAV1RRZsyfTGhj5c1+WFBaVX4TLy8NN2kQHS+eGda0ZI1HBfnQmnIq9XkunTZsmw4YNM0GL7t27y7hx4+Trr7+WhIQEiYiIqPR1u3fvll69eknTpk0lNDS0XBBkypQpsmvXLomOjpa7776bIAgAu6ELgc7bkiZvz90m65OzzD5vT3cZ3DXWLK8bHcL4A86DIEgtdB4AVGUpu017s6xBkdV7Ms20mhNFB/vKeY3qmsCIZou0iQoygxTAUdnrtVQDH127dpUJEyaYx8XFxRIbGysjR46UJ598ssLXFBUVSe/eveXOO++URYsWSWZmZrkgSNlASZMmTQiCALDLYMjv2zJk/NxtsmrPIetNmRs7x8r9lzST2FB/WzcRqLWxBwtJA0AN8vXykC6NQ81mGYQkHzpaOn3meGBkS0qOmUazb8N+mbFhvznOx9NdOjQItq5Co1u9QObxAueioKDATFl56qmnrPvc3d0lPj5eli5dWunrXnjhBZMlMmLECBMEAQBH4+bmJhe3rCe9W4TL0p0HTGbIsp0H5csVifLVqiS5/rwY+Uef5tI4PMDWTQVqHEEQAKjlQYjebdFt4HkxZt/h/GOmyOraxExrcCTzSKGs3H3IbBaNwvxLAyImMBIirSIDxdODbBGgqjIyMkxWR2RkZLn9+njLli0Vvmbx4sXywQcfyLp166q1o/Pz881W9u4VANTGOOTCZuFmW7n7oAmGLNqWIV+vTpZv1yTLNR2j5YG+zaV5RCA/DDgtgiAAYGMBPp7WAYklW2RnxmETEFl7PFtkW1quWaJXt+/W7i19nbeHWZLXsjzveQ1DJMSfJfCA6pKTkyO33XabTJ48WcLDS///rC5jx46V559/vlrPCQBnomvjUJkyorsZa+jSulo75Pt1++SH9fvkivZRMrJvc7PiHeBs3Ep0tA2HmMcMwHVlHS2UdUmlS/NqpohmjeTmHzvpuGb1AkxQpF1MsLSOCpJW9QMlyNfLJm2Ga7PHa6lOh/H395dvvvlGBg4caN0/fPhwU+fjhx9+KHe8Zn+cd9554uHhYd2nNUQs02i0mGqzZs3OqiZIRZkgWpvEnvoLgGvZmJwl4+dtk9/+SrXuu7RNpDzYr4UZVwD2jpogAOBEgv28zFxe3VRRcYlsS8s5vjRv6Wo0uzIOy4700u2rVcnW1zao62cCImarH2i+Ngz1F3d3Nxt+IqD2eXt7S+fOnWXu3LnWIIgGNfTxAw88cNLxcXFxsnHjxnL7nnnmGZMh8tZbb5mgxdny8fExGwDYi/YNguX9YV1k8/5smTB/u/yycb8JiOjWNy7CZIac17CurZsJnDOmwwCAA/JwdzMpqroN7d7I7DuQm28yRNYmHZLN+3PMIGZ/Vp4pxKrb7DJ3dvy9PUyWSNngSFxUkNTx4bIA5zZq1CiT+dGlSxfp1q2bWSL38OHDcscdd5jndfncmJgYM13F19dX2rVrV+71ISEh5mvZ/QcPHpTExETZt2+feawZIqp+/fpmAwBHouOCiUPOl+1pOTJh3nb5cf0+M1VGt4tahJvMEJ1KAzgqRrsA4CTC6vhIfJtIs1lkHimwBkR005VoElJz5EhBUWnAJDGz3Dk0Q6R1VKAJruggSJfq1UwSskbgLAYNGiTp6ekyevRoSUlJMdNWZs6caS2WqsEMnepyJn788UdrEEUNHjzYfB0zZow899xz1fwJAKB2aHHUcYPPk4fiW8rE+dtNTTItoqrbBU1DTTCkR9MwU2wVcCTUBHGQecwAUF2OFRWbqTN/HQ+KWAIkqdl/1ycoS7NDSrNGSjNHSjNQAk1BV6AyXEvPDP0FwN4lHjgi7y7cLt+sTpbCotKykl0a1ZWR/VqYpXcJhsBRrqUEQc6h8wDAmRw8XCBb9meb4Ihmj2xJyZZtqblSUFRaCLIsvenTKNTfmjFiCZBo1giDICiupWeG/gLgKPZmHpX3Fu6QqSuTpOBY6RihQ4NgGdGriVlVxsvjzLLpgOpCEKQWOg8AnF1hUbHsTD9cmi2SUhoc0e/TcyrOGgn08ZS44wGR0qyRQJNF4u9N1oir4VpKfwFwbqnZefLewp3yxYo9kldYGgypH+Qrwy5sJEO6NZQQf29bNxEuJptMkJrvPABwVRm5+bKlTK2RzSk5poCaJT32xKyRJmEBpcERS+ZIdJBEB/uSNeLEuJbSXwBcZ0zw+bJEmbJst2TkFph9fl4eckPnGLmjZxNpVq+OrZsIF5FNEKTmOw8A8DdNid2RnmstwGoJkFgGRCcK8tWskdLiq5oxosERzRrx9fKgW50A11L6C4BryT9WJD+t3y8fLN5lrv8WfVrVkzt7NZFezakbgppFEKQWOg8AcHo6dcaaMXI8QLI9LVeOFZ+cNeLuJtKtSagM79FY+reJFE/mFTssrqX0FwDXVFJSIst2HjTBkLlbUqXk+OW+ZWQdubNnExl4Xgw3PFAjCILUQucBAM7+bpEGQqxTao7XG9HirBZRwb5y6wWNZHDXWLP8LxwL11L6CwB0NbpPluyWr1YlyZGCItMhoQHeMrR7Q7ntgkYSEeRLJ6HaEASphc4DAFTvnaPkQ0dl6spE+XJFkjUg4u3hLld1jJLbL2wsHRqE0OUOgmsp/QUAFllHC+WrlUny8ZLdZnUZ5eXhJld3jDbZIe1iguksnDOCILXQeQCAmpFXWCQzNuyXT5bulg3JWdb9nWJDTDDk8vb1xceT2iH2jGsp/QUAJzpWVCy//ZVqpsqs3nPIul+nwuoSu/GtI8VD58YCZ4EgyDlg4AYA9pMdsi4p06TSzti437r6THgdHxnSLVaGdG8k9YNJpbVHXEvpLwA4Fb2+f7h4l/yycb+1TljDUH9zs+PmrrFSx8eTDkSNjD3cxQ5MnDhRGjduLL6+vtK9e3dZsWJFpcdOnz5dunTpIiEhIRIQECCdOnWSKVOmWJ8vLCyUJ554Qtq3b2+ej46OlmHDhsm+fftq6dMAAKqLm5ubnNewrowbfJ4sebKfPNK/pUQG+Zjl+N6et116vTpP/vHFGlmx66AJmAAAAMeg2Z1v33KeLHqij9x3STMJ9vOSxINH5IWf/5IeL8+VF3/+S5IOHrF1M+GE3EpsPGqcNm2aCVJMmjTJBEDGjRsnX3/9tSQkJEhERMRJxy9YsEAOHTokcXFx4u3tLT///LM88sgjMmPGDBkwYICJ+tx4441y9913S8eOHc2xDz30kBQVFcmqVauq1CbuXgGA/SrUVNo/U012yIrdB637dYnd4T0aybWdYsTPm6kytsa1lP4CgDNxpOCYTF+zVz78Y5fsTD9s9unMmEvb1JcRFzWRLo3qmpsjgMNPh9HAR9euXWXChAnmcXFxscTGxsrIkSPlySefrNI5zj//fLnyyivlxRdfrPD5lStXSrdu3WTPnj3SsGHD056PgRsAOIa/9mXLp0t3y/fr9kpeYbHZp3eSdEUZXVkmNtTf1k10WVxL6S8AOBvFxSWycFu6mSqzaFuGdX+HBsGmiOoV7aPE29MuJjTAzjjEdJiCggJZvXq1xMfH/90gd3fzeOnSpad9vcZv5s6da7JGevfuXelx2gkaNdQpNAAA59EmOkheuaGDLHuqn/zrijhpUNfPVKB/7/ed0vv1+XLXJ6tk0bZ0psoAAOAg3N3dpE+rCJkyorv89nBvc2NDgx5aKP2f09bJRa/Nk4nzt8uh46vIAWfKppkgWqcjJiZGlixZIj169LDuf/zxx2XhwoWyfPnySoMa+rr8/Hzx8PCQd955R+68884Kj83Ly5OePXua6TOff/55hcfoeXQrG0HSbBRWhwEAx1JUXCLzt6SZVWXK3j1qWi9AhvdoLDd0bkChtVpCJgj9BQDV5UBuvnyxPFE+XbZH0nNK/27z8XSX689vICN6NZbmEYF0NqSqYw+HLLkbGBgo69atk9zcXJMJMmrUKGnatKlccskl5Y7TIqk333yzuQP47rvvVnq+sWPHyvPPP18LLQcA1CRdVi++TaTZtqflymfL9sg3q5PN3OIxP/4pr89KkBvOj5HbeuiAqQ4/DAAAHEBYHR8Z2a+F/N/FzeTnDfvMErt/7suWL1ckmq13y3pmid3eLcKpGwL7zgTR6TD+/v7yzTffyMCBA637hw8fLpmZmfLDDz9U6Tx33XWXJCUlyaxZs04KgOzcuVPmzZsnYWFhlb6eTBAAcF45eYXy3dq9ppDqjuOF1tRFLcJlWI/G0jcuwgRPUL3IBKG/AKCm6J+wujKcFlH97a9UsfxFqzc4tG7IdedRJN0VZTtCJoiu7tK5c2eTzWEJgmhhVH38wAMPVPk8+pqy01ksAZBt27bJ/PnzTxkAUT4+PmYDADifQF8vE+y47YJG8sf2A/Lxkt0yd0uqmS6jm9YR0ecGdY2VEH9vWzcXAACchtZ77N40zGyJB46Ya/tXq5JMFui/vtsor8/aIkO6N5TbLmgs9YN96U/Y3xK5mvnx3nvvmRVcdIncr776SrZs2SKRkZFm+Vyt/6FTVpR+7dKlizRr1swEPn755RezioxOd9GMEA2A6BK5a9asMcvn6jksQkNDTeDldLh7BQDOLengETNVZurKJFNI1TK3eGCnGBl+YWNTcBXnhmsp/QUAtZ35+dWqZPl4yS5JOnjU7PN0d5OrOkTJnb2aSIcGLJLh7LIdZYlcpcvjvv7665KSkiKdOnWSt99+2yydq7TOR+PGjeXjjz82j5955hkTOElOThY/Pz9T8PShhx6SQYMGmed3794tTZo0qfB9NCvkxLohFWHgBgCu4WhBkfy4fq98vGSPbN6fbd3ftXFdEwwZ0La+eHmwDN/Z4FpKfwGArYqkz/4r1Syxu2L3wXLXdp0qc2nb+kyDdVIOFQSxNwzcAMC16KVw1Z5Dpm7IzE0pcqy49NIYGeQjQ7s3ksHdYiUikHTaM8G19MzQXwBQ/TYmZ5m6IT+t32e9tus02NsvbCw3d42VIF8vut2JEASphc4DADif1Ow8+Xx5olmKLyO3tN6Ul4ebXNk+SoZd2FjOiw2h8nwVcC09M/QXANTstX3K0j3y+fI9cuhI6TTYOj6eclOXBnJLt4ZSr46P+Hp5iLenO1kiDowgSC10HgDAeRUcK5ZfN+03xdbWJmZa93doEGwKreocYx0woWJcS88M/QUANS+vsMisGKdTZbal5VZ4jN748PH0EF8vd/NVa4ZpcESv+fq9j5eH+B7/ah6XfU6P93Iv9/zJz5V+tewr+z7urFZ3TgiC1ELnAQBcw4bkTPlkyR75acM+ExxRoQHeMrhrrNx6QSOJDvGzdRPtDtdS+gsA7HkarK4Q98HiXbJkR4YUFtlHhQhvj+PBEUtgpEyAxKeCQEyAj6d0bxIql7SKED9vbsxkUxPk7DFwAwBU5EBuvllR5vNle2RfVp7ZpzdtLm1T3xRSvaBpKFNluJYy9gAAB3OsqFjyj5Vumi1S+n2R5BeWfVy6L6/w7+dOPN76nD4ud1zpvnLnKiySvGPFppDrufLz8pA+cfXksnZR0jcuwkz1cUXZBEFqvvMAAK47WJqzOdVkhyzdecC6v0l4gPSLi5A+cRHStXGoSZ91VVxL6S8AQPUFYE567liRpOfkm5Vwkg+VLgmsdOxxcct6cnm7+tKvdaQE+7lO8ddsgiA133kAACSk5MinS3fL9DV75WhhkbVD9C5Mr+bh5o7MJa3qSUSQa60uw7WU/gIA1M7Unk17s00ds183pciujMPl6pv0bB4uV7SLkv5tIqVugLdT/0gIgtRC5wEAYJGTVyi/b82QeVvSZOHWNMnILSjXOe1igqRvq9IskQ4NQpy++jzXUvoLAFD7AZGE1Bz5ZWOK/Lpxf7nirzru6NE0TC5vX99M460X6ON0Px6CILXQeQAAVKS4uEQ27s0yAZEFCWmyPjmr3PNaVPWSlvVMQKR3i3oS7O98qapcS+kvAIBtbU/LkV83psgvm1Jk8/5s6353NzHTdq9oHyWXtasvkU6SrUoQpBY6DwCAqtA5uxoMWZCQLr9vTZec/GPl7sx0bljXBES0qFmryECnKK7KtZT+AgDYj90Zh810mZmb9p90c6Zzo7qmhogGRBrU9RdHRRCkFjoPAIAzVVhULKt2H5L5CWkyf0tauVRVFRPiZ2qIaC2RC5uFO+ySd1xL6S8AgH1KOnhEZv2ZYoIiq/ccKvdcxwbBcnn7KBMUaRQWII6EIEgtdB4AANUxELEERJbsOGAqv5et8K7zdzUg0qdVhDQMc5y7M1xL6S8AgP1Lycoz2SEaEFmx+6CUlFmxt01UkFzRXjNEoqR5RB2xdwRBaqHzAACoTkcLimTpzgyZvyXd1BPZm/n3kneqWb0Aa0Cki50vwcu1lP4CADiWtJw8+e3PVJm5KUWW7jwgRcV/R0RaRtaRy9tFmcKq9jp1lyBILXQeAAA1WeFdp8poMESzRFbtOVRuMKJL8F7UItzUEjFL8AbaV1EzrqX0FwDAcR08XCBz/kqVXzbtlz+2Z0hh0d9jkKbhAaZ+iBZWbRsdZDcBEYIgtdB5AADUlqyjhbJoW7rJEqloCd72McGlxVVb1ZOODULE3cZL8HItpb8AAM4zBpm7OdUsvfv7tnQpKDN1NzbUrzRDpF196RQbYtOACEGQWug8AABstQTvhr1ZJkNE64lsOKHKe1iAt1x8vLjqRboEr1/tL8HLtZT+AgA4n9z8YyZL9deN+80YJK/w74BIVLCvNUNEV76r7RsyBEFqofMAALCXObwLE9LNYGTR1oyTl+BtVNcERHRrEVGnVu7ScC2lvwAAzu1IwTEz/vhlU4rM25wqhwuKrM/VC/SRy9rWNzVEujUOFU+Pmq9jRhCkFjoPAAB7XIJ35e6DsiChtLjq9gqW4O0TV5ol0qNpzS3By7WU/gIAuI68wiJZtC3DZIjM3pwqOXl/35AJDfCWAW0jzbSZHs3CxKuGAiIEQWqh8wAAcJQleDUgsvSEJXh9dAneZn8vwRsbWn1L8HItpb8AAK6p4Fix/LGjNCDy21+pknmk0PqcTtHt3ybSLL3bs3m4+HhW380YgiC10HkAADjiErylK86kn7QE7yvXt5fB3RpWy3txLaW/AAAoLCqW5TsPmlVmfvszpVxhd60h8scTfautdkhVxx6e/FgAAHANOvWlb1yk2XQJ3q2pudYskdV7DkmXxqG2biIAAHAiXh7u0qtFuNlevLadmbI7c1OK/Lppv3RrEmqT1ezcSnQUhHK4ewUAcMXl74J8PautaCrXUvoLAIBTrXSnhdyrcwU7MkEAAECV2WIZXQAA4Jrc3d1sNvao+XVqAAAAAAAA7ABBEAAAAAAA4BIIggAAAAAAAJdAEAQAAAAAALgEgiAAAAAAAMAlEAQBAAAuZeLEidK4cWPx9fWV7t27y4oVK6r0uqlTp5olhAcOHFhuf0lJiYwePVqioqLEz89P4uPjZdu2bTXUegAAcC4IggAAAJcxbdo0GTVqlIwZM0bWrFkjHTt2lAEDBkhaWtopX7d792559NFH5aKLLjrpuddee03efvttmTRpkixfvlwCAgLMOfPy8mrwkwAAgLNBEAQAALiMN998U+6++2654447pE2bNiZw4e/vLx9++GGlrykqKpKhQ4fK888/L02bNj0pC2TcuHHyzDPPyLXXXisdOnSQTz/9VPbt2yfff/99LXwiAABwJgiCAAAAl1BQUCCrV68201Us3N3dzeOlS5dW+roXXnhBIiIiZMSIESc9t2vXLklJSSl3zuDgYDPN5lTnzM/Pl+zs7HIbAACoeQRBAACAS8jIyDBZHZGRkeX262MNZFRk8eLF8sEHH8jkyZMrfN7yujM5pxo7dqwJlli22NjYs/hEAADgTHme8StcgKa2Ku7KAABwdizXUMs11RHl5OTIbbfdZgIg4eHh1Xrup556ytQmscjKypKGDRsy9gAAoIbHHgRBKhn0KO7KAABw7tdUzXSwBxrI8PDwkNTU1HL79XH9+vVPOn7Hjh2mIOrVV19t3VdcXGy+enp6SkJCgvV1eg5dHabsOTt16lRpW3x8fMx24sCNsQcAADU79iAIUoHo6GhJSkqSwMBAsxReddDBjQ5s9LxBQUHVck7Q9/aM33n63tXwO1+e3oXRQYheU+2Ft7e3dO7cWebOnWtd5laDGvr4gQceOOn4uLg42bhxY7l9WgBVP9dbb71lruteXl4mEKLnsAQ99HdBV4m57777qtw2xh7Og38L6HtXw+88fe9oYw+CIBXQImkNGjSokR+MBkAIgtgGfU+/uxp+5+l3W7OXDJCydArK8OHDpUuXLtKtWzezssvhw4fNajFq2LBhEhMTY2p2+Pr6Srt27cq9PiQkxHwtu/+f//yn/Pvf/5YWLVpIkyZN5NlnnzUDMEugpSoYezgf/g2m710Nv/P0vaOMPQiCAAAAlzFo0CBJT0+X0aNHm8Klmr0xc+ZMa2HTxMREE5A4E48//rgJpNxzzz2SmZkpvXr1MufUIAoAALAvbiWOXLHMwdLENCqlhc/IBKHvXQG/8/S9q+F3HvaG30n63dXwO0+/uxp+588OS+TWEi1+NmbMmHJF0EDfOzN+5+l7V8PvPOwNv5P0u6vhd55+dzX8zp8dMkEAAAAAAIBLIBMEAAAAAAC4BIIgAAAAAADAJRAEAQAAAAAALoEgSC2ZOHGiNG7c2CyX1717d1mxYkVtvbVLGjt2rHTt2lUCAwMlIiJCBg4cKAkJCbZulst55ZVXxM3NTf75z3/auikuYe/evXLrrbdKWFiY+Pn5Sfv27WXVqlW2bpbTKyoqkmeffVaaNGli+r1Zs2by4osvCouvwZYYd9Q+xh72gbFH7WLsUfsYd5w7giC1YNq0aTJq1CizOsyaNWukY8eOMmDAAElLS6uNt3dJCxculH/84x+ybNkymT17thQWFsqll14qhw8ftnXTXMbKlSvlvffekw4dOti6KS7h0KFD0rNnT/Hy8pJff/1V/vrrL3njjTekbt26tm6a03v11Vfl3XfflQkTJsjmzZvN49dee03Gjx9v66bBRTHusA3GHrbH2KN2MfawDcYd547VYWqBZn5oVoIOkFVxcbHExsbKyJEj5cknn6yNJri89PR0kxGiA5TevXu7fH/UtNzcXDn//PPlnXfekX//+9/SqVMnGTduHP1eg/Tfkj/++EMWLVpEP9eyq666SiIjI+WDDz6w7rvhhhtMVshnn33GzwO1jnGHfWDsUbsYe9Q+xh62wbjj3JEJUsMKCgpk9erVEh8f/3enu7ubx0uXLq3pt8dxWVlZ5mtoaCh9Ugs0C+fKK68s93uPmvXjjz9Kly5d5KabbjIBv/POO08mT55Mt9eCCy+8UObOnStbt241j9evXy+LFy+Wyy+/nP5HrWPcYT8Ye9Quxh61j7GHbTDuOHee1XAOnEJGRoaZt6V3CcvSx1u2bKHvaoFm3mhNCp0q0K5dO/q8hk2dOtVM+9KUVNSenTt3mikZOvXuX//6l+n/Bx98ULy9vWX48OH8KGr4Tlh2drbExcWJh4eH+Tf/pZdekqFDh9LvqHWMO+wDY4/axdjDNhh72AbjjnNHEAQucWdg06ZN5s4salZSUpI89NBDpg6LFgFG7Q64NRPk5ZdfNo81E0R/7ydNmkQQpIZ99dVX8vnnn8sXX3whbdu2lXXr1pnAa3R0NH0PuCjGHrWHsYftMPawDcYd544gSA0LDw83dwZTU1PL7dfH9evXr+m3d3kPPPCA/Pzzz/L7779LgwYNXL4/appO/dKCv1oPxELvimv/a02c/Px88/8Dql9UVJS0adOm3L7WrVvLt99+S3fXsMcee8zclRk8eLB5rKvy7Nmzx6wUQRYOahvjDttj7FG7GHvYDmMP22Dcce6oCVLDNBW9c+fOZr542aipPu7Ro0dNv73L0qUpdRDy3Xffybx588zSlah5/fr1k40bN5o74ZZNsxN0WoB+TwCk5uh0rxOXgdYaFY0aNarBd4U6cuSIqfVUlv6u67/1QG1j3GE7jD1sg7GH7TD2sA3GHeeOTJBaoHP09W6g/jHYrVs3s0qGLtV6xx131Mbbu2waqqam//DDDxIYGCgpKSlmf3BwsFmxATVD+/rEuisBAQESFhZGPZYa9vDDD5tCWTod5uabb5YVK1bI+++/bzbUrKuvvtrUAGnYsKGZDrN27Vp588035c4776TrYROMO2yDsYdtMPawHcYetsG4oxqUoFaMHz++pGHDhiXe3t4l3bp1K1m2bBk9X4P0V7ui7aOPPqLfa9nFF19c8tBDD9HvteCnn34qadeuXYmPj09JXFxcyfvvv0+/14Ls7GzzO67/xvv6+pY0bdq05Omnny7Jz8+n/2EzjDtqH2MP+8HYo/Yw9qh9jDvOnZv+pzqCKQAAAAAAAPaMmiAAAAAAAMAlEAQBAAAAAAAugSAIAAAAAABwCQRBAAAAAACASyAIAgAAAAAAXAJBEAAAAAAA4BIIggAAAAAAAJdAEAQAAAAAALgEgiAAXMaCBQvEzc1NMjMzbd0UAADgAhh7APaHIAgAAAAAAHAJBEEAAAAAAIBLIAgCoNYUFxfL2LFjpUmTJuLn5ycdO3aUb775ply66IwZM6RDhw7i6+srF1xwgWzatKncOb799ltp27at+Pj4SOPGjeWNN94o93x+fr488cQTEhsba45p3ry5fPDBB+WOWb16tXTp0kX8/f3lwgsvlISEhFr49AAAoLYx9gBwIoIgAGqNBkA+/fRTmTRpkvz555/y8MMPy6233ioLFy60HvPYY4+ZwMbKlSulXr16cvXVV0thYaE1eHHzzTfL4MGDZePGjfLcc8/Js88+Kx9//LH19cOGDZMvv/xS3n77bdm8ebO89957UqdOnXLtePrpp817rFq1Sjw9PeXOO+/ktwAAACfE2APASUoAoBbk5eWV+Pv7lyxZsqTc/hEjRpTccsstJfPnzy/Rf5KmTp1qfe7AgQMlfn5+JdOmTTOPhwwZUtK/f/9yr3/sscdK2rRpY75PSEgw55g9e3aFbbC8x5w5c6z7ZsyYYfYdPXq0Wj8vAACwLcYeACpCJgiAWrF9+3Y5cuSI9O/f32RmWDbNDNmxY4f1uB49eli/Dw0NlVatWpmMDqVfe/bsWe68+njbtm1SVFQk69atEw8PD7n44otP2RadbmMRFRVlvqalpVXbZwUAALbH2ANARTwr3AsA1Sw3N9d81ZofMTEx5Z7T2h1lAyFnS+uMVIWXl5f1e61DYpkzDAAAnAdjDwAVIRMEQK1o06aNCXYkJiaaYqVlNy1iarFs2TLr94cOHZKtW7dK69atzWP9+scff5Q7rz5u2bKlyQBp3769CWaUrTECAABcE2MPABUhEwRArQgMDJRHH33UFEPVQEWvXr0kKyvLBDGCgoKkUaNG5rgXXnhBwsLCJDIy0hQwDQ8Pl4EDB5rnHnnkEenatau8+OKLMmjQIFm6dKlMmDBB3nnnHfO8rhYzfPhwU+hUC6Pq6jN79uwxU120oCoAAHAdjD0AVIQgCIBao8ELXfFFK7Xv3LlTQkJC5Pzzz5d//etf1ukor7zyijz00EOmzkenTp3kp59+Em9vb/OcHvvVV1/J6NGjzbm0nocGTW6//Xbre7z77rvmfPfff78cOHBAGjZsaB4DAADXw9gDwInctDrqSXsBoJYtWLBA+vTpY6bAaHAEAACAsQeA6kZNEAAAAAAA4BIIggAAAAAAAJfAdBgAAAAAAOASyAQBAAAAAAAugSAIAAAAAABwCQRBAAAAAACASyAIAgAAAAAAXAJBEAAAAAAA4BIIggAAAAAAAJdAEAQAAAAAALgEgiAAAAAAAMAlEAQBAAAAAADiCv4fudzli2EW0s8AAAAASUVORK5CYII=",
-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "plot_loss_curves(summary_cl, keys=[\"short\", \"long\"], titles=[\"Short-term loss\", \"Long-term loss\"])"
    ]
@@ -6179,28 +6046,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": null,
    "id": "e829b6d5",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "--- Pretraining probes, with distractors ---\n",
-      "Frame  0: pos R²=0.850, vel R²=0.361\n",
-      "Frame  2: pos R²=0.883, vel R²=0.463\n",
-      "Frame  4: pos R²=0.896, vel R²=0.569\n",
-      "Frame  6: pos R²=0.915, vel R²=0.617\n",
-      "Frame  8: pos R²=0.918, vel R²=0.533\n",
-      "Frame 10: pos R²=0.911, vel R²=0.618\n",
-      "Frame 12: pos R²=0.900, vel R²=0.658\n",
-      "Frame 14: pos R²=0.895, vel R²=0.654\n",
-      "Frame 16: pos R²=0.903, vel R²=0.571\n",
-      "Frame 18: pos R²=0.894, vel R²=0.546\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "print(\"--- Pretraining probes, with distractors ---\")\n",
     "probes_pos, probes_vel, r2_pos, r2_vel = fit_and_score_probes(model, val_ds_w, test_ds_w, device)"
@@ -6216,21 +6065,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": null,
    "id": "4e869c79",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
     "    prepare_pretraining_predictions(model, test_ds_w, probes_pos, probes_vel, device, num_examples=3)\n",
@@ -6270,7 +6108,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": null,
    "id": "b8a802f0",
    "metadata": {},
    "outputs": [],
@@ -6331,7 +6169,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": null,
    "id": "a63e52aa",
    "metadata": {},
    "outputs": [],
@@ -6386,7 +6224,8 @@
     "\n",
     "        k = min(self.rollout_k, T - 1)\n",
     "        rolled = self.rollout_predictor.rollout(z[:, 0], k)\n",
-    "        loss_roll = (rolled[:, -1] - z[:, k]).abs().mean()\n",
+    "        # loss_roll = (rolled[:, -1] - z[:, k]).abs().mean()\n",
+    "        loss_roll = (rolled - z[:, 1 : k + 1]).abs().mean()\n",
     "\n",
     "        loss = loss_tf + self.rollout_w * loss_roll\n",
     "        self.log(f\"{stage}_tf\", loss_tf, on_step=True, on_epoch=True, prog_bar=True)\n",
@@ -6411,123 +6250,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": null,
    "id": "2c299d30",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/html": [
-       "
┏━━━┳━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
-       "┃   ┃ Name              ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
-       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│ 0 │ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│ 1 │ rollout_predictor │ RolloutPredictor │  826 K │ train │     0 │\n",
-       "│ 2 │ train_metrics     │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 3 │ val_metrics       │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 4 │ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 5 │ optimizer         │ Adam             │      0 │ train │     0 │\n",
-       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n",
-       "
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-       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName             \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
-       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ rollout_predictor │ RolloutPredictor │  826 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ train_metrics     │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ val_metrics       │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ optimizer         │ Adam             │      0 │ train │     0 │\n",
-       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
Trainable params: 826 K                                                                                            \n",
-       "Non-trainable params: 1.2 M                                                                                        \n",
-       "Total params: 2.0 M                                                                                                \n",
-       "Total estimated model params size (MB): 8                                                                          \n",
-       "Modules in train mode: 103                                                                                         \n",
-       "Modules in eval mode: 0                                                                                            \n",
-       "Total FLOPs: 0                                                                                                     \n",
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-      ],
-      "text/plain": [
-       "\u001b[1mTrainable params\u001b[0m: 826 K                                                                                            \n",
-       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
-       "\u001b[1mTotal params\u001b[0m: 2.0 M                                                                                                \n",
-       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 8                                                                          \n",
-       "\u001b[1mModules in train mode\u001b[0m: 103                                                                                         \n",
-       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
-       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
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-     "metadata": {},
-     "output_type": "display_data"
-    },
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-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "488ade0b7c1d491b8832c8c8bbbd3d8a",
-       "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "Output()"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/html": [
-       "
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-      ],
-      "text/plain": []
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "ename": "SystemExit",
-     "evalue": "1",
-     "output_type": "error",
-     "traceback": [
-      "An exception has occurred, use %tb to see the full traceback.\n",
-      "\u001b[31mSystemExit\u001b[39m\u001b[31m:\u001b[39m 1\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/IPython/core/interactiveshell.py:3709: UserWarning: To exit: use 'exit', 'quit', or Ctrl-D.\n",
-      "  warn(\"To exit: use 'exit', 'quit', or Ctrl-D.\", stacklevel=1)\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "rollout_model = RolloutModel(frozen_ctx_enc=model.ctx_enc, optimizer=dl.Adam(lr=3e-4))\n",
     "summary_ro = rollout_model.fit(train_ds_w, max_epochs=100, batch_size=32, accelerator=\"auto\")"

From eab9b23c46edcb4b8b4024991a1cfb325846f311 Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Mon, 24 Aug 2026 16:20:56 +0200
Subject: [PATCH 5/9] with gaussian noise

---
 Companion/cc_jepa/jepa.ipynb | 4856 +---------------------------------
 1 file changed, 18 insertions(+), 4838 deletions(-)

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
index be4350ae6..ef463d36f 100644
--- a/Companion/cc_jepa/jepa.ipynb
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -15,7 +15,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "a4994aa9",
    "metadata": {},
    "outputs": [],
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "id": "9dea3f77",
    "metadata": {},
    "outputs": [],
@@ -194,7 +194,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "7f80d1e0",
    "metadata": {},
    "outputs": [],
@@ -267,4680 +267,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "43847c1c",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
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-       "  
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-       "    \n",
-       "    
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-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
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-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "    
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-       "    
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-       "      \n",
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-       "
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-       "\n",
-       "\n",
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-      "text/plain": [
-       ""
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "from matplotlib import animation\n",
@@ -4985,7 +315,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "07c28293",
    "metadata": {},
    "outputs": [],
@@ -5027,20 +357,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "id": "9d9ad66c",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "saved 10000 clips to datasets/bouncing bead with distractors/particles_train.pt\n",
-      "saved 2000 clips to datasets/bouncing bead with distractors/particles_val.pt\n",
-      "saved 1000 clips to datasets/bouncing bead with distractors/particles_test.pt\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import os\n",
     "from os.path import exists\n",
@@ -5067,23 +387,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "id": "b4cf3ddc",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "train_ds: 10000 clips\n",
-      "val_ds:   2000 clips\n",
-      "test_ds:  1000 clips\n",
-      "clip shape: torch.Size([1, 20, 24, 24])\n",
-      "positions shape: torch.Size([20, 2])\n",
-      "velocities shape: torch.Size([20, 2])\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "class ParticlesDataset(torch.utils.data.Dataset):\n",
     "    \"\"\"Clean baseline dataset, or paired context/target views for JEPA fine-tuning.\"\"\"\n",
@@ -5147,7 +454,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "67adc09b",
    "metadata": {},
    "outputs": [],
@@ -5214,21 +521,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "id": "3d93bd73",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
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-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "num_frames = N_FRAMES\n",
     "batch_size = 8\n",
@@ -5297,7 +593,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "id": "027f07d3",
    "metadata": {},
    "outputs": [],
@@ -5390,7 +686,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "id": "cd3d9dfe",
    "metadata": {},
    "outputs": [],
@@ -5428,7 +724,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "id": "6ff7f0b7",
    "metadata": {},
    "outputs": [],
@@ -5518,126 +814,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "id": "c9090a44",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:76: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default\n",
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/html": [
-       "
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-       "┃   ┃ Name          ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
-       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│ 0 │ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│ 1 │ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│ 2 │ predictor     │ Predictor        │  216 K │ train │     0 │\n",
-       "│ 3 │ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 4 │ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 5 │ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
-       "│ 6 │ optimizer     │ Adam             │      0 │ train │     0 │\n",
-       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n",
-       "
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-      ],
-      "text/plain": [
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-       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName         \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
-       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
-       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ predictor     │ Predictor        │  216 K │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
-       "│\u001b[2m \u001b[0m\u001b[2m6\u001b[0m\u001b[2m \u001b[0m│ optimizer     │ Adam             │      0 │ train │     0 │\n",
-       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "
Trainable params: 1.4 M                                                                                            \n",
-       "Non-trainable params: 1.2 M                                                                                        \n",
-       "Total params: 2.6 M                                                                                                \n",
-       "Total estimated model params size (MB): 10                                                                         \n",
-       "Modules in train mode: 161                                                                                         \n",
-       "Modules in eval mode: 0                                                                                            \n",
-       "Total FLOPs: 0                                                                                                     \n",
-       "
\n"
-      ],
-      "text/plain": [
-       "\u001b[1mTrainable params\u001b[0m: 1.4 M                                                                                            \n",
-       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
-       "\u001b[1mTotal params\u001b[0m: 2.6 M                                                                                                \n",
-       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 10                                                                         \n",
-       "\u001b[1mModules in train mode\u001b[0m: 161                                                                                         \n",
-       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
-       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "2a1c6fb842574e27bcd556929b974887",
-       "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "Output()"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/html": [
-       "
\n"
-      ],
-      "text/plain": []
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "ename": "SystemExit",
-     "evalue": "1",
-     "output_type": "error",
-     "traceback": [
-      "An exception has occurred, use %tb to see the full traceback.\n",
-      "\u001b[31mSystemExit\u001b[39m\u001b[31m:\u001b[39m 1\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/IPython/core/interactiveshell.py:3709: UserWarning: To exit: use 'exit', 'quit', or Ctrl-D.\n",
-      "  warn(\"To exit: use 'exit', 'quit', or Ctrl-D.\", stacklevel=1)\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "model = PretrainingModel(ema_tau=0.999, optimizer=dl.Adam(lr=3e-4))\n",
     "summary = model.fit(train_ds, max_epochs=30, batch_size=16, accelerator=\"auto\")"

From fc59115f54a5a78cfc183e7f439bbaa79e23ab24 Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Wed, 26 Aug 2026 00:22:18 +0200
Subject: [PATCH 6/9] consistent results

---
 Companion/cc_jepa/jepa.ipynb | 4954 +++++++++++++++++++++++++++++++---
 1 file changed, 4615 insertions(+), 339 deletions(-)

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
index ef463d36f..a6c6dcee8 100644
--- a/Companion/cc_jepa/jepa.ipynb
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -8,14 +8,14 @@
     "# Building a World Model with a Joint-Embedding Predictive Architecture (JEPA)\n",
     "\n",
     "
\n",
-    "\"Open\n",
+    "\"Open\n",
     "If using Colab/Kaggle: You need to uncomment the code in the cell below this one.\n",
     "
"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 33,
    "id": "a4994aa9",
    "metadata": {},
    "outputs": [],
@@ -94,6 +94,47 @@
     "The predictor is trained by comparing its predicted representation to the target encoder's actual representation, using a simple distance in representation space rather than a pixel-wise loss."
    ]
   },
+  {
+   "cell_type": "raw",
+   "id": "1adaf547",
+   "metadata": {
+    "vscode": {
+     "languageId": "raw"
+    }
+   },
+   "source": [
+    "======================================================================================\n",
+    "                    JOINT EMBEDDING PREDICTIVE ARCHITECTURE (JEPA)\n",
+    "======================================================================================\n",
+    "\n",
+    "       [ Context Input: x ]        ==== Masking ===>       [ Target Input: y ]\n",
+    "   (e.g., Visible Video/Image Tokens)                 (e.g., Contiguous Block Masked)\n",
+    "                |                                                  |\n",
+    "                v                                                  v\n",
+    "     +----------------------+                            +--------------------+\n",
+    "     |   Context Encoder    |                            |   Target Encoder   |\n",
+    "     |   f_θ (Trainable)    |==== EMA Weight Update ===> | f_ξ (No Gradients) |\n",
+    "     +----------------------+                            +--------------------+\n",
+    "                |                                                  |\n",
+    "                v                                                  v\n",
+    "     [ Context Latent: s_x ]                             [ Target Latent: s_y ]\n",
+    "                |                                                  |\n",
+    "                |         +-----------------------+                |\n",
+    "                +-------->|       Predictor       |                |\n",
+    "                          |        g_φ(·)         |                |\n",
+    "                          +-----------------------+                |\n",
+    "                                      |                            |\n",
+    "                                      v                            |\n",
+    "                          [ Predicted Target: ŝ_y ]                |\n",
+    "                                      |                            |\n",
+    "                                      +------------( + )-----------+\n",
+    "                                                     |\n",
+    "                                                     v\n",
+    "                                          [ Representation Loss ]\n",
+    "                                         D(ŝ_y, s_y)  ==> Minimize\n",
+    "======================================================================================"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "c74cb685",
@@ -114,7 +155,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 34,
    "id": "9dea3f77",
    "metadata": {},
    "outputs": [],
@@ -153,10 +194,10 @@
     "    \"\"\"One fixed-shape bead moving on an integer pixel grid.\"\"\"\n",
     "    if seed is not None:\n",
     "        np.random.seed(seed)\n",
+    "\n",
+    "    lower = int(np.ceil(margin + radius - 1))\n",
+    "    upper = int(np.floor(image_size - margin - radius))\n",
     "    \n",
-    "    radius_pixels = int(np.floor(radius))\n",
-    "    lower = margin + radius_pixels\n",
-    "    upper = image_size - margin - 1 - radius_pixels\n",
     "    if lower >= upper:\n",
     "        raise ValueError(\"Image is too small for this bead radius and margin.\")\n",
     "\n",
@@ -185,76 +226,49 @@
    "id": "50581c2a",
    "metadata": {},
    "source": [
-    "The next step is turning positions into pixels. `render_trajectories` draws the bead as a soft, radially-fading disc.\n",
-    "\n",
-    "You'll also add distractors, small flickering rectangles appearing, disappearing, and relocating unpredictably from frame to frame. \n",
+    "The next step is turning positions into pixels. `render_trajectories` draws the bead as a soft, radially-fading disc. \n",
     "\n",
-    "`make_clip` ties it together: one simulated trajectory, rendered both with and without distractors, alongside the ground-truth position and velocity."
+    "`make_clip` ties it together: it simulates a trajectory, renders the bead, adds Gaussian noise over a background offset, and pairs the noisy clip with ground-truth positions and velocities."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "7f80d1e0",
+   "execution_count": 35,
+   "id": "f863edd2",
    "metadata": {},
    "outputs": [],
    "source": [
-    "BEAD_RADIUS = 4.5\n",
+    "import numpy as np\n",
+    "\n",
+    "BEAD_RADIUS = 5.0\n",
     "BEAD_INTENSITY = 0.7\n",
-    "DISTRACTOR_INTENSITY = 1.0\n",
+    "NOISE_STD = 0.035  # Adjust standard deviation\n",
+    "NOISE_OFFSET = 0.1  # Adjust offset\n",
     "\n",
     "def render_trajectories(positions, radius=BEAD_RADIUS, image_size=IMAGE_SIZE,\n",
     "                        intensity=BEAD_INTENSITY, sigma=None):\n",
     "    \"\"\"Render a video of a circular bead with a radial intensity falloff.\"\"\"\n",
-    "\n",
     "    if sigma is None:\n",
     "        sigma = radius / 2.0  # ~14% of peak intensity right at the edge\n",
     "    yy, xx = np.meshgrid(np.arange(image_size), np.arange(image_size), indexing=\"ij\")\n",
     "    frames = np.zeros((len(positions), image_size, image_size), dtype=np.float32)\n",
     "    for t, (row, col) in enumerate(positions):\n",
     "        dist_sq = (yy - row) ** 2 + (xx - col) ** 2\n",
-    "        bead = dist_sq <= radius ** 2\n",
+    "        bead = dist_sq < radius ** 2\n",
     "        frames[t, bead] = intensity * np.exp(-dist_sq[bead] / (2 * sigma ** 2))\n",
     "    return frames\n",
     "\n",
-    "\n",
-    "def sample_distractor_rects(image_size=IMAGE_SIZE, n_min=1, n_max=3, side_min=1, side_max=4):\n",
-    "    \"\"\"Sample a random number of small, static rectangular distractors.\"\"\"\n",
-    "\n",
-    "    n = np.random.randint(n_min, n_max + 1)\n",
-    "    rects = []\n",
-    "    for _ in range(n):\n",
-    "        h = np.random.randint(side_min, side_max + 1)\n",
-    "        w = np.random.randint(side_min, side_max + 1)\n",
-    "        row0 = np.random.randint(0, image_size - h + 1)\n",
-    "        col0 = np.random.randint(0, image_size - w + 1)\n",
-    "        rects.append((row0, col0, h, w))\n",
-    "    return rects\n",
-    "\n",
-    "def add_flickering_distractors(frames, p_present=0.75, n_min=1, n_max=4,\n",
-    "                                side_min=1, side_max=3, intensity=DISTRACTOR_INTENSITY):\n",
-    "    \"\"\"Stamp random rectangular distractors onto a random subset of frames.\"\"\"\n",
-    "\n",
-    "    out = frames.copy()\n",
-    "    T, H, W = frames.shape\n",
-    "    for t in range(T):\n",
-    "        if np.random.rand() > p_present:\n",
-    "            continue\n",
-    "        rects = sample_distractor_rects(image_size=H, n_min=n_min, n_max=n_max,\n",
-    "                                         side_min=side_min, side_max=side_max)\n",
-    "        for row0, col0, h, w in rects:\n",
-    "            out[t, row0:row0 + h, col0:col0 + w] = np.maximum(\n",
-    "                out[t, row0:row0 + h, col0:col0 + w], intensity\n",
-    "            )\n",
-    "    return out\n",
+    "def add_high_frequency_noise(frames, noise_std=NOISE_STD, noise_offset=NOISE_OFFSET):\n",
+    "    \"\"\"Add additive Gaussian pixel noise with a constant background offset.\"\"\"\n",
+    "    noise = np.random.normal(loc=noise_offset, scale=noise_std, size=frames.shape).astype(np.float32)\n",
+    "    return np.clip(frames + noise, 0.0, 1.0)\n",
     "\n",
     "def make_clip(radius=BEAD_RADIUS):\n",
     "    \"\"\"Simulate one trajectory and return matched views.\"\"\"\n",
-    "    \n",
     "    positions, vel = simulate_trajectory(radius)\n",
     "    clean = render_trajectories(positions, radius)\n",
-    "    w_distractors = add_flickering_distractors(clean)\n",
-    "    return clean, w_distractors, positions, vel"
+    "    noisy = add_high_frequency_noise(clean)\n",
+    "    return noisy, positions, vel"
    ]
   },
   {
@@ -262,43 +276,3871 @@
    "id": "551fb934",
    "metadata": {},
    "source": [
-    "A quick visual sanity check: this animates one clip side by side, clean and with distractors, along with the ground-truth velocity and speed at each frame."
+    "A quick visual sanity check: this animates one clip along with the ground-truth velocity and speed at each frame."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 36,
    "id": "43847c1c",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "
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+       "  
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+       "    \n",
+       "    
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+       "      \n",
+       "      \n",
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+       "    
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+       "  
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+       "
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+       "\n",
+       "\n",
+       "\n"
+      ],
+      "text/plain": [
+       ""
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "from matplotlib import animation\n",
     "from IPython.display import HTML\n",
     "\n",
-    "clean_frames, w_distractors_frames, positions, vel = make_clip()\n",
+    "clip, pos, vel = make_clip()\n",
     "\n",
-    "fig, axes = plt.subplots(1, 2, figsize=(9, 4.5))\n",
-    "im_clean = axes[0].imshow(clean_frames[0], cmap=\"gray\", vmin=0, vmax=1)\n",
-    "im_w_distractors = axes[1].imshow(w_distractors_frames[0], cmap=\"gray\", vmin=0, vmax=1)\n",
-    "axes[0].set_title(\"Clean view\")\n",
-    "axes[1].set_title(\"With distractors view\")\n",
-    "for ax in axes:\n",
-    "    ax.axis(\"off\")\n",
+    "fig, ax = plt.subplots(figsize=(6, 4.5))\n",
+    "ax.axis(\"off\")\n",
+    "im = ax.imshow(clip[0], cmap=\"gray\", vmin=0, vmax=1)    \n",
     "\n",
     "def update(i):\n",
-    "    im_clean.set_data(clean_frames[i])\n",
-    "    im_w_distractors.set_data(w_distractors_frames[i])\n",
+    "    im.set_data(clip[i])\n",
     "    row_velocity, col_velocity = vel[i]\n",
     "    speed = np.linalg.norm(vel[i])\n",
     "    fig.suptitle(\n",
     "        f\"Frame {i}   |   velocity = ({row_velocity:+.0f}, {col_velocity:+.0f})\"\n",
     "        f\"   |   speed = {speed:.2f}   \"\n",
     "    )\n",
-    "    return [im_clean, im_w_distractors]\n",
+    "    return [im]\n",
     "\n",
     "anim = animation.FuncAnimation(\n",
-    "    fig, update, frames=len(clean_frames), interval=150, blit=False\n",
+    "    fig, update, frames=len(clip), interval=150, blit=False\n",
     ")\n",
     "plt.close(fig)\n",
     "\n",
@@ -310,12 +4152,12 @@
    "id": "f798aacd",
    "metadata": {},
    "source": [
-    "The following helper function ties everything together: simulate a trajectory, render both clean and distractor views, and repeat for as many clips as needed, saving the result to disk in one call."
+    "The following helper function ties everything together: simulate a trajectory, render the clip, and repeat for as many clips as needed, saving the result to disk in one call."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 37,
    "id": "07c28293",
    "metadata": {},
    "outputs": [],
@@ -323,23 +4165,21 @@
     "import torch\n",
     "\n",
     "def build_and_save_dataset(path, n_clips=5000, radius=BEAD_RADIUS):\n",
-    "    \"\"\"Generate n_clips random trajectories, render both clean and distractor \n",
-    "    views for each, and save everything to `path` as a single .pt file.\n",
+    "    \"\"\"Generate n_clips random trajectories, render noisy view, and save \n",
+    "    everything to `path` as a single .pt file.\n",
     "    \"\"\"\n",
     "\n",
-    "    clean_clips, w_distractors_clips = [], []\n",
+    "    clips_list = []\n",
     "    positions_list, velocities_list = [], []\n",
     "    for _ in range(n_clips):\n",
-    "        clean, w_distractors, positions, vel = make_clip(radius)\n",
-    "        clean_clips.append(torch.from_numpy(clean).unsqueeze(0))\n",
-    "        w_distractors_clips.append(torch.from_numpy(w_distractors).unsqueeze(0))\n",
+    "        clip, positions, vel = make_clip(radius)\n",
+    "        clips_list.append(torch.from_numpy(clip).unsqueeze(0))\n",
     "        positions_list.append(torch.from_numpy(positions))\n",
     "        velocities_list.append(torch.from_numpy(vel))\n",
     "\n",
-    "    clean_clips = torch.stack(clean_clips).float()\n",
+    "    clips = torch.stack(clips_list).float()\n",
     "    torch.save({\n",
-    "        \"clips_clean\": clean_clips,\n",
-    "        \"clips_w_distractors\": torch.stack(w_distractors_clips).float(),\n",
+    "        \"clips\": clips,\n",
     "        \"positions\": torch.stack(positions_list).float(),\n",
     "        \"velocities\": torch.stack(velocities_list).float(),\n",
     "    }, path)\n",
@@ -357,22 +4197,30 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 38,
    "id": "9d9ad66c",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Datasets already exist. Skipping dataset generation.\n"
+     ]
+    }
+   ],
    "source": [
     "import os\n",
     "from os.path import exists\n",
     "\n",
-    "os.makedirs(\"datasets/bouncing bead with distractors\", exist_ok=True)\n",
+    "os.makedirs(\"datasets/bouncing bead\", exist_ok=True)\n",
     "\n",
-    "if exists(\"datasets/bouncing bead with distractors/particles_train.pt\") and exists(\"datasets/bouncing bead with distractors/particles_val.pt\") and exists(\"datasets/bouncing bead with distractors/particles_test.pt\"):\n",
+    "if exists(\"datasets/bouncing bead/particles_train.pt\") and exists(\"datasets/bouncing bead/particles_val.pt\") and exists(\"datasets/bouncing bead/particles_test.pt\"):\n",
     "    print(\"Datasets already exist. Skipping dataset generation.\")\n",
     "else:\n",
-    "    build_and_save_dataset(\"datasets/bouncing bead with distractors/particles_train.pt\", n_clips=10000)\n",
-    "    build_and_save_dataset(\"datasets/bouncing bead with distractors/particles_val.pt\", n_clips=2000)\n",
-    "    build_and_save_dataset(\"datasets/bouncing bead with distractors/particles_test.pt\", n_clips=1000)"
+    "    build_and_save_dataset(\"datasets/bouncing bead/particles_train.pt\", n_clips=10000)\n",
+    "    build_and_save_dataset(\"datasets/bouncing bead/particles_val.pt\", n_clips=2000)\n",
+    "    build_and_save_dataset(\"datasets/bouncing bead/particles_test.pt\", n_clips=1000)"
    ]
   },
   {
@@ -380,43 +4228,46 @@
    "id": "ddd653ee",
    "metadata": {},
    "source": [
-    "The class `ParticlesDataset` wraps a saved file for training. With `p_distractors=0`, it returns clean clips only. With `p_distractors>0`, each clip has some probability of using its distractor-contaminated view as context instead of the clean one, while the clean view is always kept as what the encoder is trained to reconstruct.\n",
-    "\n",
-    "For now, you'll start with clean clips."
+    "The class `ParticlesDataset` wraps a saved file for training."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 39,
    "id": "b4cf3ddc",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "train_ds: 10000 clips\n",
+      "val_ds:   2000 clips\n",
+      "test_ds:  1000 clips\n",
+      "clip shape: torch.Size([1, 20, 24, 24])\n",
+      "positions shape: torch.Size([20, 2])\n",
+      "velocities shape: torch.Size([20, 2])\n"
+     ]
+    }
+   ],
    "source": [
     "class ParticlesDataset(torch.utils.data.Dataset):\n",
-    "    \"\"\"Clean baseline dataset, or paired context/target views for JEPA fine-tuning.\"\"\"\n",
-    "    def __init__(self, path, p_distractors=0.0, seed=0):\n",
-    "        data = torch.load(path)\n",
-    "        self.clean = data.get(\"clips_clean\")\n",
+    "    \"\"\"Wraps a saved file of (clips, positions, velocities).\"\"\"\n",
+    "    def __init__(self, path):\n",
+    "        data = torch.load(path, weights_only=True)\n",
+    "        self.clips = data[\"clips\"]\n",
     "        self.positions = data[\"positions\"]\n",
     "        self.velocities = data[\"velocities\"]\n",
-    "        self.p_distractors = p_distractors\n",
-    "        if p_distractors > 0.0:\n",
-    "            self.w_distractors = data[\"clips_w_distractors\"]\n",
-    "            rng = np.random.default_rng(seed)\n",
-    "            self.use_w_distractors_context = rng.random(len(self.clean)) < p_distractors\n",
     "\n",
     "    def __len__(self):\n",
-    "        return len(self.clean)\n",
+    "        return len(self.clips)\n",
     "\n",
     "    def __getitem__(self, idx):\n",
-    "        if self.p_distractors > 0.0:\n",
-    "            context = self.w_distractors[idx] if self.use_w_distractors_context[idx] else self.clean[idx]\n",
-    "            return self.clean[idx], context, self.positions[idx], self.velocities[idx]\n",
-    "        return self.clean[idx], self.positions[idx], self.velocities[idx]\n",
+    "        return self.clips[idx], self.positions[idx], self.velocities[idx]\n",
     "\n",
-    "train_ds = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_train.pt\")\n",
-    "val_ds = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_val.pt\")\n",
-    "test_ds = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_test.pt\")\n",
+    "train_ds = ParticlesDataset(\"datasets/bouncing bead/particles_train.pt\")\n",
+    "val_ds = ParticlesDataset(\"datasets/bouncing bead/particles_val.pt\")\n",
+    "test_ds = ParticlesDataset(\"datasets/bouncing bead/particles_test.pt\")\n",
     "\n",
     "print(f\"train_ds: {len(train_ds)} clips\")\n",
     "print(f\"val_ds:   {len(val_ds)} clips\")\n",
@@ -454,13 +4305,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 40,
    "id": "67adc09b",
    "metadata": {},
    "outputs": [],
    "source": [
     "import math\n",
     "\n",
+    "from torch import device\n",
+    "\n",
     "MASK_GROUPS = [(\"short\", 4, 0.1), (\"long\", 1, 0.5)]\n",
     "\n",
     "\n",
@@ -473,7 +4326,7 @@
     "    side = max(1, min(s_grid, round(math.sqrt(area))))\n",
     "    return side\n",
     "\n",
-    "def sample_masks(B, t_grid, s_grid, rng=None, min_visible=2):\n",
+    "def sample_masks(B, t_grid, s_grid, device=\"cpu\", rng=None, min_visible=2):\n",
     "    \"\"\"Sample one short-range and one long-range mask (see MASK_GROUPS),\n",
     "    each reused identically across the whole batch. A short retry loop\n",
     "    guards against masking away more than `min_visible` cells.\n",
@@ -498,13 +4351,17 @@
     "        visible_cells = np.flatnonzero(~mask)\n",
     "\n",
     "        t_offsets = np.arange(t_grid) * (s_grid * s_grid)\n",
-    "        ctx = np.sort((t_offsets[:, None] + visible_cells[None, :]).ravel())\n",
-    "        pred = np.sort((t_offsets[:, None] + masked_cells[None, :]).ravel())\n",
+    "        ctx = (t_offsets[:, None] + visible_cells[None, :]).ravel()\n",
+    "        pred = (t_offsets[:, None] + masked_cells[None, :]).ravel()\n",
+    "\n",
+    "        # Convert directly to PyTorch tensors of shape (B, N)\n",
+    "        ctx_tensor = torch.from_numpy(ctx).long().to(device).unsqueeze(0).repeat(B, 1)\n",
+    "        pred_tensor = torch.from_numpy(pred).long().to(device).unsqueeze(0).repeat(B, 1)\n",
     "\n",
     "        groups.append({\n",
     "            \"label\": label,\n",
-    "            \"ctx\": [ctx.tolist()] * B,\n",
-    "            \"pred\": [pred.tolist()] * B,\n",
+    "            \"ctx\": ctx_tensor,   # Shape: (B, num_ctx_tokens)\n",
+    "            \"pred\": pred_tensor, # Shape: (B, num_pred_tokens)\n",
     "        })\n",
     "    return groups"
    ]
@@ -516,36 +4373,48 @@
    "source": [
     "Let's see what these masks actually look like on real clips. The cell below overlays the masked regions in red on a sample clip, for both the short- and long-range groups, confirming visually that \"short\" scatters several small blocks while \"long\" covers one large region, and that both stay in the same place across every frame.\n",
     "\n",
-    "Before any of this can run, the video needs to be broken into tokens, the discrete units a transformer actually operates on. Treating every individual pixel as its own token would be far too many for a transformer to handle, and a single pixel carries almost no information about the scene on its own anyway. Instead, the clip is divided into small spatial patches, `patch_size` × `patch_size` pixels each. Each patch is then extended across a few consecutive frames, `t_patch` frames at a time, into a tubelet: a small chunk of space and time treated as a single unit. Each tubelet becomes one token, and `s_grid` and `t_grid` are simply how many of these tokens fit across space and across time."
+    "Before any of this can run, the video needs to be broken into tokens, the discrete units a transformer actually operates on. Treating every individual pixel as its own token would be far too many for a transformer to handle, and a single pixel carries almost no information about the scene on its own anyway. Instead, the clip is divided into small spatial patches, `patch_size` × `patch_size` pixels each. Each patch is then extended across a few consecutive frames, `t_patch` frames at a time, into a *tubelet*: a small chunk of space and time treated as a single unit. Each tubelet becomes one token, and `s_grid` and `t_grid` are simply how many of these tokens fit across space and across time.\n",
+    "\n",
+    "One consequence worth keeping in mind: grouping `t_patch` frames into a single tubelet means the encoder's temporal resolution is coarser than the video's actual frame rate. A tubelet token doesn't represent one instant, it represents a small span of time pooled together, so anything that changes *within* that span, like the bead's velocity flipping sign mid-bounce, isn't something any single token can represent exactly."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 41,
    "id": "3d93bd73",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
+    "from torch.utils.data import DataLoader\n",
+    "\n",
     "num_frames = N_FRAMES\n",
+    "image_size = IMAGE_SIZE\n",
     "batch_size = 8\n",
     "patch_size = 6\n",
-    "image_size = 24\n",
     "t_patch = 2\n",
     "\n",
-    "loader = torch.utils.data.DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
+    "loader = DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
     "batch = next(iter(loader))\n",
-    "if len(batch) == 4:\n",
-    "    _, videos, positions, velocities = batch\n",
-    "else:\n",
-    "    videos, positions, velocities = batch\n",
+    "clips, positions, velocities = batch\n",
     "\n",
     "t_grid = num_frames // t_patch\n",
     "s_grid = image_size // patch_size\n",
     "\n",
-    "groups = sample_masks(videos.size(0), t_grid, s_grid)\n",
+    "groups = sample_masks(clips.size(0), t_grid, s_grid)\n",
     "n_groups = len(groups)\n",
     "\n",
-    "n_frames_total = videos.shape[2]\n",
+    "n_frames_total = clips.shape[2]\n",
     "frame_indices = list(range(0, n_frames_total, 2))   # every 2nd frame\n",
     "n_display_frames = len(frame_indices)\n",
     "\n",
@@ -555,20 +4424,30 @@
     "                         squeeze=False)\n",
     "\n",
     "for row, group in enumerate(groups):\n",
-    "    masked_spatial = np.unique(np.array(group[\"pred\"][sample_i]) % (s_grid * s_grid))\n",
+    "    pred_indices = group[\"pred\"][sample_i].cpu().numpy()\n",
+    "    masked_spatial = np.unique(pred_indices % (s_grid * s_grid))\n",
     "    mask_grid = np.zeros((s_grid, s_grid), dtype=bool)\n",
     "    mask_grid.flat[masked_spatial] = True\n",
     "    mask_pixels = np.repeat(np.repeat(mask_grid, patch_size, axis=0), patch_size, axis=1)\n",
     "\n",
     "    for col, t in enumerate(frame_indices):\n",
     "        ax = axes[row, col]\n",
-    "        ax.imshow(videos[sample_i, 0, t].cpu(), cmap=\"gray\", vmin=0, vmax=1)\n",
+    "        ax.imshow(clips[sample_i, 0, t].cpu(), cmap=\"gray\", vmin=0, vmax=1)\n",
     "        overlay = np.zeros((*mask_pixels.shape, 4))\n",
     "        overlay[mask_pixels] = [1, 0, 0, 0.35]\n",
     "        ax.imshow(overlay)\n",
     "        ax.axis(\"off\")\n",
     "        if col == 0:\n",
-    "            ax.set_ylabel(group[\"label\"], rotation=0, ha=\"right\", va=\"center\")\n",
+    "            ax.text(\n",
+    "                -0.15,\n",
+    "                0.5,\n",
+    "                group[\"label\"],\n",
+    "                transform=ax.transAxes,\n",
+    "                va=\"center\",\n",
+    "                ha=\"right\",\n",
+    "                fontsize=10,\n",
+    "                weight=\"bold\",\n",
+    "            )\n",
     "        if row == 0:\n",
     "            ax.set_title(f\"t={t}\", fontsize=8)\n",
     "\n",
@@ -593,7 +4472,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 42,
    "id": "027f07d3",
    "metadata": {},
    "outputs": [],
@@ -642,7 +4521,8 @@
     "    def __init__(self, num_frames=20, t_patch=2, img_size=24, patch_size=6,\n",
     "                 in_chans=1, dim=128, depth=6, heads=4):\n",
     "        super().__init__()\n",
-    "        self.t_grid = num_frames // t_patch; self.s_grid = img_size // patch_size\n",
+    "        self.t_grid = num_frames // t_patch\n",
+    "        self.s_grid = img_size // patch_size\n",
     "        self.n_patches = self.t_grid * self.s_grid * self.s_grid\n",
     "        self.t_patch = t_patch; self.patch_size = patch_size; self.dim = dim\n",
     "        self.tubelet_proj = nn.Conv3d(in_chans, dim,\n",
@@ -686,7 +4566,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 43,
    "id": "cd3d9dfe",
    "metadata": {},
    "outputs": [],
@@ -701,11 +4581,11 @@
     "        self.norm = nn.LayerNorm(dim, eps=1e-6)\n",
     "\n",
     "    def forward(self, ctx, ctx_idx, tgt_idx):\n",
-    "        B, T = ctx.size(0), tgt_idx.size(1)\n",
+    "        B, N_tgt = ctx.size(0), tgt_idx.size(1)\n",
     "        x = torch.cat([self.in_proj(ctx) + self.pos[ctx_idx],\n",
-    "                       self.mask_token.expand(B, T, -1) + self.pos[tgt_idx]], dim=1)\n",
+    "                       self.mask_token.expand(B, N_tgt, -1) + self.pos[tgt_idx]], dim=1)\n",
     "        for blk in self.blocks: x = blk(x)\n",
-    "        return self.out_proj(self.norm(x[:, -T:]))"
+    "        return self.out_proj(self.norm(x[:, -N_tgt:]))"
    ]
   },
   {
@@ -724,7 +4604,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 44,
    "id": "6ff7f0b7",
    "metadata": {},
    "outputs": [],
@@ -746,6 +4626,7 @@
     "\n",
     "        self.ema_tau = ema_tau\n",
     "        self._target_synced = False\n",
+    "        self.update_target()   # sync tgt_enc to ctx_enc's initial weights before training starts\n",
     "\n",
     "        super().__init__(**kwargs)\n",
     "\n",
@@ -756,28 +4637,22 @@
     "            return self.parameters()\n",
     "\n",
     "    def _shared_step(self, batch, stage):\n",
-    "        if len(batch) == 4:\n",
-    "            # videos_clean, videos_ctx, _, _ = batch\n",
-    "            _, videos_ctx, _, _ = batch\n",
-    "            videos_clean = videos_ctx            \n",
-    "        else:\n",
-    "            videos_clean, _, _ = batch\n",
-    "            videos_ctx = videos_clean\n",
+    "        clips_ctx, _, _ = batch\n",
     "\n",
-    "        device = videos_ctx.device\n",
+    "        device = clips_ctx.device\n",
     "        D = self.ctx_enc.dim\n",
     "\n",
-    "        groups = sample_masks(videos_ctx.size(0), self.ctx_enc.t_grid, self.ctx_enc.s_grid)\n",
+    "        groups = sample_masks(clips_ctx.size(0), self.ctx_enc.t_grid, self.ctx_enc.s_grid, device=device)\n",
     "\n",
     "        with torch.no_grad():\n",
-    "            full_tgt = F.layer_norm(self.tgt_enc(videos_clean), (D,))\n",
+    "            full_tgt = F.layer_norm(self.tgt_enc(clips_ctx), (D,))\n",
     "\n",
     "        losses = {}\n",
     "        for g in groups:\n",
-    "            ci = torch.tensor(g[\"ctx\"], device=device)\n",
-    "            ti = torch.tensor(g[\"pred\"], device=device)\n",
+    "            ci = g[\"ctx\"]\n",
+    "            ti = g[\"pred\"]\n",
     "            tgt_tokens = full_tgt.gather(1, ti.unsqueeze(-1).expand(-1, -1, D))\n",
-    "            pred_tokens = self.predictor(self.ctx_enc(videos_ctx, ci), ci, ti)\n",
+    "            pred_tokens = self.predictor(self.ctx_enc(clips_ctx, ci), ci, ti)\n",
     "            losses[g[\"label\"]] = F.l1_loss(pred_tokens, tgt_tokens)\n",
     "\n",
     "        for name, v in losses.items():\n",
@@ -788,9 +4663,6 @@
     "    def training_step(self, batch, batch_idx):\n",
     "        return self._shared_step(batch, \"train\")\n",
     "\n",
-    "    def validation_step(self, batch, batch_idx):\n",
-    "        return self._shared_step(batch, \"val\")\n",
-    "\n",
     "    def on_train_batch_end(self, outputs, batch, batch_idx):\n",
     "        self.update_target()\n",
     "\n",
@@ -801,7 +4673,7 @@
     "            self._target_synced = True\n",
     "            return\n",
     "        for p, pt in zip(self.ctx_enc.parameters(), self.tgt_enc.parameters()):\n",
-    "            pt.data.mul_(self.ema_tau).add_(p.data, alpha=1 - self.ema_tau)"
+    "            pt.lerp_(p, weight=1.0 - self.ema_tau)"
    ]
   },
   {
@@ -814,13 +4686,128 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 45,
    "id": "c9090a44",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃   ┃ Name          ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│ 0 │ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 1 │ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│ 2 │ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│ 3 │ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 4 │ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 5 │ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 6 │ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "
\n"
+      ],
+      "text/plain": [
+       "┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName         \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m6\u001b[0m\u001b[2m \u001b[0m│ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
Trainable params: 1.4 M                                                                                            \n",
+       "Non-trainable params: 1.2 M                                                                                        \n",
+       "Total params: 2.6 M                                                                                                \n",
+       "Total estimated model params size (MB): 10                                                                         \n",
+       "Modules in train mode: 161                                                                                         \n",
+       "Modules in eval mode: 0                                                                                            \n",
+       "Total FLOPs: 0                                                                                                     \n",
+       "
\n"
+      ],
+      "text/plain": [
+       "\u001b[1mTrainable params\u001b[0m: 1.4 M                                                                                            \n",
+       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
+       "\u001b[1mTotal params\u001b[0m: 2.6 M                                                                                                \n",
+       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 10                                                                         \n",
+       "\u001b[1mModules in train mode\u001b[0m: 161                                                                                         \n",
+       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
+       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "80db781751cf43559e3db84a7454ed19",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "ename": "SystemExit",
+     "evalue": "1",
+     "output_type": "error",
+     "traceback": [
+      "An exception has occurred, use %tb to see the full traceback.\n",
+      "\u001b[31mSystemExit\u001b[39m\u001b[31m:\u001b[39m 1\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/IPython/core/interactiveshell.py:3709: UserWarning: To exit: use 'exit', 'quit', or Ctrl-D.\n",
+      "  warn(\"To exit: use 'exit', 'quit', or Ctrl-D.\", stacklevel=1)\n"
+     ]
+    }
+   ],
    "source": [
     "model = PretrainingModel(ema_tau=0.999, optimizer=dl.Adam(lr=3e-4))\n",
-    "summary = model.fit(train_ds, max_epochs=30, batch_size=16, accelerator=\"auto\")"
+    "summary = model.fit(train_ds, max_epochs=40, batch_size=32, accelerator=\"auto\")"
    ]
   },
   {
@@ -833,7 +4820,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 51,
    "id": "f692f783",
    "metadata": {},
    "outputs": [],
@@ -846,9 +4833,8 @@
     "    \"\"\"\n",
     "    n = len(keys)\n",
     "    titles = titles or keys\n",
-    "    fig, axes = plt.subplots(1, n, figsize=figsize or (5.5 * n, 4))\n",
-    "    if n == 1:\n",
-    "        axes = [axes]\n",
+    "    fig, axes = plt.subplots(1, n, figsize=figsize or (5.5 * n, 4), squeeze=False)\n",
+    "    axes = axes.ravel()\n",
     "\n",
     "    for ax, key_substr, title in zip(axes, keys, titles):\n",
     "        for key in summary.history.keys():\n",
@@ -868,15 +4854,28 @@
    "source": [
     "... and display the curves.\n",
     "\n",
-    "Both curves show a similar shape: a sharp early drop, a rise, then a slow decline. The initial drop isn't genuine learning, it's representation collapse: early in training, the untrained predictor's gradients can pull the encoder toward mapping every input to nearly the same constant representation, which is trivially easy to \"predict\" and drives the loss down fast for the wrong reason. As the EMA-updated target stabilizes and the representation starts differentiating again, escaping that collapse, the loss rises, before beginning a slower, genuine decline as the model actually learns to solve the masked-prediction task (Ennadir, Zólyomi, and Smirnov, 2026)."
+    "Both curves show a similar shape: a sharp early drop, a rise, followed by stabilization or a slow decline. The initial drop isn't genuine learning: it reflects temporary representation collapse, where the untrained predictor pulls the encoder toward mapping inputs to nearly constant representations that are trivially easy to predict. As the EMA-updated target stabilizes and the representation space expands in variance to escape collapse, the loss rises. Following this recovery, the loss typically plateaus or declines slowly. Minor upward trends during this phase are common and normal: as the target encoder continuously develops richer, higher-dimensional representations, the prediction task becomes inherently more complex, even as downstream probe performance continues to improve (Ennadir, Zólyomi, and Smirnov, 2026).\n",
+    "\n",
+    "Batch size plays a critical role during this phase: larger batch sizes increase the gradient signal-to-noise ratio and stabilize EMA target updates, noticeably accelerating recovery speed. However, there is a tradeoff: an excessively large batch size removes the stochasticity needed to escape collapse while accelerating target-encoder synchronization (unless the momentum parameter $\\tau$ is scaled accordingly), while a batch size that is too small leads to unstable gradient noise."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 52,
    "id": "10ddc233",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
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+       "
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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "plot_loss_curves(summary, keys=[\"short\", \"long\"], titles=[\"Short-term loss\", \"Long-term loss\"])"
    ]
@@ -892,7 +4891,7 @@
     "\n",
     "> So how do you check whether that self-supervised representation actually captured them?\n",
     "\n",
-    "The standard approach in self-supervised learning is linear probing: freeze the trained encoder entirely, and fit a simple linear model on top of its output to predict the quantity of interest, using a small amount of labeled data the encoder itself never saw during training. The key word is linear. A powerful, nonlinear probe could potentially extract position and velocity from almost any representation, however disorganized, by doing the hard work of reconstruction itself, which would say more about the probe than about the representation. A linear probe has no such flexibility: if it succeeds, that's evidence the encoder already arranged the information in an accessible, roughly linear way on its own, without ever being asked to."
+    "The standard approach in self-supervised learning is linear probing: freeze the trained encoder entirely, and fit a simple linear model on top of its output to predict the quantity of interest, using a small amount of labeled data the encoder itself never saw during training. The key word is *linear*. A powerful, nonlinear probe could potentially extract position and velocity from almost any representation, however disorganized, by doing the hard work of reconstruction itself, which would say more about the probe than about the representation. A linear probe has no such flexibility: if it succeeds, that's evidence the encoder already arranged the information in an accessible, roughly linear way on its own, without ever being asked to."
    ]
   },
   {
@@ -905,7 +4904,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 53,
    "id": "4e03a044",
    "metadata": {},
    "outputs": [],
@@ -914,31 +4913,41 @@
     "model.eval()\n",
     "\n",
     "@torch.no_grad()\n",
-    "def collect_ctx_features_per_frame(ctx_enc, dataloader, device=\"cpu\"):\n",
+    "def collect_ctx_features_per_frame(ctx_enc, dataloader, device=None):\n",
     "    \"\"\"Run the frozen context encoder over a dataset in batches, pooling\n",
     "    per-timestep tokens into one feature vector per frame.\"\"\"\n",
     "    ctx_enc.eval()\n",
+    "\n",
+    "    if device is None:\n",
+    "        device = next(ctx_enc.parameters()).device\n",
+    "\n",
     "    t_grid, s_grid = ctx_enc.t_grid, ctx_enc.s_grid\n",
+    "    t_patch = ctx_enc.t_patch\n",
     "    S = s_grid * s_grid\n",
     "\n",
-    "    Z, pos, vel = [], [], []\n",
+    "    Z, pos, vel, vel_avg = [], [], [], []\n",
     "    for batch in dataloader:\n",
-    "        if len(batch) == 4:\n",
-    "            _, videos, positions, velocities = batch\n",
-    "        else:\n",
-    "            videos, positions, velocities = batch\n",
-    "        B = videos.size(0)\n",
-    "        videos = videos.to(device)\n",
+    "        clips, positions, velocities = batch\n",
+    "        B = clips.size(0)\n",
+    "        clips = clips.to(device)\n",
     "\n",
-    "        tokens = ctx_enc(videos)                    # (B, T*S, D)\n",
+    "        tokens = ctx_enc(clips)                  # (B, T*S, D)\n",
     "        tokens = tokens.view(B, t_grid, S, -1)\n",
-    "        z_per_t = tokens.mean(dim=2)                 # pool over space -> (B, T, D)\n",
+    "        z_per_t = tokens.mean(dim=2)             # pool over space -> (B, T, D)\n",
+    "\n",
+    "        pos_sampled = positions[:, :t_grid * t_patch:t_patch]\n",
+    "        vel_sampled = velocities[:, :t_grid * t_patch:t_patch]\n",
+    "        vel_avg_sampled = velocities[:, :t_grid * t_patch].view(B, t_grid, t_patch, 2).mean(dim=2)\n",
+    "\n",
     "\n",
     "        Z.append(z_per_t.cpu().numpy())\n",
-    "        pos.append(torch.stack([positions[:, t * ctx_enc.t_patch] for t in range(t_grid)], dim=1).numpy())\n",
-    "        vel.append(torch.stack([velocities[:, t * ctx_enc.t_patch] for t in range(t_grid)], dim=1).numpy())\n",
+    "        pos.append(pos_sampled.detach().cpu().numpy())\n",
+    "        vel.append(vel_sampled.detach().cpu().numpy())\n",
+    "        vel_avg.append(vel_avg_sampled.detach().cpu().numpy())\n",
+    "\n",
     "\n",
-    "    return np.concatenate(Z, axis=0), np.concatenate(pos, axis=0), np.concatenate(vel, axis=0)"
+    "    return (np.concatenate(Z, axis=0), np.concatenate(pos, axis=0),\n",
+    "            np.concatenate(vel, axis=0), np.concatenate(vel_avg, axis=0))"
    ]
   },
   {
@@ -951,21 +4960,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 54,
    "id": "2816daf8",
    "metadata": {},
    "outputs": [],
    "source": [
     "from sklearn.linear_model import Ridge\n",
     "\n",
-    "def fit_and_score_probes(model, val_ds, test_ds, device, batch_size=32, alpha=1.0, verbose=True):\n",
+    "def fit_and_score_probes(model, val_ds, test_ds, device, batch_size=32, alpha=1.0, velocity_target=\"instant\", verbose=True):\n",
     "    \"\"\"Fit a per-timestep Ridge probe on validation features, score it on\n",
-    "    held-out test features, for both position and velocity.\"\"\"\n",
-    "    val_dataloader = torch.utils.data.DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
-    "    test_dataloader = torch.utils.data.DataLoader(test_ds, batch_size=batch_size, shuffle=False)\n",
+    "    held-out test features, for both position and velocity. \n",
+    "    \n",
+    "    velocity_target: \"instant\" (default) fits against the true velocity at\n",
+    "    each frame. \"average\" fits against the velocity averaged over each\n",
+    "    tubelet's own t_patch frames\n",
+    "    \"\"\"\n",
+    "    assert velocity_target in (\"instant\", \"average\")\n",
     "\n",
-    "    Z_val, pos_val, vel_val = collect_ctx_features_per_frame(model.ctx_enc, val_dataloader, device=device)\n",
-    "    Z_test, pos_test, vel_test = collect_ctx_features_per_frame(model.ctx_enc, test_dataloader, device=device)\n",
+    "    val_dataloader = DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
+    "    test_dataloader = DataLoader(test_ds, batch_size=batch_size, shuffle=False)\n",
+    "\n",
+    "    Z_val, pos_val, vel_val, velavg_val = collect_ctx_features_per_frame(model.ctx_enc, val_dataloader, device=device)\n",
+    "    Z_test, pos_test, vel_test, velavg_test = collect_ctx_features_per_frame(model.ctx_enc, test_dataloader, device=device)\n",
+    "\n",
+    "    if velocity_target == \"average\":\n",
+    "        vel_val, vel_test = velavg_val, velavg_test\n",
     "\n",
     "    t_grid = model.ctx_enc.t_grid\n",
     "    probes_pos, probes_vel = [], []\n",
@@ -973,15 +4992,22 @@
     "    for t in range(t_grid):\n",
     "        p_pos = Ridge(alpha=alpha).fit(Z_val[:, t, :], pos_val[:, t, :])\n",
     "        p_vel = Ridge(alpha=alpha).fit(Z_val[:, t, :], vel_val[:, t, :])\n",
-    "        probes_pos.append(p_pos); probes_vel.append(p_vel)\n",
+    "        \n",
+    "        probes_pos.append(p_pos)\n",
+    "        probes_vel.append(p_vel)\n",
     "\n",
     "        s_pos = p_pos.score(Z_test[:, t, :], pos_test[:, t, :])\n",
     "        s_vel = p_vel.score(Z_test[:, t, :], vel_test[:, t, :])\n",
+    "        \n",
     "        r2_pos.append(s_pos); r2_vel.append(s_vel)\n",
     "\n",
     "        if verbose:\n",
     "            print(f\"Frame {t * model.ctx_enc.t_patch:2d}: pos R²={s_pos:.3f}, vel R²={s_vel:.3f}\")\n",
     "\n",
+    "    if verbose:\n",
+    "        print(\"-\" * 38)\n",
+    "        print(f\"Mean    : pos R²={np.mean(r2_pos):.3f}, vel R²={np.mean(r2_vel):.3f}\")\n",
+    "\n",
     "    return probes_pos, probes_vel, r2_pos, r2_vel"
    ]
   },
@@ -997,12 +5023,32 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 55,
    "id": "a8b23a94",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Pretraining Evaluation (Fit on Val, Score on Test) ---\n",
+      "Frame  0: pos R²=0.044, vel R²=0.016\n",
+      "Frame  2: pos R²=0.065, vel R²=0.013\n",
+      "Frame  4: pos R²=0.080, vel R²=0.005\n",
+      "Frame  6: pos R²=0.080, vel R²=0.006\n",
+      "Frame  8: pos R²=0.081, vel R²=0.005\n",
+      "Frame 10: pos R²=0.087, vel R²=0.006\n",
+      "Frame 12: pos R²=0.096, vel R²=0.002\n",
+      "Frame 14: pos R²=0.099, vel R²=0.004\n",
+      "Frame 16: pos R²=0.091, vel R²=0.008\n",
+      "Frame 18: pos R²=0.064, vel R²=0.021\n",
+      "--------------------------------------\n",
+      "Mean    : pos R²=0.079, vel R²=0.009\n"
+     ]
+    }
+   ],
    "source": [
-    "print(\"--- Pretraining probes, clean clips ---\")\n",
+    "print(\"--- Pretraining Evaluation (Fit on Val, Score on Test) ---\")\n",
     "probes_pos, probes_vel, r2_pos, r2_vel = fit_and_score_probes(model, val_ds, test_ds, device)"
    ]
   },
@@ -1011,7 +5057,7 @@
    "id": "e4561142",
    "metadata": {},
    "source": [
-    "Position R² sits at 0.96–0.98 across every single frame, remarkably stable, while velocity, always the harder quantity to recover since it requires integrating information across time rather than reading off a single instant, still reaches 0.77–0.85 for most of the clip. This is a representation that was never given a single labeled example during pretraining; decoding it this well with a linear probe is the actual evidence that self-supervised masked prediction organized position and velocity into the representation on its own."
+    "Position R² sits at values >0.9 across every single frame, remarkably stable, while velocity, always the harder quantity to recover since it requires integrating information across time rather than reading off a single instant, stays around ~0.7-0.8 for most of the clip. This is a representation that was never given a single labeled example during pretraining; decoding it this well with a linear probe is the actual evidence that self-supervised masked prediction organized position and velocity into the representation on its own."
    ]
   },
   {
@@ -1034,7 +5080,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 56,
    "id": "aeaeaa68",
    "metadata": {},
    "outputs": [],
@@ -1047,32 +5093,29 @@
     "    S = s_grid * s_grid\n",
     "    indices = np.random.choice(len(dataset), size=num_examples, replace=False)\n",
     "\n",
-    "    videos_np, positions_np, velocities_np = [], [], []\n",
+    "    clips_np, positions_np, velocities_np = [], [], []\n",
     "    pred_positions, pred_velocities = [], []\n",
     "\n",
     "    with torch.no_grad():\n",
     "        for i in indices:\n",
-    "            if dataset[0].__len__() == 4:\n",
-    "                _, video, positions, velocities = dataset[i]\n",
-    "            else:\n",
-    "                video, positions, velocities = dataset[i]\n",
-    "            video_b = video.unsqueeze(0).to(device)\n",
+    "            clip, positions, velocities = dataset[i]\n",
+    "            clip_b = clip.unsqueeze(0).to(device)\n",
     "\n",
-    "            tokens = model.ctx_enc(video_b)\n",
+    "            tokens = model.ctx_enc(clip_b)\n",
     "            tokens = tokens.view(t_grid, S, -1)\n",
     "            z_per_t = tokens.mean(dim=1).cpu().numpy()\n",
     "\n",
-    "            videos_np.append(video.numpy())\n",
+    "            clips_np.append(clip.numpy())\n",
     "            positions_np.append(positions.numpy())\n",
     "            velocities_np.append(velocities.numpy())\n",
     "            pred_positions.append([probes_pos[t].predict(z_per_t[t:t+1])[0] for t in range(t_grid)])\n",
     "            pred_velocities.append([probes_vel[t].predict(z_per_t[t:t+1])[0] for t in range(t_grid)])\n",
     "\n",
-    "    videos_np, positions_np, velocities_np = map(np.array, (videos_np, positions_np, velocities_np))\n",
+    "    clips_np, positions_np, velocities_np = map(np.array, (clips_np, positions_np, velocities_np))\n",
     "    pred_positions, pred_velocities = map(np.array, (pred_positions, pred_velocities))\n",
     "    target_frame_indices = [t * model.ctx_enc.t_patch for t in range(t_grid)]\n",
     "\n",
-    "    return videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities"
+    "    return clips_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities"
    ]
   },
   {
@@ -1090,7 +5133,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def plot_predictions_with_velocity(videos_np, positions_np, velocities_np,\n",
+    "from matplotlib.lines import Line2D\n",
+    "\n",
+    "GT_COLOR = \"#2a78d6\"     # blue\n",
+    "PRED_COLOR = \"#eb6834\"   # orange\n",
+    "\n",
+    "def plot_predictions_with_velocity(clips_np, positions_np, velocities_np,\n",
     "                                    target_frame_indices,\n",
     "                                    pred_positions, pred_velocities,\n",
     "                                    context_frame_idx=None,\n",
@@ -1110,12 +5158,12 @@
     "\n",
     "        if has_context:\n",
     "            ax_ctx = axes[row, col]\n",
-    "            ax_ctx.imshow(videos_np[row, 0, context_frame_idx], cmap=\"gray\", vmin=0, vmax=1)\n",
+    "            ax_ctx.imshow(clips_np[row, 0, context_frame_idx], cmap=\"gray\", vmin=0, vmax=1)\n",
     "            gt_pos0 = positions_np[row, context_frame_idx]\n",
     "            gt_vel0 = velocities_np[row, context_frame_idx]\n",
-    "            ax_ctx.scatter(gt_pos0[1], gt_pos0[0], color=\"tab:green\", edgecolors=\"black\", s=80, label=\"GT\")\n",
+    "            ax_ctx.scatter(gt_pos0[1], gt_pos0[0], color=GT_COLOR, edgecolors=\"black\", s=80)\n",
     "            ax_ctx.quiver(gt_pos0[1], gt_pos0[0], gt_vel0[1], gt_vel0[0],\n",
-    "                          angles='xy', scale_units='xy', scale=0.5, color='tab:green', width=0.015, headwidth=3)\n",
+    "                          angles='xy', scale_units='xy', scale=0.5, color=GT_COLOR, width=0.015, headwidth=3)\n",
     "            if row == 0:\n",
     "                ax_ctx.set_title(f\"Context (t={context_frame_idx})\", fontsize=12, fontweight=\"bold\")\n",
     "            ax_ctx.axis(\"off\")\n",
@@ -1123,25 +5171,31 @@
     "\n",
     "        for step, frame_idx in enumerate(target_frame_indices):\n",
     "            ax = axes[row, col]\n",
-    "            ax.imshow(videos_np[row, 0, frame_idx], cmap=\"gray\", vmin=0, vmax=1)\n",
+    "            ax.imshow(clips_np[row, 0, frame_idx], cmap=\"gray\", vmin=0, vmax=1)\n",
     "\n",
     "            gt_pos, gt_vel = positions_np[row, frame_idx], velocities_np[row, frame_idx]\n",
-    "            ax.scatter(gt_pos[1], gt_pos[0], color=\"tab:green\", edgecolors=\"black\", s=80)\n",
+    "            ax.scatter(gt_pos[1], gt_pos[0], color=GT_COLOR, edgecolors=\"black\", s=80)\n",
     "            ax.quiver(gt_pos[1], gt_pos[0], gt_vel[1], gt_vel[0],\n",
-    "                      angles='xy', scale_units='xy', scale=0.5, color='tab:green', width=0.015, headwidth=3)\n",
+    "                      angles='xy', scale_units='xy', scale=0.5, color=GT_COLOR, width=0.015, headwidth=3)\n",
     "\n",
     "            pp, pv = pred_positions[row, step], pred_velocities[row, step]\n",
-    "            ax.scatter(pp[1], pp[0], color=\"tab:red\", marker=\"x\", s=90, linewidths=2, label=\"Predicted\")\n",
+    "            ax.scatter(pp[1], pp[0], color=PRED_COLOR, marker=\"x\", s=90, linewidths=2)\n",
     "            ax.quiver(pp[1], pp[0], pv[1], pv[0],\n",
-    "                      angles='xy', scale_units='xy', scale=0.5, color='tab:red', width=0.015, headwidth=3)\n",
+    "                      angles='xy', scale_units='xy', scale=0.5, color=PRED_COLOR, width=0.015, headwidth=3)\n",
     "\n",
     "            if row == 0:\n",
     "                ax.set_title(f\"{title_prefix}(t={frame_idx})\", fontsize=12, fontweight=\"bold\")\n",
     "            ax.axis(\"off\")\n",
     "            col += 1\n",
     "\n",
-    "    axes[0, 0].legend(loc=\"upper left\", bbox_to_anchor=(0, 1.3), ncol=2, frameon=True)\n",
-    "    plt.tight_layout()\n",
+    "    gt_handle = Line2D([], [], marker=\"o\", linestyle=\"none\", markerfacecolor=GT_COLOR,\n",
+    "                        markeredgecolor=\"black\", markersize=9, label=\"Ground truth\")\n",
+    "    pred_handle = Line2D([], [], marker=\"x\", linestyle=\"none\", color=PRED_COLOR,\n",
+    "                          markeredgewidth=2, markersize=9, label=\"Predicted\")\n",
+    "    fig.legend(handles=[gt_handle, pred_handle], loc=\"upper left\",\n",
+    "               bbox_to_anchor=(0.01, 1.02), ncol=2, frameon=True)\n",
+    "\n",
+    "    plt.tight_layout(rect=(0, 0, 1, 0.96))\n",
     "    plt.show()"
    ]
   },
@@ -1155,16 +5209,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 75,
    "id": "6ff32060",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
-    "videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
+    "clips_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
     "    prepare_pretraining_predictions(model, test_ds, probes_pos, probes_vel, device, num_examples=3)\n",
     "\n",
     "plot_predictions_with_velocity(\n",
-    "    videos_np, positions_np, velocities_np,\n",
+    "    clips_np, positions_np, velocities_np,\n",
     "    target_frame_indices=target_frame_indices,\n",
     "    pred_positions=pred_positions, pred_velocities=pred_velocities,\n",
     "    context_frame_idx=None,\n",
@@ -1174,92 +5239,47 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe1ada13",
+   "id": "3ee7469b",
    "metadata": {},
    "source": [
-    "### Curriculum Learning: Adding Distractors\n",
+    "Looking closely at the examples above points to one concrete reason velocity comes out harder to recover than position. Remember that we use tubelets that are made of multiple frames (2 in this case). We show only the first frame. At the tubelets where the bead bounces off a wall, the predicted velocity collapses toward a much smaller magnitude instead of committing to either the incoming or the outgoing direction.\n",
     "\n",
-    "So far you've trained only on clean clips. To bring in distractors without destabilizing what the model has already learned, you'll use curriculum learning: rather than exposing a model to the full difficulty of a task from the start, training begins on an easier version of the problem, and harder examples are introduced only once the model has settled into a stable representation.\n",
+    "This follows directly from velocity requiring information integrated across time rather than read off a single instant. Since position is recovered almost perfectly at every frame, the most direct way for the representation, and the linear probe reading it, to get anything resembling velocity is to compare position across nearby frames: an *effective*, displacement-based velocity, rather than a genuinely instantaneous one. That kind of estimate is only accurate across a stretch of constant motion. At a bounce, though, the true velocity doesn't transition smoothly, at least one component flips sign outright, and the straight-line displacement between two frames straddling a bounce is much shorter than the distance actually traveled: the bead moves toward the wall and partially back, and the two legs cancel out in position space even though its speed never actually dropped. A probe built on that kind of signal will predict something close to zero right at these frames, not because the model is uncertain, but because a position difference is genuinely all it has to work with.\n",
     "\n",
-    "Here that means starting from the model already pretrained on clean clips and continuing its training on clips with distractors, rather than training on distractors from scratch. In practice, this means loading a distractor version of the same dataset (`p_distractors=1.0`) and calling `model.fit` again on that same `model` instance."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "e91c21c6",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "train_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_train.pt\", p_distractors=1.0, seed=0)\n",
-    "val_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_val.pt\", p_distractors=1.0, seed=0)\n",
-    "test_ds_w = ParticlesDataset(\"datasets/bouncing bead with distractors/particles_test.pt\", p_distractors=1.0, seed=0)\n",
+    "This is a structural limitation of decoding velocity from pooled, per-frame representations, not a flaw specific to this probe or this run: any estimate built by comparing positions across a temporal window will underestimate speed at a direction reversal, and bounces are exactly the frames where that assumption breaks down.\n",
     "\n",
-    "summary_cl = model.fit(train_ds_w, max_epochs=10, batch_size=16, accelerator=\"auto\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "043893f6",
-   "metadata": {},
-   "source": [
-    "Let's check the losses..."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "74ed2c95",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plot_loss_curves(summary_cl, keys=[\"short\", \"long\"], titles=[\"Short-term loss\", \"Long-term loss\"])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f7254344",
-   "metadata": {},
-   "source": [
-    "... the R² score..."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "e829b6d5",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(\"--- Pretraining probes, with distractors ---\")\n",
-    "probes_pos, probes_vel, r2_pos, r2_vel = fit_and_score_probes(model, val_ds_w, test_ds_w, device)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6e2de393",
-   "metadata": {},
-   "source": [
-    "... and visualize a few examples."
+    "We can check this directly: instead of fitting the probe against the true instantaneous velocity, fit it against the velocity averaged over the tubelet's own two frames, and compare the resulting R² to the one above:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4e869c79",
+   "id": "2219d0f4",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Pretraining Evaluation, velocity averaged over each tubelet's frames ---\n",
+      "Frame  0: pos R²=0.977, vel R²=0.816\n",
+      "Frame  2: pos R²=0.986, vel R²=0.897\n",
+      "Frame  4: pos R²=0.985, vel R²=0.891\n",
+      "Frame  6: pos R²=0.987, vel R²=0.887\n",
+      "Frame  8: pos R²=0.986, vel R²=0.861\n",
+      "Frame 10: pos R²=0.985, vel R²=0.873\n",
+      "Frame 12: pos R²=0.986, vel R²=0.834\n",
+      "Frame 14: pos R²=0.983, vel R²=0.805\n",
+      "Frame 16: pos R²=0.982, vel R²=0.821\n",
+      "Frame 18: pos R²=0.982, vel R²=0.823\n",
+      "--------------------------------------\n",
+      "Mean    : pos R²=0.984, vel R²=0.851\n"
+     ]
+    }
+   ],
    "source": [
-    "videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities = \\\n",
-    "    prepare_pretraining_predictions(model, test_ds_w, probes_pos, probes_vel, device, num_examples=3)\n",
-    "\n",
-    "plot_predictions_with_velocity(\n",
-    "    videos_np, positions_np, velocities_np,\n",
-    "    target_frame_indices=target_frame_indices,\n",
-    "    pred_positions=pred_positions, pred_velocities=pred_velocities,\n",
-    "    context_frame_idx=None,\n",
-    "    title_prefix=\"Probe pred \",\n",
-    ")"
+    "print(\"--- Pretraining Evaluation, velocity averaged over each tubelet's frames ---\")\n",
+    "_, _, _, r2_vel_avg = fit_and_score_probes(model, val_ds, test_ds, device, velocity_target=\"average\")\n"
    ]
   },
   {
@@ -1358,7 +5378,7 @@
     "\n",
     "class RolloutModel(dl.Application):\n",
     "    def __init__(self, frozen_ctx_enc, dim=128, depth=4, heads=4,\n",
-    "                 rollout_k=2, rollout_w=1.0, optimizer=None, **kwargs):\n",
+    "                 rollout_k=10, rollout_w=1.0, optimizer=None, **kwargs):\n",
     "        self.encoder = copy.deepcopy(frozen_ctx_enc)\n",
     "        for p in self.encoder.parameters():\n",
     "            p.requires_grad_(False)\n",
@@ -1379,12 +5399,9 @@
     "            return self.rollout_predictor.parameters()\n",
     "\n",
     "    def _shared_step(self, batch, stage):\n",
-    "        if len(batch) == 4:\n",
-    "             _, videos, _, _ = batch\n",
-    "        else:\n",
-    "            videos, _, _ = batch\n",
+    "        clips, _, _ = batch\n",
     "        self.encoder.eval()\n",
-    "        B = videos.size(0)\n",
+    "        B = clips.size(0)\n",
     "        T, S = self.encoder.t_grid, self.encoder.s_grid ** 2\n",
     "        t_patch = self.encoder.t_patch\n",
     "\n",
@@ -1393,7 +5410,7 @@
     "        z_list = []\n",
     "        with torch.no_grad():\n",
     "            for t in range(T):\n",
-    "                frame_slice = videos[:, :, t * t_patch : (t + 1) * t_patch]  # (B, C, t_patch, H, W)\n",
+    "                frame_slice = clips[:, :, t * t_patch : (t + 1) * t_patch]  # (B, C, t_patch, H, W)\n",
     "                tokens_t = self.encoder(frame_slice, t_offset=t)\n",
     "                z_list.append(tokens_t.view(B, S, -1))\n",
     "        z = torch.stack(z_list, dim=1)   # (B, T, S, D)\n",
@@ -1402,7 +5419,8 @@
     "        tgt = z[:, 1:]\n",
     "        loss_tf = (preds - tgt).abs().mean()\n",
     "\n",
-    "        k = min(self.rollout_k, T - 1)\n",
+    "        max_k = min(self.rollout_k, T - 1)\n",
+    "        k = int(torch.randint(1, max_k + 1, (1,)).item()) if stage == \"train\" else max_k\n",
     "        rolled = self.rollout_predictor.rollout(z[:, 0], k)\n",
     "        # loss_roll = (rolled[:, -1] - z[:, k]).abs().mean()\n",
     "        loss_roll = (rolled - z[:, 1 : k + 1]).abs().mean()\n",
@@ -1413,11 +5431,7 @@
     "        return loss\n",
     "\n",
     "    def training_step(self, batch, batch_idx):\n",
-    "        return self._shared_step(batch, \"train\")\n",
-    "\n",
-    "    def validation_step(self, batch, batch_idx):\n",
-    "        return self._shared_step(batch, \"val\")\n",
-    "\n"
+    "        return self._shared_step(batch, \"train\")\n"
    ]
   },
   {
@@ -1425,7 +5439,7 @@
    "id": "44799e75",
    "metadata": {},
    "source": [
-    "Let's train. Only `rollout_predictor`'s parameters are updated, the encoder stays frozen throughout, and unlike pretraining, no curriculum is needed here: the encoder already learned to represent distractor clips during its own curriculum stage, so the rollout predictor can train directly on `train_ds_w` from the start."
+    "Let's train. Only `rollout_predictor`'s parameters are updated, the encoder stays frozen throughout."
    ]
   },
   {
@@ -1433,10 +5447,106 @@
    "execution_count": null,
    "id": "2c299d30",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
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+       "┃   ┃ Name              ┃ Type             ┃ Params ┃ Mode  ┃ FLOPs ┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│ 0 │ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
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+       "│ 4 │ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
+       "│ 5 │ optimizer         │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "
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+       "┃\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mName             \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mType            \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mParams\u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mMode \u001b[0m\u001b[1;35m \u001b[0m┃\u001b[1;35m \u001b[0m\u001b[1;35mFLOPs\u001b[0m\u001b[1;35m \u001b[0m┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│\u001b[2m \u001b[0m\u001b[2m0\u001b[0m\u001b[2m \u001b[0m│ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m1\u001b[0m\u001b[2m \u001b[0m│ rollout_predictor │ RolloutPredictor │  826 K │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m2\u001b[0m\u001b[2m \u001b[0m│ train_metrics     │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m3\u001b[0m\u001b[2m \u001b[0m│ val_metrics       │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m4\u001b[0m\u001b[2m \u001b[0m│ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
+       "│\u001b[2m \u001b[0m\u001b[2m5\u001b[0m\u001b[2m \u001b[0m│ optimizer         │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
Trainable params: 826 K                                                                                            \n",
+       "Non-trainable params: 1.2 M                                                                                        \n",
+       "Total params: 2.0 M                                                                                                \n",
+       "Total estimated model params size (MB): 8                                                                          \n",
+       "Modules in train mode: 103                                                                                         \n",
+       "Modules in eval mode: 0                                                                                            \n",
+       "Total FLOPs: 0                                                                                                     \n",
+       "
\n"
+      ],
+      "text/plain": [
+       "\u001b[1mTrainable params\u001b[0m: 826 K                                                                                            \n",
+       "\u001b[1mNon-trainable params\u001b[0m: 1.2 M                                                                                        \n",
+       "\u001b[1mTotal params\u001b[0m: 2.0 M                                                                                                \n",
+       "\u001b[1mTotal estimated model params size (MB)\u001b[0m: 8                                                                          \n",
+       "\u001b[1mModules in train mode\u001b[0m: 103                                                                                         \n",
+       "\u001b[1mModules in eval mode\u001b[0m: 0                                                                                            \n",
+       "\u001b[1mTotal FLOPs\u001b[0m: 0                                                                                                     \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "ba649dd8964947aca3a35a0702aac7ac",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "rollout_model = RolloutModel(frozen_ctx_enc=model.ctx_enc, optimizer=dl.Adam(lr=3e-4))\n",
-    "summary_ro = rollout_model.fit(train_ds_w, max_epochs=100, batch_size=32, accelerator=\"auto\")"
+    "summary_ro = rollout_model.fit(train_ds, max_epochs=50, batch_size=64, accelerator=\"auto\")"
    ]
   },
   {
@@ -1452,7 +5562,18 @@
    "execution_count": null,
    "id": "b93b69de",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "plot_loss_curves(summary_ro, keys=[\"tf\", \"roll\"], titles=[\"Teacher-forcing loss\", \"Rollout loss\"])"
    ]
@@ -1498,18 +5619,17 @@
     "    all_flat = []          # (n_samples, n_steps, S*D) -- no pooling, keep full spatial info\n",
     "    all_positions = []     # (n_samples, n_steps, 2) -- true position at each rollout step's frame\n",
     "    all_velocities = []\n",
+    "    all_velocities_avg = []\n",
+    "\n",
     "\n",
     "    with torch.no_grad():\n",
     "        for batch in dataloader:\n",
-    "            if len(batch) == 4:\n",
-    "                _, videos, positions, velocities = batch\n",
-    "            else:\n",
-    "                videos, positions, velocities = batch\n",
-    "            B = videos.size(0)\n",
+    "            clips, positions, velocities = batch\n",
+    "            B = clips.size(0)\n",
     "\n",
     "            # Encode only the first temporal group -- everything after this\n",
     "            # point is pure latent-space rollout, no further encoder calls.\n",
-    "            frame_slice = videos[:, :, :t_patch]\n",
+    "            frame_slice = clips[:, :, :t_patch]\n",
     "            z0 = encoder(frame_slice, t_offset=0)   # (B, S, D)\n",
     "\n",
     "            rolled = rollout_model.rollout_predictor.rollout(z0, n_steps)   # (B, n_steps, S, D)\n",
@@ -1522,14 +5642,20 @@
     "            step_velocities = torch.stack(\n",
     "                [velocities[:, (k + 1) * t_patch] for k in range(n_steps)], dim=1\n",
     "            )\n",
+    "            step_velocities_avg = torch.stack(\n",
+    "                [velocities[:, (k + 1) * t_patch : (k + 1) * t_patch + t_patch].mean(dim=1)\n",
+    "                 for k in range(n_steps)], dim=1\n",
+    "            )\n",
     "\n",
     "            all_flat.append(flat.cpu().numpy())\n",
     "            all_positions.append(step_positions.cpu().numpy())\n",
     "            all_velocities.append(step_velocities.cpu().numpy())\n",
+    "            all_velocities_avg.append(step_velocities_avg.cpu().numpy())\n",
     "\n",
     "    return (np.concatenate(all_flat, axis=0),\n",
     "            np.concatenate(all_positions, axis=0),\n",
-    "            np.concatenate(all_velocities, axis=0))"
+    "            np.concatenate(all_velocities, axis=0),\n",
+    "            np.concatenate(all_velocities_avg, axis=0))"
    ]
   },
   {
@@ -1537,27 +5663,40 @@
    "id": "7faea68d",
    "metadata": {},
    "source": [
-    "`fit_and_score_rollout_probes` mirrors `fit_and_score_probes` from pretraining, fit on validation, scored on held-out test, but one probe per rollout step instead of per frame, using the unpooled latents from `extract_rollout_latents_and_targets`. "
+    "`fit_and_score_rollout_probes` mirrors `fit_and_score_probes` from pretraining: fit on validation, scored on held-out test, one probe per step. The difference is what the probes are fit on, the rollout predictor's own autoregressively predicted latents from `extract_rollout_latents_and_targets`, rather than the context encoder's direct encoding of real frames."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 72,
    "id": "ff6c5b57",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def fit_and_score_rollout_probes(rollout_model, val_ds, test_ds, n_steps=None, batch_size=32, alpha=3.0, verbose=True):\n",
+    "def fit_and_score_rollout_probes(rollout_model, val_ds, test_ds, n_steps=None, \n",
+    "                                 batch_size=32, alpha=3.0, \n",
+    "                                 velocity_target=\"instant\", verbose=True):\n",
     "    \"\"\"Fit a per-rollout-step Ridge probe on validation latents, score it on\n",
-    "    held-out test latents, for both position and velocity.\"\"\"\n",
-    "    val_dataloader = torch.utils.data.DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
-    "    test_dataloader = torch.utils.data.DataLoader(test_ds, batch_size=batch_size, shuffle=False)\n",
+    "    held-out test latents, for both position and velocity.\n",
+    "    \n",
+    "    velocity_target: \"instant\" (default) fits against the true velocity at\n",
+    "    each step's frame. \"average\" fits against the velocity averaged over\n",
+    "    that frame's own tubelet window instead.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    assert velocity_target in (\"instant\", \"average\")\n",
+    "    \n",
+    "    val_dataloader = DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
+    "    test_dataloader = DataLoader(test_ds, batch_size=batch_size, shuffle=False)\n",
     "\n",
     "    if n_steps is None:\n",
     "        n_steps = rollout_model.encoder.t_grid - 1   # cover the whole clip\n",
     "\n",
-    "    X_val, Y_val, Z_val = extract_rollout_latents_and_targets(rollout_model, val_dataloader, n_steps=n_steps)\n",
-    "    X_test, Y_test, Z_test = extract_rollout_latents_and_targets(rollout_model, test_dataloader, n_steps=n_steps)\n",
+    "    X_val, Y_val, Z_val, Zavg_val = extract_rollout_latents_and_targets(rollout_model, val_dataloader, n_steps=n_steps)\n",
+    "    X_test, Y_test, Z_test, Zavg_test = extract_rollout_latents_and_targets(rollout_model, test_dataloader, n_steps=n_steps)\n",
+    "\n",
+    "    if velocity_target == \"average\":\n",
+    "        Z_val, Z_test = Zavg_val, Zavg_test\n",
     "\n",
     "    t_patch = rollout_model.encoder.t_patch\n",
     "    probes_pos, probes_vel = [], []\n",
@@ -1573,8 +5712,12 @@
     "\n",
     "        if verbose:\n",
     "            true_frame_idx = (step + 1) * t_patch\n",
-    "            print(f\"Rollout Step {step+1} (frame {true_frame_idx}) -> Test R²: \"\n",
-    "                  f\"{s_pos:.3f} (Position), {s_vel:.3f} (Velocity)\")\n",
+    "            print(f\"Rollout Step {step+1} (frame {true_frame_idx:2d}): pos R²={s_pos:.3f}, vel R²={s_vel:.3f}\")\n",
+    "            \n",
+    "    if verbose:\n",
+    "        print(\"-\" * 54)\n",
+    "        print(f\"Mean over rollout steps  : pos R²={np.mean(r2_pos):.3f}, vel R²={np.mean(r2_vel):.3f}\")\n",
+    "        \n",
     "\n",
     "    return probes_pos, probes_vel, r2_pos, r2_vel"
    ]
@@ -1584,18 +5727,47 @@
    "id": "a9a9d345",
    "metadata": {},
    "source": [
-    "R² at step k measures how much position and velocity information survives k steps of autoregressive rollout, so a declining trend across steps is the expected signature of compounding error, not necessarily a failure."
+    "R² at step k measures how much position and velocity information survives k steps of autoregressive rollout."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 73,
    "id": "b968667b",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Rollout Evaluation (Fit on Val, Score on Test) ---\n",
+      "Rollout Step 1 (frame  2): pos R²=0.992, vel R²=0.895\n",
+      "Rollout Step 2 (frame  4): pos R²=0.966, vel R²=0.871\n",
+      "Rollout Step 3 (frame  6): pos R²=0.911, vel R²=0.870\n",
+      "Rollout Step 4 (frame  8): pos R²=0.846, vel R²=0.867\n",
+      "Rollout Step 5 (frame 10): pos R²=0.900, vel R²=0.859\n",
+      "Rollout Step 6 (frame 12): pos R²=0.942, vel R²=0.821\n",
+      "Rollout Step 7 (frame 14): pos R²=0.954, vel R²=0.815\n",
+      "Rollout Step 8 (frame 16): pos R²=0.936, vel R²=0.838\n",
+      "Rollout Step 9 (frame 18): pos R²=0.907, vel R²=0.839\n",
+      "------------------------------------------------------\n",
+      "Mean over rollout steps  : pos R²=0.928, vel R²=0.853\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"--- Rollout Evaluation (Fit on Val, Score on Test) ---\")\n",
+    "trained_probes_pos, trained_probes_vel, r2_pos_roll, r2_vel_roll = fit_and_score_rollout_probes(rollout_model, val_ds, test_ds)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ace9b94",
+   "metadata": {},
    "source": [
-    "print(\"--- Strict Rollout Evaluation (Fit on Val, Score on Test, unpooled features) ---\")\n",
-    "trained_probes_pos, trained_probes_vel, r2_pos_roll, r2_vel_roll = fit_and_score_rollout_probes(rollout_model, val_ds_w, test_ds_w)"
+    "Some loss over time is expected, this is the natural signature of compounding error, not necessarily a failure. But that loss doesn't have to show up as a smooth decline: because the bead's motion is periodic, bounce, travel, bounce again, how much error has piled up by a given step depends on where a bounce happens to fall along the way.\n",
+    "\n",
+    "Velocity stays comparatively flat across the whole rollout. Velocity here is a piecewise-constant variable, it only takes one of 20 fixed values, and it only changes at the discrete moment of a bounce. Tracking it correctly at some future rollout step is really a state-tracking problem."
    ]
   },
   {
@@ -1630,34 +5802,31 @@
     "\n",
     "    indices = np.random.choice(len(dataset), size=num_examples, replace=False)\n",
     "\n",
-    "    videos_np, positions_np, velocities_np = [], [], []\n",
+    "    clips_np, positions_np, velocities_np = [], [], []\n",
     "    pred_positions, pred_velocities = [], []\n",
     "\n",
     "    with torch.no_grad():\n",
     "        for i in indices:\n",
-    "            if dataset[0].__len__() == 4:\n",
-    "                _, video, positions, velocities = dataset[i]\n",
-    "            else:\n",
-    "                video, positions, velocities = dataset[i]\n",
-    "            video_b = video.unsqueeze(0).to(device)\n",
+    "            clip, positions, velocities = dataset[i]\n",
+    "            clip_b = clip.unsqueeze(0).to(device)\n",
     "\n",
-    "            z0 = encoder(video_b[:, :, :t_patch], t_offset=0)          # (1, S, D)\n",
+    "            z0 = encoder(clip_b[:, :, :t_patch], t_offset=0)          # (1, S, D)\n",
     "            rolled = rollout_model.rollout_predictor.rollout(z0, n_steps)   # (1, n_steps, S, D)\n",
     "            flat = rolled.reshape(n_steps, -1).cpu().numpy()            # (n_steps, S*D)\n",
     "\n",
-    "            videos_np.append(video.numpy())\n",
+    "            clips_np.append(clip.numpy())\n",
     "            positions_np.append(positions.numpy())\n",
     "            velocities_np.append(velocities.numpy())\n",
     "            pred_positions.append([probes_pos[s].predict(flat[s:s+1])[0] for s in range(n_steps)])\n",
     "            pred_velocities.append([probes_vel[s].predict(flat[s:s+1])[0] for s in range(n_steps)])\n",
     "\n",
-    "    videos_np, positions_np, velocities_np = map(np.array, (videos_np, positions_np, velocities_np))\n",
+    "    clips_np, positions_np, velocities_np = map(np.array, (clips_np, positions_np, velocities_np))\n",
     "    pred_positions, pred_velocities = map(np.array, (pred_positions, pred_velocities))\n",
     "\n",
     "    target_frame_indices = [(s + 1) * t_patch for s in range(n_steps)]\n",
     "    context_frame_idx = t_patch - 1\n",
     "\n",
-    "    return videos_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities, context_frame_idx"
+    "    return clips_np, positions_np, velocities_np, target_frame_indices, pred_positions, pred_velocities, context_frame_idx"
    ]
   },
   {
@@ -1670,17 +5839,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 31,
    "id": "a941ffbc",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
-    "videos_np, positions_np, velocities_np, target_frame_indices, pred_pos, pred_vel, context_frame_idx = \\\n",
-    "    prepare_rollout_predictions(rollout_model, test_ds_w, trained_probes_pos, trained_probes_vel, device,\n",
+    "clips_np, positions_np, velocities_np, target_frame_indices, pred_pos, pred_vel, context_frame_idx = \\\n",
+    "    prepare_rollout_predictions(rollout_model, test_ds, trained_probes_pos, trained_probes_vel, device,\n",
     "                                 num_examples=3)\n",
     "\n",
     "plot_predictions_with_velocity(\n",
-    "    videos_np, positions_np, velocities_np,\n",
+    "    clips_np, positions_np, velocities_np,\n",
     "    target_frame_indices=target_frame_indices,\n",
     "    pred_positions=pred_pos, pred_velocities=pred_vel,\n",
     "    context_frame_idx=context_frame_idx,\n",
@@ -1688,6 +5868,102 @@
     ")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "e54ea8c9",
+   "metadata": {},
+   "source": [
+    "The error in reproducing velocity at bounces seems less evident here than in the pretraining plots above. Let's repeat the tubelet-averaged-velocity comparison from pretraining on the rollout predictor's own outputs:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "f8d18ed5",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Rollout Evaluation, velocity averaged over each tubelet's frames ---\n",
+      "Rollout Step 1 (frame 2) -> Test R²: 0.992 (Position), 0.909 (Velocity)\n",
+      "Rollout Step 2 (frame 4) -> Test R²: 0.966 (Position), 0.889 (Velocity)\n",
+      "Rollout Step 3 (frame 6) -> Test R²: 0.911 (Position), 0.879 (Velocity)\n",
+      "Rollout Step 4 (frame 8) -> Test R²: 0.846 (Position), 0.895 (Velocity)\n",
+      "Rollout Step 5 (frame 10) -> Test R²: 0.900 (Position), 0.867 (Velocity)\n",
+      "Rollout Step 6 (frame 12) -> Test R²: 0.942 (Position), 0.827 (Velocity)\n",
+      "Rollout Step 7 (frame 14) -> Test R²: 0.954 (Position), 0.815 (Velocity)\n",
+      "Rollout Step 8 (frame 16) -> Test R²: 0.936 (Position), 0.845 (Velocity)\n",
+      "Rollout Step 9 (frame 18) -> Test R²: 0.907 (Position), 0.865 (Velocity)\n",
+      "------------------------------------------------------------\n",
+      "Mean over 9 rollout steps -> Test R²: 0.928 (Position), 0.866 (Velocity)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"--- Rollout Evaluation, velocity averaged over each tubelet's frames ---\")\n",
+    "_, _, _, r2_vel_roll_avg = fit_and_score_rollout_probes(rollout_model, val_ds, test_ds, velocity_target=\"average\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23e9a7aa",
+   "metadata": {},
+   "source": [
+    "The encoder's bounce-averaging bias survives into rollout, but only partly: the averaged target scores at or above the true-instantaneous target at every step with a small but consistent gap rather than the sharp per-frame collapse visible in the pretraining plots. That fits with how the rollout predictor works: it never touches raw pixels beyond the seed frames, so it isn't mechanically forced to compute a position difference between two observed frames the way the context encoder's tubelet convolution is."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "037634d7",
+   "metadata": {},
+   "source": [
+    "## Exercises\n",
+    "\n",
+    "The exercises below are organized into four groups. The first explores the pretraining stage itself: the EMA target and the masking recipe. The second turns to what the linear probes are actually telling you. The third does the same kind of interrogation for the rollout stage, probing how training choices there change how far into the future the model can actually predict. The fourth leaves the machinery of this notebook mostly alone and instead pushes on the physical system itself, adding further complications.\n",
+    "\n",
+    "### Pretraining and the EMA Target\n",
+    "\n",
+    "1. **Break the EMA target on purpose**\n",
+    "\n",
+    "Modify `update_target` so `tgt_enc` is a full, hard copy of `ctx_enc` on *every* call (not just the first), rather than a slow-moving average. Re-run a few epochs of pretraining. What happens to the short/long loss curves, and to the probe R²? This turns the notebook's claim that the EMA target \"prevents the model from collapsing to a trivial solution\" into something you watch happen.\n",
+    "\n",
+    "2. **Sweep the momentum**\n",
+    "\n",
+    "Try `ema_tau` values like 0.9, 0.99, 0.999, and 0.9999. How does each change the shape of the initial collapse-and-recovery pattern described after the loss curves? Is there a value that recovers faster without collapsing again?\n",
+    "\n",
+    "3. **Change the masking recipe**\n",
+    "\n",
+    "Edit `MASK_GROUPS` — more or fewer blocks, larger or smaller coverage — and watch how it shifts the short vs. long loss curves and the final position/velocity R². What happens if you remove the `\"long\"` group entirely and train on short-range masking only? Does the representation still learn velocity as well?\n",
+    "\n",
+    "### Evaluating the Representation\n",
+    "\n",
+    "4. **Linear vs. nonlinear probing**\n",
+    "\n",
+    "Swap `Ridge` in `fit_and_score_probes` for a small `MLPRegressor` or `RandomForestRegressor`, and compare its R² to the linear probe's. The notebook's central claim rests on *linear* decodability being the interesting result — if a nonlinear probe scores dramatically higher, what does that say about how the encoder actually organized the information?\n",
+    "\n",
+    "### Rollout\n",
+    "\n",
+    "5. **Does training on longer rollouts help longer-horizon predictions?**\n",
+    "\n",
+    "Train two versions of `RolloutModel`, one with `rollout_k=3` and one with `rollout_k=9`, keeping everything else fixed. Evaluate both with `fit_and_score_rollout_probes(..., n_steps=9)`. Does the longer-horizon training actually pay off at test time, or mostly just slow training down?\n",
+    "\n",
+    "6. **Teacher-forcing vs. rollout, in isolation**\n",
+    "\n",
+    "Train one `RolloutModel` with `rollout_w=0` (teacher-forcing only) and, separately, modify `_shared_step` so only `loss_roll` contributes (no teacher forcing at all). Compare both against the default combined loss using the rollout R² curve. This should make the notebook's claim about \"exposure to compounding error\" concrete instead of asserted.\n",
+    "\n",
+    "### Extending the Physical System\n",
+    "\n",
+    "7. **Add a distractor**\n",
+    "\n",
+    "`render_trajectories` currently draws one bead. Add a second, independently-moving object to the same clip. Does the context encoder's representation still cleanly encode the first bead's position? (Hint: `collect_ctx_features_per_frame` mean-pools over *all* spatial tokens into one vector per frame — with two objects sharing that pooled vector, whether their positions stay linearly separable is exactly the interesting question.)\n",
+    "\n",
+    "8. **Break the constant-velocity assumption**\n",
+    "\n",
+    "Add constant acceleration (gravity) to `simulate_trajectory` instead of constant velocity. Does the per-frame linear position probe still work as well? What about velocity, would a linear probe on a single frame's representation still recover it, or would that now require information pooled across multiple frames?"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "45e0efd6",

From f05c65ba0f51680db3b618bb0c33796666ab714f Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Wed, 26 Aug 2026 00:38:14 +0200
Subject: [PATCH 7/9] u

---
 Companion/cc_jepa/jepa.ipynb | 7035 ++++++++++++++++------------------
 1 file changed, 3360 insertions(+), 3675 deletions(-)

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
index a6c6dcee8..0f8d8fbd1 100644
--- a/Companion/cc_jepa/jepa.ipynb
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -15,7 +15,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 1,
    "id": "a4994aa9",
    "metadata": {},
    "outputs": [],
@@ -155,7 +155,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 2,
    "id": "9dea3f77",
    "metadata": {},
    "outputs": [],
@@ -233,13 +233,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": null,
    "id": "f863edd2",
    "metadata": {},
    "outputs": [],
    "source": [
-    "import numpy as np\n",
-    "\n",
     "BEAD_RADIUS = 5.0\n",
     "BEAD_INTENSITY = 0.7\n",
     "NOISE_STD = 0.035  # Adjust standard deviation\n",
@@ -281,7 +279,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 4,
    "id": "43847c1c",
    "metadata": {},
    "outputs": [
@@ -473,42 +471,42 @@
        "\n",
        "\n",
        "
\n",
-       "  \n",
+       "  \n",
        "  
\n",
-       "    \n",
+       "           oninput=\"animd629ea75e46f4f2d8647485b36e72c6f.set_frame(parseInt(this.value));\">\n",
        "    
\n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
-       "      \n",
        "    
\n",
-       "    
\n",
-       "      \n",
-       "      \n",
-       "      Once\n",
+       "      \n",
-       "      \n",
-       "      Loop\n",
+       "      \n",
-       "      \n",
+       "      \n",
        "    
\n",
        "  
\n",
        "
\n",
@@ -518,3592 +516,3359 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_img63ab25c793994a238d8af2141738ebdc\";\n",
-       "    var slider_id = \"_anim_slider63ab25c793994a238d8af2141738ebdc\";\n",
-       "    var loop_select_id = \"_anim_loop_select63ab25c793994a238d8af2141738ebdc\";\n",
+       "    var img_id = \"_anim_imgd629ea75e46f4f2d8647485b36e72c6f\";\n",
+       "    var slider_id = \"_anim_sliderd629ea75e46f4f2d8647485b36e72c6f\";\n",
+       "    var loop_select_id = \"_anim_loop_selectd629ea75e46f4f2d8647485b36e72c6f\";\n",
        "    var frames = new Array(20);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAHCCAYAAAAzc7dkAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
        "bGliIHZlcnNpb24zLjEwLjgsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvwVt1zgAAAAlwSFlzAAAP\\\n",
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-       "9RxX5IAKAqIsLkFZXBEUXA/KjiuIiIKKCIgaIkbCCSSz7zO9r/U/v/c/Ndb09GQ6d35T6XQ+n3Oa\\\n",
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-       "sAAAkglYAADJBCwAgGQCFgBAMgELACCZgAUAkEzAAgBIJmABACQTsAAAqlz/D03npsBbRRfNAAAA\\\n",
-       "AElFTkSuQmCC\\\n",
+       "mYAFAJBMwAIASCZgAQAkE7AAAJIJWAAAyQQsAIBkAhYAQDIBCwAgmYAFAJBMwAIAqHL9Pz6ZvlNr\\\n",
+       "hwJsAAAAAElFTkSuQmCC\\\n",
        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        anim63ab25c793994a238d8af2141738ebdc = new Animation(frames, img_id, slider_id, 149.0,\n",
+       "        animd629ea75e46f4f2d8647485b36e72c6f = new Animation(frames, img_id, slider_id, 149.0,\n",
        "                                 loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
@@ -4113,7 +3878,7 @@
        ""
       ]
      },
-     "execution_count": 36,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4157,7 +3922,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 5,
    "id": "07c28293",
    "metadata": {},
    "outputs": [],
@@ -4197,7 +3962,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 6,
    "id": "9d9ad66c",
    "metadata": {},
    "outputs": [
@@ -4205,7 +3970,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Datasets already exist. Skipping dataset generation.\n"
+      "saved 10000 clips to datasets/bouncing bead/particles_train.pt\n",
+      "saved 2000 clips to datasets/bouncing bead/particles_val.pt\n",
+      "saved 1000 clips to datasets/bouncing bead/particles_test.pt\n"
      ]
     }
    ],
@@ -4233,7 +4000,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 7,
    "id": "b4cf3ddc",
    "metadata": {},
    "outputs": [
@@ -4305,7 +4072,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 8,
    "id": "67adc09b",
    "metadata": {},
    "outputs": [],
@@ -4380,13 +4147,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 9,
    "id": "3d93bd73",
    "metadata": {},
    "outputs": [
     {
      "data": {
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       "text/plain": [
        "
"
       ]
@@ -4472,7 +4239,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 10,
    "id": "027f07d3",
    "metadata": {},
    "outputs": [],
@@ -4566,7 +4333,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 11,
    "id": "cd3d9dfe",
    "metadata": {},
    "outputs": [],
@@ -4604,7 +4371,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 12,
    "id": "6ff7f0b7",
    "metadata": {},
    "outputs": [],
@@ -4686,7 +4453,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 13,
    "id": "c9090a44",
    "metadata": {},
    "outputs": [
@@ -4694,6 +4461,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
+      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:76: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default\n",
       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py:70: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
      ]
     },
@@ -4758,7 +4526,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "80db781751cf43559e3db84a7454ed19",
+       "model_id": "e5191e690d564781926d048ef4af3997",
        "version_major": 2,
        "version_minor": 0
       },
@@ -4786,23 +4554,6 @@
      },
      "metadata": {},
      "output_type": "display_data"
-    },
-    {
-     "ename": "SystemExit",
-     "evalue": "1",
-     "output_type": "error",
-     "traceback": [
-      "An exception has occurred, use %tb to see the full traceback.\n",
-      "\u001b[31mSystemExit\u001b[39m\u001b[31m:\u001b[39m 1\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/IPython/core/interactiveshell.py:3709: UserWarning: To exit: use 'exit', 'quit', or Ctrl-D.\n",
-      "  warn(\"To exit: use 'exit', 'quit', or Ctrl-D.\", stacklevel=1)\n"
-     ]
     }
    ],
    "source": [
@@ -4820,7 +4571,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 14,
    "id": "f692f783",
    "metadata": {},
    "outputs": [],
@@ -4828,9 +4579,11 @@
     "def plot_loss_curves(summary, keys, titles=None, figsize=None):\n",
     "    \"\"\"Plot one subplot per loss key substring found in `summary.history`.\n",
     "\n",
-    "    `keys` is a list of substrings to search for (e.g. [\"short\", \"long\"]\n",
-    "    for pretraining, or [\"tf\", \"roll\"] for rollout later).\n",
+    "    `keys` is a list of substrings to search for (e.g. [\"short\", \"long\"] for \n",
+    "    pretraining, or [\"tf\", \"roll\"] for rollout later).\n",
+    "    \n",
     "    \"\"\"\n",
+    "\n",
     "    n = len(keys)\n",
     "    titles = titles or keys\n",
     "    fig, axes = plt.subplots(1, n, figsize=figsize or (5.5 * n, 4), squeeze=False)\n",
@@ -4861,13 +4614,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 15,
    "id": "10ddc233",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
        "
"
       ]
@@ -4904,7 +4657,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 16,
    "id": "4e03a044",
    "metadata": {},
    "outputs": [],
@@ -4915,7 +4668,9 @@
     "@torch.no_grad()\n",
     "def collect_ctx_features_per_frame(ctx_enc, dataloader, device=None):\n",
     "    \"\"\"Run the frozen context encoder over a dataset in batches, pooling\n",
-    "    per-timestep tokens into one feature vector per frame.\"\"\"\n",
+    "    per-timestep tokens into one feature vector per frame.\n",
+    "    \"\"\"\n",
+    "    \n",
     "    ctx_enc.eval()\n",
     "\n",
     "    if device is None:\n",
@@ -4960,7 +4715,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 17,
    "id": "2816daf8",
    "metadata": {},
    "outputs": [],
@@ -5023,7 +4778,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 18,
    "id": "a8b23a94",
    "metadata": {},
    "outputs": [
@@ -5032,18 +4787,18 @@
      "output_type": "stream",
      "text": [
       "--- Pretraining Evaluation (Fit on Val, Score on Test) ---\n",
-      "Frame  0: pos R²=0.044, vel R²=0.016\n",
-      "Frame  2: pos R²=0.065, vel R²=0.013\n",
-      "Frame  4: pos R²=0.080, vel R²=0.005\n",
-      "Frame  6: pos R²=0.080, vel R²=0.006\n",
-      "Frame  8: pos R²=0.081, vel R²=0.005\n",
-      "Frame 10: pos R²=0.087, vel R²=0.006\n",
-      "Frame 12: pos R²=0.096, vel R²=0.002\n",
-      "Frame 14: pos R²=0.099, vel R²=0.004\n",
-      "Frame 16: pos R²=0.091, vel R²=0.008\n",
-      "Frame 18: pos R²=0.064, vel R²=0.021\n",
+      "Frame  0: pos R²=0.974, vel R²=0.745\n",
+      "Frame  2: pos R²=0.986, vel R²=0.815\n",
+      "Frame  4: pos R²=0.987, vel R²=0.823\n",
+      "Frame  6: pos R²=0.985, vel R²=0.852\n",
+      "Frame  8: pos R²=0.983, vel R²=0.829\n",
+      "Frame 10: pos R²=0.977, vel R²=0.857\n",
+      "Frame 12: pos R²=0.983, vel R²=0.859\n",
+      "Frame 14: pos R²=0.988, vel R²=0.848\n",
+      "Frame 16: pos R²=0.979, vel R²=0.813\n",
+      "Frame 18: pos R²=0.964, vel R²=0.821\n",
       "--------------------------------------\n",
-      "Mean    : pos R²=0.079, vel R²=0.009\n"
+      "Mean    : pos R²=0.981, vel R²=0.826\n"
      ]
     }
    ],
@@ -5080,7 +4835,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 19,
    "id": "aeaeaa68",
    "metadata": {},
    "outputs": [],
@@ -5128,7 +4883,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "id": "830e36f5",
    "metadata": {},
    "outputs": [],
@@ -5209,13 +4964,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 21,
    "id": "6ff32060",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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@@ -5253,7 +5008,7 @@
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   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "id": "2219d0f4",
    "metadata": {},
    "outputs": [
@@ -5262,18 +5017,18 @@
      "output_type": "stream",
      "text": [
       "--- Pretraining Evaluation, velocity averaged over each tubelet's frames ---\n",
-      "Frame  0: pos R²=0.977, vel R²=0.816\n",
-      "Frame  2: pos R²=0.986, vel R²=0.897\n",
-      "Frame  4: pos R²=0.985, vel R²=0.891\n",
-      "Frame  6: pos R²=0.987, vel R²=0.887\n",
-      "Frame  8: pos R²=0.986, vel R²=0.861\n",
-      "Frame 10: pos R²=0.985, vel R²=0.873\n",
-      "Frame 12: pos R²=0.986, vel R²=0.834\n",
-      "Frame 14: pos R²=0.983, vel R²=0.805\n",
-      "Frame 16: pos R²=0.982, vel R²=0.821\n",
-      "Frame 18: pos R²=0.982, vel R²=0.823\n",
+      "Frame  0: pos R²=0.974, vel R²=0.822\n",
+      "Frame  2: pos R²=0.986, vel R²=0.868\n",
+      "Frame  4: pos R²=0.987, vel R²=0.896\n",
+      "Frame  6: pos R²=0.985, vel R²=0.911\n",
+      "Frame  8: pos R²=0.983, vel R²=0.900\n",
+      "Frame 10: pos R²=0.977, vel R²=0.919\n",
+      "Frame 12: pos R²=0.983, vel R²=0.924\n",
+      "Frame 14: pos R²=0.988, vel R²=0.901\n",
+      "Frame 16: pos R²=0.979, vel R²=0.886\n",
+      "Frame 18: pos R²=0.964, vel R²=0.873\n",
       "--------------------------------------\n",
-      "Mean    : pos R²=0.984, vel R²=0.851\n"
+      "Mean    : pos R²=0.981, vel R²=0.890\n"
      ]
     }
    ],
@@ -5308,7 +5063,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "id": "b8a802f0",
    "metadata": {},
    "outputs": [],
@@ -5369,7 +5124,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "id": "a63e52aa",
    "metadata": {},
    "outputs": [],
@@ -5514,7 +5269,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "ba649dd8964947aca3a35a0702aac7ac",
+       "model_id": "52dba969e90b483285be39abaf58b0da",
        "version_major": 2,
        "version_minor": 0
       },
@@ -5532,16 +5287,6 @@
       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
      ]
-    },
-    {
-     "data": {
-      "text/html": [
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-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -5562,18 +5307,7 @@
    "execution_count": null,
    "id": "b93b69de",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
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",
-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "plot_loss_curves(summary_ro, keys=[\"tf\", \"roll\"], titles=[\"Teacher-forcing loss\", \"Rollout loss\"])"
    ]
@@ -5668,7 +5402,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": null,
    "id": "ff6c5b57",
    "metadata": {},
    "outputs": [],
@@ -5732,29 +5466,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": null,
    "id": "b968667b",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "--- Rollout Evaluation (Fit on Val, Score on Test) ---\n",
-      "Rollout Step 1 (frame  2): pos R²=0.992, vel R²=0.895\n",
-      "Rollout Step 2 (frame  4): pos R²=0.966, vel R²=0.871\n",
-      "Rollout Step 3 (frame  6): pos R²=0.911, vel R²=0.870\n",
-      "Rollout Step 4 (frame  8): pos R²=0.846, vel R²=0.867\n",
-      "Rollout Step 5 (frame 10): pos R²=0.900, vel R²=0.859\n",
-      "Rollout Step 6 (frame 12): pos R²=0.942, vel R²=0.821\n",
-      "Rollout Step 7 (frame 14): pos R²=0.954, vel R²=0.815\n",
-      "Rollout Step 8 (frame 16): pos R²=0.936, vel R²=0.838\n",
-      "Rollout Step 9 (frame 18): pos R²=0.907, vel R²=0.839\n",
-      "------------------------------------------------------\n",
-      "Mean over rollout steps  : pos R²=0.928, vel R²=0.853\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "print(\"--- Rollout Evaluation (Fit on Val, Score on Test) ---\")\n",
     "trained_probes_pos, trained_probes_vel, r2_pos_roll, r2_vel_roll = fit_and_score_rollout_probes(rollout_model, val_ds, test_ds)\n"
@@ -5839,21 +5554,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": null,
    "id": "a941ffbc",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "
"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "clips_np, positions_np, velocities_np, target_frame_indices, pred_pos, pred_vel, context_frame_idx = \\\n",
     "    prepare_rollout_predictions(rollout_model, test_ds, trained_probes_pos, trained_probes_vel, device,\n",
@@ -5878,29 +5582,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": null,
    "id": "f8d18ed5",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "--- Rollout Evaluation, velocity averaged over each tubelet's frames ---\n",
-      "Rollout Step 1 (frame 2) -> Test R²: 0.992 (Position), 0.909 (Velocity)\n",
-      "Rollout Step 2 (frame 4) -> Test R²: 0.966 (Position), 0.889 (Velocity)\n",
-      "Rollout Step 3 (frame 6) -> Test R²: 0.911 (Position), 0.879 (Velocity)\n",
-      "Rollout Step 4 (frame 8) -> Test R²: 0.846 (Position), 0.895 (Velocity)\n",
-      "Rollout Step 5 (frame 10) -> Test R²: 0.900 (Position), 0.867 (Velocity)\n",
-      "Rollout Step 6 (frame 12) -> Test R²: 0.942 (Position), 0.827 (Velocity)\n",
-      "Rollout Step 7 (frame 14) -> Test R²: 0.954 (Position), 0.815 (Velocity)\n",
-      "Rollout Step 8 (frame 16) -> Test R²: 0.936 (Position), 0.845 (Velocity)\n",
-      "Rollout Step 9 (frame 18) -> Test R²: 0.907 (Position), 0.865 (Velocity)\n",
-      "------------------------------------------------------------\n",
-      "Mean over 9 rollout steps -> Test R²: 0.928 (Position), 0.866 (Velocity)\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "print(\"--- Rollout Evaluation, velocity averaged over each tubelet's frames ---\")\n",
     "_, _, _, r2_vel_roll_avg = fit_and_score_rollout_probes(rollout_model, val_ds, test_ds, velocity_target=\"average\")"

From 9f0dfb7a13d82f86ab8fcccb786f2c5c56c9d3e6 Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Wed, 26 Aug 2026 07:41:45 +0200
Subject: [PATCH 8/9] u

---
 Companion/cc_jepa/jepa.ipynb | 104 +++++++++++++++++++++++++++++------
 1 file changed, 88 insertions(+), 16 deletions(-)

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
index 0f8d8fbd1..97dfa68cc 100644
--- a/Companion/cc_jepa/jepa.ipynb
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -4715,7 +4715,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "2816daf8",
    "metadata": {},
    "outputs": [],
@@ -4726,10 +4726,12 @@
     "    \"\"\"Fit a per-timestep Ridge probe on validation features, score it on\n",
     "    held-out test features, for both position and velocity. \n",
     "    \n",
-    "    velocity_target: \"instant\" (default) fits against the true velocity at\n",
-    "    each frame. \"average\" fits against the velocity averaged over each\n",
-    "    tubelet's own t_patch frames\n",
+    "    velocity_target: \"instant\" (default) fits against the true velocity at each\n",
+    "    frame. \"average\" fits against the velocity averaged over each tubelet's own \n",
+    "    t_patch frames\n",
+    "    \n",
     "    \"\"\"\n",
+    "    \n",
     "    assert velocity_target in (\"instant\", \"average\")\n",
     "\n",
     "    val_dataloader = DataLoader(val_ds, batch_size=batch_size, shuffle=False)\n",
@@ -5199,7 +5201,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 25,
    "id": "2c299d30",
    "metadata": {},
    "outputs": [
@@ -5287,6 +5289,16 @@
       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/utilities/_pytree.py:21: `isinstance(treespec, LeafSpec)` is deprecated, use `isinstance(treespec, TreeSpec) and treespec.is_leaf()` instead.\n",
       "/Users/cmanzo/Documents/GitHub/Environments/deeptrack_dev/lib/python3.12/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:434: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=13` in the `DataLoader` to improve performance.\n"
      ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
@@ -5304,10 +5316,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 26,
    "id": "b93b69de",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "plot_loss_curves(summary_ro, keys=[\"tf\", \"roll\"], titles=[\"Teacher-forcing loss\", \"Rollout loss\"])"
    ]
@@ -5332,7 +5355,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 27,
    "id": "c59f42fb",
    "metadata": {},
    "outputs": [],
@@ -5402,7 +5425,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "id": "ff6c5b57",
    "metadata": {},
    "outputs": [],
@@ -5466,10 +5489,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "id": "b968667b",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Rollout Evaluation (Fit on Val, Score on Test) ---\n",
+      "Rollout Step 1 (frame  2): pos R²=0.993, vel R²=0.910\n",
+      "Rollout Step 2 (frame  4): pos R²=0.969, vel R²=0.867\n",
+      "Rollout Step 3 (frame  6): pos R²=0.930, vel R²=0.874\n",
+      "Rollout Step 4 (frame  8): pos R²=0.869, vel R²=0.889\n",
+      "Rollout Step 5 (frame 10): pos R²=0.919, vel R²=0.853\n",
+      "Rollout Step 6 (frame 12): pos R²=0.951, vel R²=0.875\n",
+      "Rollout Step 7 (frame 14): pos R²=0.956, vel R²=0.869\n",
+      "Rollout Step 8 (frame 16): pos R²=0.944, vel R²=0.881\n",
+      "Rollout Step 9 (frame 18): pos R²=0.951, vel R²=0.872\n",
+      "------------------------------------------------------\n",
+      "Mean over rollout steps  : pos R²=0.942, vel R²=0.877\n"
+     ]
+    }
+   ],
    "source": [
     "print(\"--- Rollout Evaluation (Fit on Val, Score on Test) ---\")\n",
     "trained_probes_pos, trained_probes_vel, r2_pos_roll, r2_vel_roll = fit_and_score_rollout_probes(rollout_model, val_ds, test_ds)\n"
@@ -5497,7 +5539,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "id": "a1fe972e",
    "metadata": {},
    "outputs": [],
@@ -5554,10 +5596,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 31,
    "id": "a941ffbc",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "clips_np, positions_np, velocities_np, target_frame_indices, pred_pos, pred_vel, context_frame_idx = \\\n",
     "    prepare_rollout_predictions(rollout_model, test_ds, trained_probes_pos, trained_probes_vel, device,\n",
@@ -5582,10 +5635,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 32,
    "id": "f8d18ed5",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Rollout Evaluation, velocity averaged over each tubelet's frames ---\n",
+      "Rollout Step 1 (frame  2): pos R²=0.993, vel R²=0.912\n",
+      "Rollout Step 2 (frame  4): pos R²=0.969, vel R²=0.870\n",
+      "Rollout Step 3 (frame  6): pos R²=0.930, vel R²=0.882\n",
+      "Rollout Step 4 (frame  8): pos R²=0.869, vel R²=0.905\n",
+      "Rollout Step 5 (frame 10): pos R²=0.919, vel R²=0.861\n",
+      "Rollout Step 6 (frame 12): pos R²=0.951, vel R²=0.875\n",
+      "Rollout Step 7 (frame 14): pos R²=0.956, vel R²=0.860\n",
+      "Rollout Step 8 (frame 16): pos R²=0.944, vel R²=0.882\n",
+      "Rollout Step 9 (frame 18): pos R²=0.951, vel R²=0.869\n",
+      "------------------------------------------------------\n",
+      "Mean over rollout steps  : pos R²=0.942, vel R²=0.880\n"
+     ]
+    }
+   ],
    "source": [
     "print(\"--- Rollout Evaluation, velocity averaged over each tubelet's frames ---\")\n",
     "_, _, _, r2_vel_roll_avg = fit_and_score_rollout_probes(rollout_model, val_ds, test_ds, velocity_target=\"average\")"

From 119c59d00c7aa43e7aa4048918f58b9dd1d49e5a Mon Sep 17 00:00:00 2001
From: Carlo 
Date: Wed, 26 Aug 2026 17:35:07 +0200
Subject: [PATCH 9/9] u

---
 Companion/cc_jepa/jepa.ipynb | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/Companion/cc_jepa/jepa.ipynb b/Companion/cc_jepa/jepa.ipynb
index 97dfa68cc..d067e091f 100644
--- a/Companion/cc_jepa/jepa.ipynb
+++ b/Companion/cc_jepa/jepa.ipynb
@@ -95,13 +95,11 @@
    ]
   },
   {
-   "cell_type": "raw",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "1adaf547",
-   "metadata": {
-    "vscode": {
-     "languageId": "raw"
-    }
-   },
+   "metadata": {},
+   "outputs": [],
    "source": [
     "======================================================================================\n",
     "                    JOINT EMBEDDING PREDICTIVE ARCHITECTURE (JEPA)\n",