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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "506ba7f1",
+   "metadata": {},
+   "source": [
+    "# Building a World Model with a Joint-Embedding Predictive Architecture (JEPA)\n",
+    "\n",
+    "<div style=\"background-color: #f0f8ff; border: 2px solid #4682b4; padding: 10px;\">\n",
+    "<a href=\"https://colab.research.google.com/github/DeepTrackAI/DeepLearningCrashCourse/blob/main/Companion/cc_jepa/jepa.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
+    "<strong>If using Colab/Kaggle:</strong> You need to uncomment the code in the cell below this one.\n",
+    "</div>"
+   ]
+  },
+  {
+   "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": [
+    "<div style=\"background-color: #f0f8ff; border: 2px solid #4682b4; padding: 10px;\">\n",
+    "<strong>Note:</strong> 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",
+    "</div>"
+   ]
+  },
+  {
+   "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": "code",
+   "execution_count": null,
+   "id": "1adaf547",
+   "metadata": {},
+   "outputs": [],
+   "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",
+   "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",
+    "    lower = int(np.ceil(margin + radius - 1))\n",
+    "    upper = int(np.floor(image_size - margin - radius))\n",
+    "    \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",
+    "`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": "f863edd2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "BEAD_RADIUS = 5.0\n",
+    "BEAD_INTENSITY = 0.7\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",
+    "    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",
+    "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",
+    "    positions, vel = simulate_trajectory(radius)\n",
+    "    clean = render_trajectories(positions, radius)\n",
+    "    noisy = add_high_frequency_noise(clean)\n",
+    "    return noisy, positions, vel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "551fb934",
+   "metadata": {},
+   "source": [
+    "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": 4,
+   "id": "43847c1c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<link rel=\"stylesheet\"\n",
+       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
+       "<script language=\"javascript\">\n",
+       "  function isInternetExplorer() {\n",
+       "    ua = navigator.userAgent;\n",
+       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
+       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
+       "  }\n",
+       "\n",
+       "  /* Define the Animation class */\n",
+       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
+       "    this.img_id = img_id;\n",
+       "    this.slider_id = slider_id;\n",
+       "    this.loop_select_id = loop_select_id;\n",
+       "    this.interval = interval;\n",
+       "    this.current_frame = 0;\n",
+       "    this.direction = 0;\n",
+       "    this.timer = null;\n",
+       "    this.frames = new Array(frames.length);\n",
+       "\n",
+       "    for (var i=0; i<frames.length; i++)\n",
+       "    {\n",
+       "     this.frames[i] = new Image();\n",
+       "     this.frames[i].src = frames[i];\n",
+       "    }\n",
+       "    var slider = document.getElementById(this.slider_id);\n",
+       "    slider.max = this.frames.length - 1;\n",
+       "    if (isInternetExplorer()) {\n",
+       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
+       "        // with W3C specification. It ignores oninput and onchange behaves\n",
+       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
+       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
+       "        slider.setAttribute('oninput', null);\n",
+       "    }\n",
+       "    this.set_frame(this.current_frame);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.get_loop_state = function(){\n",
+       "    var button_group = document[this.loop_select_id].state;\n",
+       "    for (var i = 0; i < button_group.length; i++) {\n",
+       "        var button = button_group[i];\n",
+       "        if (button.checked) {\n",
+       "            return button.value;\n",
+       "        }\n",
+       "    }\n",
+       "    return undefined;\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.set_frame = function(frame){\n",
+       "    this.current_frame = frame;\n",
+       "    document.getElementById(this.img_id).src =\n",
+       "            this.frames[this.current_frame].src;\n",
+       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.next_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.previous_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.first_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(0);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.last_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(this.frames.length - 1);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.slower = function()\n",
+       "  {\n",
+       "    this.interval /= 0.7;\n",
+       "    if(this.direction > 0){this.play_animation();}\n",
+       "    else if(this.direction < 0){this.reverse_animation();}\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.faster = function()\n",
+       "  {\n",
+       "    this.interval *= 0.7;\n",
+       "    if(this.direction > 0){this.play_animation();}\n",
+       "    else if(this.direction < 0){this.reverse_animation();}\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.anim_step_forward = function()\n",
+       "  {\n",
+       "    this.current_frame += 1;\n",
+       "    if(this.current_frame < this.frames.length){\n",
+       "      this.set_frame(this.current_frame);\n",
+       "    }else{\n",
+       "      var loop_state = this.get_loop_state();\n",
+       "      if(loop_state == \"loop\"){\n",
+       "        this.first_frame();\n",
+       "      }else if(loop_state == \"reflect\"){\n",
+       "        this.last_frame();\n",
+       "        this.reverse_animation();\n",
+       "      }else{\n",
+       "        this.pause_animation();\n",
+       "        this.last_frame();\n",
+       "      }\n",
+       "    }\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.anim_step_reverse = function()\n",
+       "  {\n",
+       "    this.current_frame -= 1;\n",
+       "    if(this.current_frame >= 0){\n",
+       "      this.set_frame(this.current_frame);\n",
+       "    }else{\n",
+       "      var loop_state = this.get_loop_state();\n",
+       "      if(loop_state == \"loop\"){\n",
+       "        this.last_frame();\n",
+       "      }else if(loop_state == \"reflect\"){\n",
+       "        this.first_frame();\n",
+       "        this.play_animation();\n",
+       "      }else{\n",
+       "        this.pause_animation();\n",
+       "        this.first_frame();\n",
+       "      }\n",
+       "    }\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.pause_animation = function()\n",
+       "  {\n",
+       "    this.direction = 0;\n",
+       "    if (this.timer){\n",
+       "      clearInterval(this.timer);\n",
+       "      this.timer = null;\n",
+       "    }\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.play_animation = function()\n",
+       "  {\n",
+       "    this.pause_animation();\n",
+       "    this.direction = 1;\n",
+       "    var t = this;\n",
+       "    if (!this.timer) this.timer = setInterval(function() {\n",
+       "        t.anim_step_forward();\n",
+       "    }, this.interval);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.reverse_animation = function()\n",
+       "  {\n",
+       "    this.pause_animation();\n",
+       "    this.direction = -1;\n",
+       "    var t = this;\n",
+       "    if (!this.timer) this.timer = setInterval(function() {\n",
+       "        t.anim_step_reverse();\n",
+       "    }, this.interval);\n",
+       "  }\n",
+       "</script>\n",
+       "\n",
+       "<style>\n",
+       ".animation {\n",
+       "    display: inline-block;\n",
+       "    text-align: center;\n",
+       "}\n",
+       "input[type=range].anim-slider {\n",
+       "    width: 374px;\n",
+       "    margin-left: auto;\n",
+       "    margin-right: auto;\n",
+       "}\n",
+       ".anim-buttons {\n",
+       "    margin: 8px 0px;\n",
+       "}\n",
+       ".anim-buttons button {\n",
+       "    padding: 0;\n",
+       "    width: 36px;\n",
+       "}\n",
+       ".anim-state label {\n",
+       "    margin-right: 8px;\n",
+       "}\n",
+       ".anim-state input {\n",
+       "    margin: 0;\n",
+       "    vertical-align: middle;\n",
+       "}\n",
+       "</style>\n",
+       "\n",
+       "<div class=\"animation\">\n",
+       "  <img id=\"_anim_imgd629ea75e46f4f2d8647485b36e72c6f\">\n",
+       "  <div class=\"anim-controls\">\n",
+       "    <input id=\"_anim_sliderd629ea75e46f4f2d8647485b36e72c6f\" type=\"range\" class=\"anim-slider\"\n",
+       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
+       "           oninput=\"animd629ea75e46f4f2d8647485b36e72c6f.set_frame(parseInt(this.value));\">\n",
+       "    <div class=\"anim-buttons\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.slower()\">\n",
+       "          <i class=\"fa fa-minus\"></i></button>\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.first_frame()\">\n",
+       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.previous_frame()\">\n",
+       "          <i class=\"fa fa-step-backward\"></i></button>\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.reverse_animation()\">\n",
+       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.pause_animation()\">\n",
+       "          <i class=\"fa fa-pause\"></i></button>\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.play_animation()\">\n",
+       "          <i class=\"fa fa-play\"></i></button>\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.next_frame()\">\n",
+       "          <i class=\"fa fa-step-forward\"></i></button>\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.last_frame()\">\n",
+       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animd629ea75e46f4f2d8647485b36e72c6f.faster()\">\n",
+       "          <i class=\"fa fa-plus\"></i></button>\n",
+       "    </div>\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectd629ea75e46f4f2d8647485b36e72c6f\"\n",
+       "          class=\"anim-state\">\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_d629ea75e46f4f2d8647485b36e72c6f\"\n",
+       "             >\n",
+       "      <label for=\"_anim_radio1_d629ea75e46f4f2d8647485b36e72c6f\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_d629ea75e46f4f2d8647485b36e72c6f\"\n",
+       "             checked>\n",
+       "      <label for=\"_anim_radio2_d629ea75e46f4f2d8647485b36e72c6f\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_d629ea75e46f4f2d8647485b36e72c6f\"\n",
+       "             >\n",
+       "      <label for=\"_anim_radio3_d629ea75e46f4f2d8647485b36e72c6f\">Reflect</label>\n",
+       "    </form>\n",
+       "  </div>\n",
+       "</div>\n",
+       "\n",
+       "\n",
+       "<script language=\"javascript\">\n",
+       "  /* Instantiate the Animation class. */\n",
+       "  /* The IDs given should match those used in the template above. */\n",
+       "  (function() {\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",
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+       "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",
+       "        animd629ea75e46f4f2d8647485b36e72c6f = new Animation(frames, img_id, slider_id, 149.0,\n",
+       "                                 loop_select_id);\n",
+       "    }, 0);\n",
+       "  })()\n",
+       "</script>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "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",
+    "clip, pos, vel = make_clip()\n",
+    "\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.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]\n",
+    "\n",
+    "anim = animation.FuncAnimation(\n",
+    "    fig, update, frames=len(clip), 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 the clip, 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 noisy view, and save \n",
+    "    everything to `path` as a single .pt file.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    clips_list = []\n",
+    "    positions_list, velocities_list = [], []\n",
+    "    for _ in range(n_clips):\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",
+    "    clips = torch.stack(clips_list).float()\n",
+    "    torch.save({\n",
+    "        \"clips\": clips,\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": [
+      "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"
+     ]
+    }
+   ],
+   "source": [
+    "import os\n",
+    "from os.path import exists\n",
+    "\n",
+    "os.makedirs(\"datasets/bouncing bead\", exist_ok=True)\n",
+    "\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/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)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ddd653ee",
+   "metadata": {},
+   "source": [
+    "The class `ParticlesDataset` wraps a saved file for training."
+   ]
+  },
+  {
+   "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",
+    "    \"\"\"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",
+    "\n",
+    "    def __len__(self):\n",
+    "        return len(self.clips)\n",
+    "\n",
+    "    def __getitem__(self, idx):\n",
+    "        return self.clips[idx], self.positions[idx], self.velocities[idx]\n",
+    "\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",
+    "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",
+    "from torch import device\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, 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",
+    "    \"\"\"\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 = (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_tensor,   # Shape: (B, num_ctx_tokens)\n",
+    "            \"pred\": pred_tensor, # Shape: (B, num_pred_tokens)\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.\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": 9,
+   "id": "3d93bd73",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 1600x400 with 20 Axes>"
+      ]
+     },
+     "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",
+    "t_patch = 2\n",
+    "\n",
+    "loader = DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
+    "batch = next(iter(loader))\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(clips.size(0), t_grid, s_grid)\n",
+    "n_groups = len(groups)\n",
+    "\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",
+    "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",
+    "    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(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.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",
+    "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\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",
+    "                                      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, 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, 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[:, -N_tgt:]))"
+   ]
+  },
+  {
+   "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",
+    "        self.update_target()   # sync tgt_enc to ctx_enc's initial weights before training starts\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",
+    "        clips_ctx, _, _ = batch\n",
+    "\n",
+    "        device = clips_ctx.device\n",
+    "        D = self.ctx_enc.dim\n",
+    "\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(clips_ctx), (D,))\n",
+    "\n",
+    "        losses = {}\n",
+    "        for g in groups:\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(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",
+    "            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 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.lerp_(p, weight=1.0 - 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": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">   </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Name          </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Type             </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Params </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Mode  </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> FLOPs </span>┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 0 </span>│ ctx_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 1 </span>│ tgt_enc       │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 2 </span>│ predictor     │ Predictor        │  216 K │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 3 </span>│ train_metrics │ MetricCollection │      0 │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 4 </span>│ val_metrics   │ MetricCollection │      0 │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 5 </span>│ test_metrics  │ MetricCollection │      0 │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 6 </span>│ optimizer     │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "</pre>\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": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">Trainable params</span>: 1.4 M                                                                                            \n",
+       "<span style=\"font-weight: bold\">Non-trainable params</span>: 1.2 M                                                                                        \n",
+       "<span style=\"font-weight: bold\">Total params</span>: 2.6 M                                                                                                \n",
+       "<span style=\"font-weight: bold\">Total estimated model params size (MB)</span>: 10                                                                         \n",
+       "<span style=\"font-weight: bold\">Modules in train mode</span>: 161                                                                                         \n",
+       "<span style=\"font-weight: bold\">Modules in eval mode</span>: 0                                                                                            \n",
+       "<span style=\"font-weight: bold\">Total FLOPs</span>: 0                                                                                                     \n",
+       "</pre>\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": "e5191e690d564781926d048ef4af3997",
+       "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": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\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=40, batch_size=32, 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\"] 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",
+    "    axes = axes.ravel()\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, 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": 15,
+   "id": "10ddc233",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 1100x400 with 2 Axes>"
+      ]
+     },
+     "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=None):\n",
+    "    \"\"\"Run the frozen context encoder over a dataset in batches, pooling\n",
+    "    per-timestep tokens into one feature vector per frame.\n",
+    "    \"\"\"\n",
+    "    \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, vel_avg = [], [], [], []\n",
+    "    for batch in dataloader:\n",
+    "        clips, positions, velocities = batch\n",
+    "        B = clips.size(0)\n",
+    "        clips = clips.to(device)\n",
+    "\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",
+    "\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(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),\n",
+    "            np.concatenate(vel, axis=0), np.concatenate(vel_avg, 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": null,
+   "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, 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",
+    "    \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",
+    "    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",
+    "    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",
+    "        \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"
+   ]
+  },
+  {
+   "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 Evaluation (Fit on Val, Score on Test) ---\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=0.981, vel R²=0.826\n"
+     ]
+    }
+   ],
+   "source": [
+    "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)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4561142",
+   "metadata": {},
+   "source": [
+    "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."
+   ]
+  },
+  {
+   "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",
+    "    clips_np, positions_np, velocities_np = [], [], []\n",
+    "    pred_positions, pred_velocities = [], []\n",
+    "\n",
+    "    with torch.no_grad():\n",
+    "        for i in indices:\n",
+    "            clip, positions, velocities = dataset[i]\n",
+    "            clip_b = clip.unsqueeze(0).to(device)\n",
+    "\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",
+    "            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",
+    "    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 clips_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": [
+    "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",
+    "                                    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(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=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=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",
+    "            col += 1\n",
+    "\n",
+    "        for step, frame_idx in enumerate(target_frame_indices):\n",
+    "            ax = axes[row, col]\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=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=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=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=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",
+    "    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()"
+   ]
+  },
+  {
+   "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": [
+       "<Figure size 3000x900 with 30 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "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",
+    "    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",
+    "    title_prefix=\"Probe pred \",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ee7469b",
+   "metadata": {},
+   "source": [
+    "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",
+    "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",
+    "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",
+    "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": 22,
+   "id": "2219d0f4",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--- Pretraining Evaluation, velocity averaged over each tubelet's frames ---\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=0.981, vel R²=0.890\n"
+     ]
+    }
+   ],
+   "source": [
+    "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"
+   ]
+  },
+  {
+   "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": 23,
+   "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": 24,
+   "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=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",
+    "\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",
+    "        clips, _, _ = batch\n",
+    "        self.encoder.eval()\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",
+    "        # 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 = 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",
+    "\n",
+    "        preds = self.rollout_predictor(z[:, :-1])\n",
+    "        tgt = z[:, 1:]\n",
+    "        loss_tf = (preds - tgt).abs().mean()\n",
+    "\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",
+    "\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"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44799e75",
+   "metadata": {},
+   "source": [
+    "Let's train. Only `rollout_predictor`'s parameters are updated, the encoder stays frozen throughout."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "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": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━┳━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┓\n",
+       "┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">   </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Name              </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Type             </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Params </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> Mode  </span>┃<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\"> FLOPs </span>┃\n",
+       "┡━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━┩\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 0 </span>│ encoder           │ VideoEncoder     │  1.2 M │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 1 </span>│ rollout_predictor │ RolloutPredictor │  826 K │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 2 </span>│ train_metrics     │ MetricCollection │      0 │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 3 </span>│ val_metrics       │ MetricCollection │      0 │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 4 </span>│ test_metrics      │ MetricCollection │      0 │ train │     0 │\n",
+       "│<span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\"> 5 </span>│ optimizer         │ Adam             │      0 │ train │     0 │\n",
+       "└───┴───────────────────┴──────────────────┴────────┴───────┴───────┘\n",
+       "</pre>\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│ 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": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">Trainable params</span>: 826 K                                                                                            \n",
+       "<span style=\"font-weight: bold\">Non-trainable params</span>: 1.2 M                                                                                        \n",
+       "<span style=\"font-weight: bold\">Total params</span>: 2.0 M                                                                                                \n",
+       "<span style=\"font-weight: bold\">Total estimated model params size (MB)</span>: 8                                                                          \n",
+       "<span style=\"font-weight: bold\">Modules in train mode</span>: 103                                                                                         \n",
+       "<span style=\"font-weight: bold\">Modules in eval mode</span>: 0                                                                                            \n",
+       "<span style=\"font-weight: bold\">Total FLOPs</span>: 0                                                                                                     \n",
+       "</pre>\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": "52dba969e90b483285be39abaf58b0da",
+       "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": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\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, max_epochs=50, batch_size=64, accelerator=\"auto\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "40d2081a",
+   "metadata": {},
+   "source": [
+    "Let's plot the losses..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "b93b69de",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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nn0tqaqqp2g4AAADANhEEAYAy0EKkWoBMi5lqITUtwqqBkKLtiwEAAADYFmqCAAAAAAAAp0BNEAAAAAAA4BQIggAAAAAAAKfgdDVB8vPz5dChQ+Ln52f28QMAgIphsVjk+PHjUqtWLXF1dd7rLqw9AACwnXWH0wVBNABSt25daw8DAACnERsbK3Xq1BFnxdoDAADbWXc4XRBEM0AKJsbf39/awwEAwGFp22i98FBw7nVWrD0AALCddYfTBUEKtsBoAIQgCAAAlXfudVasPQAAsJ11h/Nu0AUAAAAAAE6FIAgAAAAAAHAKTrcdBgBg3ardubm5kpeXx4/BgXh4eIibm5u1hwEAcDK6nsjJybH2MGBn6w6CIACASpGdnS1xcXGSkZHBjDvg3lutwu7r62vtoQAAnERaWpocOHDAXGCBc3G5yHUHQRAAQIXLz8+XvXv3mqi99m739PR0+mKZjkIXn4cPHzYL0caNG5MRAgColAwQPe/4+PhIjRo1WFM4EUs5rDsIggAAKiULRAMh2rZMFyxwLLoA3bdvn0lJZlsMAKCi6flG/xjW80+VKlWYcCdT4yLXHRRGBQBUGldXTjuOyNlb4AIArIPzj3Nyuch1B6tRAAAAAADgFAiCAACc1ksvvSSZmZkX/HWHDh2S7t27l/l9NYVzwoQJxR5btmyZtGrVStq0aSNz5swRW5ib//znP9YeBgAAdsNa64oLXYMEBgYWy6pITk4WW1BZaw+CIACASqf7eDOycyv0KE21+JdffrnExYq28T0XLe76zz//lGsQZMqUKXL77bfL2rVrpW/fvmV+bZzf+PHjJSIiQry9vaVTp06yYsWKsz730ksvNQvE049+/fpZfaqzc/MlNy/f2sMAAKuylTWFNdcVF/p+zo7CqOVg9+E0GfbNasnNt8ifT1xaHi8JAA7tRE6eRI6q2GyHLa/0FR/Ps5/mHnzwQfNRr7wUdK0JCwuTXbt2SWJiomzbtk3uuOMO2b59uynsqkVdP//8c/McDWJER0cXXjnRP4pff/11+fnnn03F8lGjRsmQIUPO+d779+83rxEeHi5du3aVqVOnmuJu+nHhwoXFrtIU9fXXX8tHH31kioFpa7hx48ZJVFSUTJ48Wb766ivzmH4PwcHB5r7+sa9V9J999lmZNWuWeY3LLrtM3nvvPdOlJyUlRZ544gmTiaLz0K5dO/niiy/M87Sl8bXXXiu7d+823/e0adMkKChI7JnO74gRI0wQSgMg77//vgk66c85JCTkjOdPnz7d/PwLHDlyxMz3zTffLNY05o+t8v2KGBl7S7T0igy16lgAwNnXFNZeV+i64eGHH5bOnTvL6tWr5fnnn5f69evLY489ZloJa9D/v//9r3Tr1q1M37+jrT3IBCkHAVU8ZEdCmuxNSpfMnLzyeEkAQAUryMTQKy/r1q0zfwDrwuH33383CxWlfyCvWrVKNmzYYBY1mqZ5Nl5eXiajQE/2uug411UYfe+mTZua9/3ll1/MIuG6666Tp556yjx2tgDIv//+K99//738/fffsmbNGrNA0uyRop9/6623ZMuWLXLNNdfI/fffbx7/9NNPZeXKleb709fXhYUuhpSmneqCRL/H9evXm68vsHz5crPA0dfT+Zk4caLYu7Fjx8rQoUPNYjIyMtL8LLRjUcHi63S68NJFWMExb94883xrB0GycvMlNTNXZm2Kt+o4AADWX1eorVu3yqBBg8x79+/fX2644QYZPXq0eS899914440mIHKhHHHtQSZIOahe1VN8PN0kIztPDiafkIY1fMvjZQHAYVXxcDNXVSr6PS6U/mHr5+dXeP+7774zVz80tVUPvcJxNnp1RzVr1kzc3d0lPj5e6tSpI+Vp5syZZrGgGQwFjh49KidOnDC3NaOkefPm5rYuQl544QVzJWb+/Ply9913mwWV0iCAbgl55pln5LfffjMLjoLOPdp2rsCVV14p1atXN7e7dOkiGzduFHumV950MTZy5MjCx/T77tWrlyxdurRUr6FX7W699VapWrWqWNNVLcNk8pJ9Mm9LvGTnthJPd65rAXBOtrqmqOx1RYMGDaRnz57mtmab6PmtYHvtJZdcIqGhoSYYUecC1yaOuPYgCFIONF0pPMhHtsUfl5ijGQRBAKAU/26eL63UGjSds8DixYvlww8/NH8c65UIzdjQdNSz0VTTApraWRH7cXVP8uDBg+WNN96olNZylfE9VaakpCSzMNOFYFF6v+Aq3bnoFblNmzaZQMi5ZGVlmaNAamqqlLf2EUES7OslSWlZsnTPEenZ5P8XkADgTGx1TVHZ64qi71WebWUtDrj24LJBOdEgiIo9mlFeLwkAqGB6dUb3pZbk2LFj5vN6NUIzCMozHdPf3/+s73suumXmm2++kZiYGHM/Pz/fpNUW0IVVwR/zn332mdl/qwsIzXTQPbr6fehiQj/Xp0+fwtd89913zWsp3XuMkmnwQzv4dOzY8ZxTNGbMGAkICCg8dN93eXNzdZG+LU4Gc2ZviuNHBgBOvK44nW651fO6buFUS5YsMZkkWnfkQjni2oMgSDkHQWKOEAQBAHuhRbl69+5tFgVatKwoTcfURYQeum+3LAuHs2ndurW0aNFCWrZsaRYCpaXjePvtt+X66683Bcn0NX744YfCz2tKqqaZ6uN6halggaXpqW3btjWHfh9asKygBZ3uz9WsBf3jXj/33HPPiaPStGNdmCUkJBR7XO9rvY9zSU9PN3N97733nvd9dLuNLoILjtjYWKkIV7eqaT7O2ZxAlxgAcOJ1xem03oYW9taaILrm0HO+Fhg9X7aIs6w9XCyl7ffjIDQlVa/K6KJEr8SVl6+W7pNRMzdLn8hQ+XRQ+3J7XQBwBLrvde/evaZSedE0R5QfLSKmVeT1sJWfb0Wdcy+G7mnWTA6tbK/0KpR26HnkkUdMgdpzza9W/j948GDhXuXSqqh50Pa4HV6fL8cycuS7oZ2ka8Oz7y0HAEfCusK51x6ZF7nuIBOknNQtyARhOwwAADZL2+NOmjRJpkyZYirpDxs2zGR5FLQe1Mr6RQunFt0KM2DAgAsOgFQkdzdX6RN5MoNl1ka6xAAAUBq2WUHGzmuCaHJNWQvPAAAcR/v27c8o6KXpot9++225f51WYNcD5zZw4ECz91iL0RXsj549e3ZhsVTd81xQrb6AVtnXgnZz5861uem9slWYTF0VK7M3x8vL17UQV1fWHwDgqMq6rqio177bTtceBEHKSe3AKqJxj/TsPDmSnm0qtgMAnFvRwmGV8XUoHd36okdJFi5ceMZjun/bVncPd2sYLH7e7nL4eJasjjkmHSKCrD0kAEAFqcj1wSonWnuwHaaceHu4SZj/yf1IbIkBgJLZ6h+SuDj8XK3H091Vejc/mcXClhgAzobzj3OyXOR6kiBIBdQFoU0uABTn4eFhPmZk0EHLEWn7O6WdV1D5rjrVJUZb5fIHAQBnUHC+KTj/wLlkX+S6g+0w5ahekI+s2HuUNrkAcBo9SQUGBha2i/Px8aF2koPQ7ipaY0N/pu7uLCusoXvjYKnq6SaHUjJl/YEUia4baJVxAEBl0fONnnf0/KMXWk6v5QTHlV8O6w5WKxVQHJXtMABwprCwk10sCgIhcBy6+NQ2sxQFt96W3Mubh8qv6w/JrI1xBEEAODw939SsWdO0Sd2/f7+1hwM7W3cQBClH4dUJggDA+RYsISEhkpOTw0Q5EE9PT67CWdlVLcNOBkE2xcuzVzUjIAXAKc49jRs3ZkuME/K8yHUHQZByRE0QACjd1hhqRwDl69KmNcTbw9Vko24+lCotawcwxQAcnv4h7O19sjkFUFpsnqqA7TBxqZmSlZtXni8NAABwVj6e7nJpkxBze/ameGYKAICzIAhSjqpX9RQfTzfRjj0Hj50oz5cGAAA4p6tanay78wddYgAAOCuCIOW8370gG2T/UdpAAgCAynN5sxDxdHOVPYfTZWdiGlMPAEAJCIKUM+qCAAAAa/Dz9jDtctWsjWyJAQCgJARBKqpN7hEyQQAAQOW6qlVN83HWpjimHgCAEhAEKWf1aJMLAACspHfzUHF3dZFt8cdlz2G2xAAAcDqCIBW0HUZb1AEAAFSmAB8P6dro1JYYusQAAHAGgiAVtB0m9miGWLRNDAAAQCW6quXJLjG0ygUA4EwEQcpZ7cAq4uIikp6dJ0fTs8v75QEAAM6pT2SouLqIbDyYYi7KAACA/0cQpJx5e7hJmL+3uc2WGAAAUNmq+3pJp/rVzW2yQQAAKI4gSAWgLggAALCmq1ud3BLzB11iAAAohiBIBdcFAQAAqGx9W4SZ7blrY5LlUPIJfgAAAJxCEKQCgyD7jxAEAQAAlS/E31s6RgSZ25/+vYcfAQAApxAEqcAgCDVBAACAtTx2RWPz8dvl+2X/kXR+EAAAEASpGOHV2Q4DAACsq1ujYOnRpIbk5FnknTnb+XEAAGALQZDx48dLRESEeHt7S6dOnWTFihXnfH5ycrI8/PDDUrNmTfHy8pImTZrIH3/8IbaYCRKXmilZuXnWHg4AAHBSz17ZzNQG+W1DnKyPTbb2cAAAcO4gyNSpU2XEiBEyevRoWbNmjURFRUnfvn0lMTGxxOdnZ2dL7969Zd++fTJt2jTZvn27TJo0SWrXri22pHpVT/HxdBOLReTgMYqRAQAA64is5S/XR59cJ705a5tYdHECAIATs2oQZOzYsTJ06FAZMmSIREZGyoQJE8THx0e++OKLEp+vjx89elR+/vln6datm8kg6dmzpwme2BIXFxfqggAAAJswok8T8XRzlaV7jsjCHYetPRwAAJwzCKJZHatXr5ZevXr9/2BcXc39pUuXlvg1v/zyi3Tp0sVshwkNDZWWLVvKG2+8IXl5trflpC5tcgEAgA2oU81HBnetZ26/NWub5OWTDQIAcF5WC4IkJSWZ4IUGM4rS+/Hx8SV+zZ49e8w2GP06rQPy4osvynvvvSevvfbaWd8nKytLUlNTix2VgQ4xAADAVjx8WSPx93aXbfHHZcbag9YeDgAAzlsY9ULk5+dLSEiIfPrpp9KuXTsZOHCgPP/882YbzdmMGTNGAgICCo+6detWylgJggAAAFsR6OMpD13WyNweO3e7ZObYXhYtAAAOHQQJDg4WNzc3SUhIKPa43g8LCyvxa7QjjHaD0a8r0Lx5c5M5ottrSjJy5EhJSUkpPGJjY6UygyD7j2RUyvsBAACcy91dI6RmgLccSsmUKUv2MVkAAKdktSCIp6enyeZYsGBBsUwPva91P0qixVB37dplnldgx44dJjiir1cSbaPr7+9f7KjsmiBUYgcAANbm7eEmI3o3MbfH/7VLkjNKvoAEAIAjs+p2GG2Pqy1up0yZIlu3bpVhw4ZJenq66RajBg0aZDI5CujntTvM8OHDTfDj999/N4VRtVCqralTrYq4uIikZ+fJ0XQWGQAAwPpuaFtHmoX5SWpmrny8cLe1hwMAgHMFQbSmx7vvviujRo2S6OhoWbduncyePbuwWGpMTIzExcUVPl/recyZM0dWrlwprVu3lscee8wERJ599lmxxastYf7e5nbMUbbEAAAA63NzdZFnrmxmbk9esk8OJp+w9pAAAKhULhYn26uh3WG0QKrWB6norTG3TFwqK/YelQ9ujZb+0bUr9L0AAHDmc64ts7V50KXfbZOWybI9R+WGtrVl7C3R1h4SAACVdr61q+4w9ia8SF0QAAAAW+Di4iIjr2pubmu73C2HUq09JAAAKg1BkApEm1wAAGCLouoGSr/WNUXzgd+avc3awwEAoNIQBKlABEEAAICterpvU3F3dZFFOw7LpoMp1h4OAACVgiBIpbTJpegYAACwLfWqV5W+LcPM7WmrD1h7OAAAVAqCIJWQCXIo5YRk5eZV5FsBAABcsFva1y2sDZKZw1oFAOD4CIJUoGBfT/HxdDP7bQ8eIxsEAADYlksaBUvNAG9JOZEj87cmWHs4AABUOIIgFVx9nbogAADAVrm5usiNbeuY2z+tYksMAMDxEQSptLogtMkFAAC256Z2J4Mgf+88LHEpZK4CABwbQZAKRiYIAACwZRHBVaVT/SCzfXf6moPWHg4AABWKIEgFIwgCAABs3c2nCqT+uCpWLBoNAQDAQREEqbQgCOmlAADANl3dKkyqerrJ/iMZsmLvUWsPBwCACkMQpBJrgnBlBQAA6xs/frxERESIt7e3dOrUSVasWHHO5ycnJ8vDDz8sNWvWFC8vL2nSpIn88ccf4kh8PN3l2qha5vZPqymQCgBwXARBKlidalXMx7SsXDmWkVPRbwcAAM5h6tSpMmLECBk9erSsWbNGoqKipG/fvpKYmFji87Ozs6V3796yb98+mTZtmmzfvl0mTZoktWvXdrh5vrn9yQKpv2+IM+sWAAAcEUGQCubt4SZh/t7mdgwdYgAAsKqxY8fK0KFDZciQIRIZGSkTJkwQHx8f+eKLL0p8vj5+9OhR+fnnn6Vbt24mg6Rnz54meOJo2oZXkwY1qsqJnDz5fcMhaw8HAIAKQRCkEuuC7D+SXhlvBwAAzpLVsXr1aunVq1fhY66urub+0qVLS5yzX375Rbp06WK2w4SGhkrLli3ljTfekLy8PIebYxcXF7nlVIHUn1axJQYA4JgIglSC8Or/XxcEAABYR1JSkgleaDCjKL0fHx9f4tfs2bPHbIPRr9M6IC+++KK899578tprr531fbKysiQ1NbXYYS9uaFNb3FxdZNX+Y7L7cJq1hwMAQLkjCFIJaJMLAIB9ys/Pl5CQEPn000+lXbt2MnDgQHn++efNNpqzGTNmjAQEBBQedeuezK6wByH+3nJpkxrmNtkgAABHRBCkEhAEAQDA+oKDg8XNzU0SEhKKPa73w8LCSvwa7Qij3WD06wo0b97cZI7o9pqSjBw5UlJSUgqP2NhYsccCqdPXHJDcvHxrDwcAgHJFEKRS2+SeqIy3AwAAJfD09DTZHAsWLCiW6aH3te5HSbQY6q5du8zzCuzYscMER/T1SqJtdP39/Ysd9uTyZqESVNVTEo9nyd87D1t7OAAAlCuCIJWYCXIo5YRk53JFBQAAa9H2uNridsqUKbJ161YZNmyYpKenm24xatCgQSaTo4B+XrvDDB8+3AQ/fv/9d1MYVQulOipPd1e5vs3JFsBsiQEAOBp3aw/AGQT7ekoVDzfTcu5g8gmpH1zV2kMCAMApaU2Pw4cPy6hRo8yWlujoaJk9e3ZhsdSYmBjTMaaA1vOYM2eOPP7449K6dWupXbu2CYg888wz4sh0S8zni/fK/K0JciQtS6r7ell7SAAAlAuCIJXUck6zQbYnHJeYoxkEQQAAsKJHHnnEHCVZuHDhGY/pVplly5aJM2kW5i+t6wTIhgMp8vO6Q3LvJfWtPSQAAMoF22EquS6IBkEAAABs3c3tT3a1+WlVrFgsFmsPBwCAckEQpLI7xBxJr6y3BAAAKLPrWtcy9UG2xR+XTQdTmUkAgEMgCFJJ6lUnEwQAANiPAB8PubLFydbBP66yrza/AACcDUGQShJ+KgiyKzGtst4SAADgotxyakvMzHUHJSs3j9kEANg9giCVpHXtAPNx9+F0ScnIqay3BQAAKLOuDatLmL+3pGbmysLth5lJAIDdIwhSSbS1XEFr3DWxxyrrbQEAAMrM1dVFrouuVZgNAgCAvSMIUonahlczH9fsJwgCAADsQ/9TQZD5WxMlNZNsVgCAfSMIUona1TsZBFlNEAQAANiJyJr+0jjEV7Jz82X2pnhrDwcAgItCEMQKQZB1scmSm5dfmW8NAABQJi4uLjKgTW1zmy0xAAB7RxCkEulVFD8vd8nIzpNt8ccr860BAADK7Lqok1tiluw+IgmpmcwkAMBuEQSpzMl2dZE2p7JB1sRQFwQAANiHukE+JqPVYhH5df0haw8HAIAyIwhSydqdKo5KXRAAAGBPBpwqkPozXWIAAHaMIEglozgqAACwR/1a1xJ3VxfZdDBVdiWmWXs4AACUCUGQShZVN0BcXUQOHDvBnloAAGA3gqp6So8mNcztX8gGAQDYKYIglczP20Oahvmb22tolQsAAOxI/8ItMYfEogVCAACwMwRBrKBdvUDzkbogAADAnvSODBUfTzeJOZoha2OTrT0cAAAuGEEQa9YFoUMMAACwIz6e7tK3RZi5PXPtQWsPBwCAC0YQxArahQeZj5sOpkhmTp41hgAAAHBRW2J+2xAnOXn5zCIAwK4QBLGCukFVJNjXS3LyLCYQAgAAYC8uaRQswb6eciQ9WxbvSrL2cAAAuCAEQazAxcWFuiAAAMAuubu5yjWtT2aDsCUGAGBvCIJYuy4IHWIAAICdue7Ulpi5WxIkIzvX2sMBAKDUCIJYOQiyJuYYLeYAAIBdaVM3UOpV95GM7DyZtyXB2sMBAKDUCIJYSYtaAeLp5ipJadmmzRwAAIA9be3tH3UyG+RnusQAAOwIQRAr8fZwk5a1/QuzQQAAAOxJ/za1zce/dybJkbQsaw8HAIBSIQhiRdQFAQAA9qphDV9pVTtA8vIt8sfGOGsPBwAA+wmCjB8/XiIiIsTb21s6deokK1asOOtzJ0+ebFIwix76dfYdBEm29lAAAAAuWP9TBVJ/XneI2QMA2AWrB0GmTp0qI0aMkNGjR8uaNWskKipK+vbtK4mJiWf9Gn9/f4mLiys89u/fL/aobfjJIMj2+FQ5nplj7eEAAABckOuiaomry8lud7HUOAMA2AGrB0HGjh0rQ4cOlSFDhkhkZKRMmDBBfHx85Isvvjjr12j2R1hYWOERGhoq9ijE31vqBlWRfIvI+tgUaw8HAADggtcyXRsGm9sz1x1k9gAANs+qQZDs7GxZvXq19OrV6/8H5Opq7i9duvSsX5eWlib16tWTunXrSv/+/WXz5s1nfW5WVpakpqYWO2xJu1PZIHoFBQAAwF63xPywMlayc/OtPRwAAGw3CJKUlCR5eXlnZHLo/fj4+BK/pmnTpiZLZObMmfLNN99Ifn6+dO3aVQ4cOFDi88eMGSMBAQGFhwZObLIuCB1iAACAHbqmdS2p4eclB46dkB9Wxlh7OAAA2PZ2mAvVpUsXGTRokERHR0vPnj1l+vTpUqNGDZk4cWKJzx85cqSkpKQUHrGxsWJL2p4Kgqzdf0zydV8MAACAHani6SaPXdHY3P5wwS7JyM619pAAALDNIEhwcLC4ublJQkJCscf1vtb6KA0PDw9p06aN7Nq1q8TPe3l5mUKqRQ9b0jTUT6p6usnxrFzZmZhm7eEAAABcsIHt60p4kI8kpWXJl//uYwYBADbLqkEQT09PadeunSxYsKDwMd3eovc146M0dDvNxo0bpWbNmmKP3N1cJTo80NymLggAALBHnu6uMqJ3E3N74qLdkpJB1zsAgG2y+nYYbY87adIkmTJlimzdulWGDRsm6enppluM0q0vuqWlwCuvvCJz586VPXv2mJa6d955p2mRe99994m9ojgqAABwhHa5zcL8JDUzVz5ZtNvawwEAoETuYmUDBw6Uw4cPy6hRo0wxVK31MXv27MJiqTExMaZjTIFjx46Zlrr63GrVqplMkiVLlpj2uvaqoC7IGoqjAgAAO+Xq6iJP9mkq9321SiYv2Sv3dIswLXQBALAlLhaLxamqcWqLXO0So0VSbaU+SMqJHIl6ea65vfqFXlLd18vaQwIAwCHPudbgTPOgy8obP1kia2KS5c7O4fLagFbWHhIAwEmklvJ8a/XtMBAJqOIhTUJ9zVToogEAAMAeubi4yNNXNjO3f1gRK/uPpFt7SAAAFEMQxEa0O7UlhuKoAADAnnVuUF16NKkhufkW+e+8HdYeDgAAxRAEsRFtw0/VBdl/zNpDAQAAuChP921qPs5cf0i2xacymwAAm0EQxMYyQdYfSJbs3HxrDwcAAKDMWtYOkH6taopWnnt3znZmEgBgMwiC2Ij6wVWlmo+HZOXmy5Y4rpgAAAD7NqJPE3FzdZH5WxNl9f6j1h4OAAAGQRAbKiRGXRAAAOAoGtbwlZva1jG335693XSOAQDA2giC2JC2p7bELN2dZO2hAAAAXLThvRqLp7urLN97VP7eyfoGAGB9BEFsyOXNQsxHXSSkZ+VaezgAADik8ePHS0REhHh7e0unTp1kxYoVZ33u5MmTTbZm0UO/DqVTK7CKDOpcz9x+Z842yc8nGwQAYF0EQWxI01A/qVfdxxRGXbTjsLWHAwCAw5k6daqMGDFCRo8eLWvWrJGoqCjp27evJCYmnvVr/P39JS4urvDYv39/pY7Z3j10WSPx9XKXTQdT5Y9NcdYeDgDAyREEsSF6denKFmHm9uxN8dYeDgAADmfs2LEydOhQGTJkiERGRsqECRPEx8dHvvjii3Oen8PCwgqP0NDQSh2zvQuq6in3da9vbr/62xZJycix9pAAAE6MIIiN6dvyZBDkz22JkpWbZ+3hAADgMLKzs2X16tXSq1evwsdcXV3N/aVLl57169LS0qRevXpSt25d6d+/v2zevLmSRuw4HuzZUBoEV5WE1Cx55bct1h4OAMCJEQSxMdF1AiXEz0vSsnJlye4j1h4OAAAOIykpSfLy8s7I5ND78fElZ2A2bdrUZInMnDlTvvnmG8nPz5euXbvKgQMHzvo+WVlZkpqaWuxwdt4ebvLOza3FxUXkf2sOyIKtCdYeEgDASREEsTGuri7S99SWmDlsiQEAwKq6dOkigwYNkujoaOnZs6dMnz5datSoIRMnTjzr14wZM0YCAgIKD80ggUi7ekFy3yUnt8WMnL6RbTEAAKsgCGKDCoIg87YkSB5V1AEAKBfBwcHi5uYmCQnFsxD0vtb6KA0PDw9p06aN7Nq166zPGTlypKSkpBQesbGxFz12R/FEn6bSoEZVSTyeJS//yrYiAEDlIwhigzo1CJKAKh5yJD1bVu07au3hAADgEDw9PaVdu3ayYMGCwsd0e4ve14yP0tDtNBs3bpSaNWue9TleXl6mo0zRA/+/Lebdm6PE1UVk+tqDMn8L22IAAJWLIIgN8nBzlV7NT+5Xnr2ZLjEAAJQXbY87adIkmTJlimzdulWGDRsm6enppluM0q0vmslR4JVXXpG5c+fKnj17TEvdO++807TIve+++/ihlFHb8GoytHsDc3vkjI2SnJHNXAIAKg1BEBvVt8XJIMjczQlisVisPRwAABzCwIED5d1335VRo0aZOh/r1q2T2bNnFxZLjYmJkbi4uMLnHzt2zLTUbd68uVx99dWmyOmSJUtMe12U3eO9m0jDGlXlsNkWQ7cYAEDlcbE42V/YunjRImW6R9eW01Mzc/KkzSvz5EROnvz6yCXSqk6AtYcEAIBDnnMrGvNQsrUxx+TGT5aIlj+bNKi99I4s3rUHAICKON+SCWLDe2YvbVrD3J7DlhgAAOBg2ui2mB4nt8U8x7YYAEAlIQhiw65sebJSPXVBAACAI3q8VxNpFOJrtsW89AvdYgAAFY8giA27rFmIeLi5yK7ENHMAAAA4areYn9cdIvsVAFDhCILYMH9vD+naMNjcZksMAABwRNF1A+WBng3N7ednbJRj6XSLAQBUHIIgdrIlhiAIAABwVP/p1Vgah/hKUlq2fLJot7WHAwBwYARBbFyv5qHi4iKy4UCKHEw+Ye3hAAAAlDsvdzd55spm5vbUlbFyIjuPWQYAVAiCIDauhp+XdKgXZG7PpUsMAABw4FpodYOqSMqJHJm57qC1hwMAcFAEQexA34IuMZvirT0UAACACuHm6iKDOkeY21OW7heLxcJMAwDKHUEQO9AnMtR8XLnvqBxJy7L2cAAAACrEze3riLeHq2yNS5WV+44xywCAckcQxA7UDfKRlrX9Jd8iMn9rgrWHAwAAUCECfTzl+ja1ze0pS/YxywCAckcQxE70jSzoEkMQBAAAOK5BXU5uiZm9OV7iUzKtPRwAgIMhCGJnrXIX70yS45k51h4OAABAhWhe01861g+SvHyLfLt8P7MMALB+EGTKlCny+++/F95/+umnJTAwULp27Sr793OyqgiNQnylQY2qkp2XLwu3H66Q9wAAwFax9nAud3c9mQ3y/YoYycqlXS4AwMpBkDfeeEOqVKlibi9dulTGjx8vb7/9tgQHB8vjjz9ejsNDARcXF+nb4lSXGFrlAgCcDGsP59I7MlTC/L0lKS1b/tgYZ+3hAACcPQgSGxsrjRo1Mrd//vlnufHGG+X++++XMWPGyD///FPeY8QpV54KgizcliiZOVwVAQA4D9YezsXDzVXu7Bxubk9eQpYxAMDKQRBfX185cuSIuT137lzp3bu3ue3t7S0nTpwox+GhqNZ1AqRmgLekZ+eZ2iAAADgL1h7O59aO4eLp5irrY5NlXWyytYcDAHDmIIgGPe677z5z7NixQ66++mrz+ObNmyUi4uQeTlTMlpirWtY0t7+hUBgAwImw9nA+wb5eck3rk+uer2iXCwCwZhBEa4B06dJFDh8+LP/73/+kevXq5vHVq1fLbbfdVl5jQwkGdaknLi5iiqNujz/OHAEAnAJrD+c0+FSB1N82xElSWpa1hwMAcAAuFovFIk4kNTVVAgICJCUlRfz9/cUeDftmtczaFC83tasj794cZe3hAADgsOfc8sA8XJz+4/81W2Ke7NNEHrm8cTn9VAAAznq+LVMmyOzZs2Xx4sXFrs5ER0fL7bffLseOHSvbiFFq9/doYD7OXHdQ4lMymTkAgMNj7eG87u5az3z8ZlmM5OblW3s4AAA7V6YgyFNPPWWiLGrjxo3yxBNPmLoge/fulREjRpT3GHGaNuHVpENENcnJs8hk9sgCAJwAaw/ndXWrmhLs6ynxqZkyd0uCtYcDAHDGIIgGOyIjI81trQlyzTXXyBtvvGEyQmbNmlXeY0QJ7u/R0Hz8dvl+ScvKZY4AAA6NtYfz8nJ3k9s6FrTL3Wft4QAAnDEI4unpKRkZGeb2/PnzpU+fPuZ2UFBQYYYIKtYVzUKkQY2qcjwzV35YEcN0AwAcGmsP53ZHp3ri5uoiK/Yela1xrDUBAJUcBLnkkkvMtpdXX31VVqxYIf369TOPa7vcOnXqXMRwUFquri4ytPvJ2iBfLN4rOeyRBQA4MNYezi0swFuubBFmbn+1lGwQAEAlB0E++ugjcXd3l2nTpsknn3witWvXNo/rVpgrr7zyIoaDC3F9m9pmj+yhlEz5fUMckwcAcFisPVDQLnfGWgrDAwDKjha5dm7cgp3y3rwdElnTX35/7BJxcXGx9pAAADBoDcs8lCeLxSLXjFssmw+lSvWqnvLeLVFyadMQ/m8DAFzQusNdyigvL09+/vln2bp1q7nfokULue6668TNza2sL4kyuLNzPfl44W7ZEpcq/+46Ipc0DmYeAQAOibWHc9MLPR/d3laGfbNatsUfl7u/XClDu9eXp/o2E0/3MiU3AwCcUJnOGLt27ZLmzZvLoEGDZPr06ea48847TSBk9+7d5T9KnFW1qp5yS/uTdVgm/s3cAwAcE2sPqPrBVeXnh7vJ4C71zP1J/+yVGz9ZIvuS0pkgAEDFBUEee+wxadiwocTGxsqaNWvMERMTI/Xr1zefu1DaWjciIkK8vb2lU6dOpthqafzwww/mqsCAAQPEmd3XvYG4uoj8szOJiukAAIdU3msP2C9vDzd5uX9L+fSudhLo4yEbD6ZIvw//kRlrD1h7aAAARw2CLFq0SN5++23TErdA9erV5c033zSfuxBTp041nWZGjx5tFjRRUVHSt29fSUxMPOfX7du3T5588knp3r27OLu6QT5yVaua5vakv/dYezgAAJS78lx7wDH0aREms4Z3l471gyQ9O08en7peRvy4TtKzcq09NACAowVBvLy85Pjx42c8npaWJp6enhf0WmPHjpWhQ4fKkCFDJDIyUiZMmCA+Pj7yxRdfnHNP8B133CEvv/yyNGhwsk2ss7v/VLvcX9YfkkPJJ6w9HAAAylV5rj3gOGoGVJHvh3aWx3s1MVmx09ccNMVTNx1MsfbQAACOFAS55ppr5P7775fly5ebSt16LFu2TB588EFTHLW0srOzZfXq1dKrV6//H5Crq7m/dOnSs37dK6+8IiEhIXLvvfeWZfgOKapuoHSqHyS5+RaZvGSftYcDAEC5Kq+1BxyPm6uLDO/VWH64v4vUDPCWvUnpcvOEpRJ7NMPaQwMAOEoQ5MMPPzT7crt06WLqeOjRtWtXadSokbz//vulfp2kpCST1REaGlrscb0fHx9f4tcsXrxYPv/8c5k0aVKp3iMrK8u0yil6OKr7e5zMBvlueYykZuZYezgAAJSb8lp7wHHpthjdHtMmPFBO5OTJ+/N3WntIAAAbVKYWuYGBgTJz5kxTqb2gRa52i9GFSEXSNNi77rrLBECCg0vXCnbMmDFm24wzuKxpiDQK8ZVdiWnyw4oYub9HQ2sPCQCAcmGttQfsS6CPp7x0bQvpP/5fUyh12KUNpFGIn7WHBQCwxyCIFi89l7/++qtYnY/S0ECGm5ubJCQkFHtc74eFhZ3xfG2/qwVRr7322sLH8vPzzUd3d3fZvn27uUpU1MiRI4uNXTNB6tatK47I1dXF1AZ5+n8b5IvF++TurvXF071MyT4AAFhdRaw94BxbhPtEhsrcLQkydt4O+fiOdtYeEgDAHoMga9euLdXztGVtaWkhs3bt2smCBQsK29xqUEPvP/LII2c8v1mzZrJx48Zij73wwgsmQ+SDDz4oMbihhdT0cBb929SSd+Zul/jUTPlq6T7TPhcAAHtUEWsPOIcn+jSVeVsT5I+N8aZIasvaAdYeEgDA3oIgRa+2lPdVnsGDB0v79u2lY8eOZl9venq66RajBg0aJLVr1zbbWnT/b8uWLc9Ij1WnP+6svNzdZETvJjJy+kZ5d+526RMZJuHVfaw9LAAALlhFrT3g+JqG+cl1UbVk5rpD8t7c7fLlkI7WHhIAwEZYfa/EwIED5d1335VRo0ZJdHS0rFu3TmbPnl1YLDUmJkbi4uKsPUy7cmuHutKlQXXJzMmXkTM2mAr6AAAAzkTb5mrnmL+2H5bV+49aezgAABvhYnGyv5C1JkhAQICkpKSIv7+/OKp9SenS9/2/JSs3X96+sbXc0sEx66AAAGyXs5xzz4d5sJ6R0zfI9ytipXODIPl+aGe2TgGAAyvt+dbqmSCoGBHBVeWJPk3M7dd+3yKJqZlMNQAAcCqPXt5YPN1cZdmeo/LvriPWHg4AwAYQBHFg93SrL61qB0hqZq6MmrnZ2sMBAACoVLUCq8gdncPNbS0c72QJ0ACAEhAEcWDubq7y1o2txd3VRWZvjpdZG6mtAgAAnMtDlzaSKh5usj42WeZtSbD2cAAAVkYQxMFF1vKXB3s2NLdfnLlZUjJyrD0kAACASlPDz0uGdIswt8fO2yH5+WSDAIAzIwjiBB65vJE0rFFVktKyTH0QAAAAZ/JAj4bi5+0u2+KPy68bDll7OAAAKyII4gS8PdzMthgXF5GfVh+QxTuTrD0kAACsZvz48RIRESHe3t7SqVMnWbFiRam+7ocffjDdRQYMGFDhY0T5CvDxkAd6NDC335+/U3Lz8pliAHBSBEGcRPuIIBnUuZ65/ez0DZKRnWvtIQEAUOmmTp0qI0aMkNGjR8uaNWskKipK+vbtK4mJief8un379smTTz4p3bt3r7SxonwN6VZfqlf1lL1J6fK/NQeYXgBwUgRBnMhTVzaT2oFV5MCxE/Le3B3WHg4AAJVu7NixMnToUBkyZIhERkbKhAkTxMfHR7744ouzfk1eXp7ccccd8vLLL0uDBiezCWB/qnq5y7BLT9ZJ+3DBLsnKzbP2kAAAVkAQxIn4ernL69e3NLe/+HevrI05Zu0hAQBQabKzs2X16tXSq1evwsdcXV3N/aVLl57161555RUJCQmRe++9t1Tvk5WVJampqcUO2IY7O9eTMH9vOZh8Qr5fHmPt4QAArIAgiJO5tGmI3NCmtlgsIs/8b4Nk5nAVBADgHJKSkkxWR2hoaLHH9X58fHyJX7N48WL5/PPPZdKkSaV+nzFjxkhAQEDhUbdu3YseO8qvTtqjVzQytz/8c5ckHs9kagHAyRAEcUIvXhMpwb6esiMhTUZO3ygWjYgAAIBijh8/LnfddZcJgAQHB5d6dkaOHCkpKSmFR2xsLDNrQ25pX1eahfnJ0fRsGTF1PS1zAcDJEARxQtWqesqHt7URN1cXmbH2oHy+eK+1hwQAQIXTQIabm5skJCQUe1zvh4WFnfH83bt3m4Ko1157rbi7u5vjq6++kl9++cXc1s+XxMvLS/z9/YsdsB0ebq7y0e1tpIqHmyzelSSfLCr55wgAcEwEQZxU14bB8mK/5ub2G39slb93HLb2kAAAqFCenp7Srl07WbBgQeFj+fn55n6XLl3OeH6zZs1k48aNsm7dusLjuuuuk8suu8zcZpuL/WoU4iev9G9hbr83d7us3HfU2kMCAFQSgiBObHDXCLmlfR3Jt4g88t0a2ZeUbu0hAQBQobQ9rm5vmTJlimzdulWGDRsm6enppluMGjRokNnOory9vaVly5bFjsDAQPHz8zO3NagC+3VTuzpyfZvaZh302Pdr5Vh6trWHBACoBARBnJiLi4u8OqCltAkPlNTMXLnvq1VyPDPH2sMCAKDCDBw4UN59910ZNWqUREdHm4yO2bNnFxZLjYmJkbi4OH4CTrQOahBcVeJSMuWpaeupkwYATsDF4mRVMbVNnVZq10Jl7NE9KTE1U679aLEkpGZJr+ah8uld7cTV1cXKPykAgL3jnMs82IPNh1Lk+o+XSHZuvikef+8l9a09JABABa47yASBhPh7y8S72ounu6vM35og78/fwawAAACn0KJWgLxwqk7am7O2yoYDydYeEgCgAhEEgRFdN1DGXN/K3P7wz13yx0ZSgQEAgHO4q3M9ubJFmOTkWeSR79ZKKtuDAcBhEQRBoRvb1SlMAX3ix/WyNS6V2QEAAE5RH+Stm1pL7cAqEnM0Q56bvpH6IADgoAiCoJiRVzWTSxoFy4mcPBn61So5SqV0AADgBAKqeMi429uIu6uL/LYhTn5YGWvtIQEAKgBBEBTj7uYqH93eRsKDfOTAsRPy8LdrTKEwAAAAR9c2vJo81bepuf3SL5tN0VQAgGMhCIIzBPp4ymeD20tVTzdZuueIPDeDlFAAAOAchnZvIJc2rSFZuflyzbjFcsvEpTJlyT7TTQ8AYP8IgqBETUL95KM72oqbq4tMW31Axv25i5kCAAAOz9XVRd67OUq6NaouFovIir1HZfQvm6XTmAUycOJS+XrpPkk8TkAEAOyVi8Wi/7w7j9L2DsZJ3y7fL8/P2GRu/3dglFzfpg5TAwDgnMvawykcSj5hOub9vjFO1sb8f+tcVxeRjvWDpF/rWnJzuzri7eFm1XECAKTUf+sTBMF5jZm1VSYu2iMebi7y1T2dpEvD6swaAOC8uPDAPDiSA8cyZNbGePltY5ysj/3/gIhmjOj6SLNnAQC2v+5gOwzO65m+zaRfq5qSk2eRB75eJbsSjzNrAADAqdSp5iNDezSQmQ93k3+evkyevaqZ+Hi6yb+7jsgH83dYe3gAgFIiCILS7Y29JUrahgdKamau3P3lSjl8PIuZAwAATqlukI882LOhvHF9K3N/3F+7ZNGOw9YeFgCgFAiCoFR0r+ukQe2lXvWTrXPv+2qVnMjOY/YAAIDTGtCmttzeKdwUUP3PD2tNDREAgG0jCIJSq+7rJV/e3UECfTzMXtj/TF0reflOVVcXAACgmFHXRErL2v5yLCNHHvlujeTk5TNDAGDDCILggjSo4WsyQjzdXGXO5gQZ88dWZhAAADh1tuzHt7cTP293WROTLG/O2mbtIQEAzoEgCC5Yh4ggefeWKHP7s8V75eOFu8TJOi0DAAAUCq/uI+/efHJt9PnivTJ7UxyzAwA2iiAIyuS6qFryVN+m5vbbs7fL0K9WydH0bGYTAAA4pb4twmRo9/rm9lM/bZD9R9KtPSQAQAkIgqDMHrq0oYy+NtJsjZm/NVGufP9v+XdXEjMKAACc0tNXNpP29arJ8axceejbNZKZQxF5ALA1BEFQZi4uLjKkW335+eFu0rBGVUk8niV3fr7c7IXNzqUoGAAAcC4ebq4y7vY2ElTVUzYfSpWXf91i7SEBAE5DEAQXLbKWv/z2aHe5rePJFnETFu2WmyYskX1JpIECAADnUjOgirw/MFpcXES+XxEjM9YesPaQAABFEARBuaji6SZjbmglE+5sKwFVPGTDgRTp9+E/8r/VByiaCgAAnEqPJjXk0csbm9vPTd8kGw+kWHtIAIBTCIKgXF3ZsqbMGt5dOtYPkvTsPHnip/Xyn6nr5HhmDjMNAACcxvArGssljYLlRE6e3DJxqczZHG/tIQEACIKgItQKrCLfD+0sT/RuIm6uLjJz3SEZOHGZHEnLYsIBAIBT0DXQx3e2le6NTwZCHvxmtXyycDcZsgBgZWSCoMJO/I9e0Vh+fKCLBPt6ypa4VBn46TJJSM1kxgEAgFPw9/aQL+/uIHd1rmfqpr01e5s8+dMGycqlawwAWAtBEFSodvWqmUBIzQBv2ZWYJjdPWCqxRzOYdQAA4BTc3Vzl1QEt5ZX+LcxFov+tOSB3fracDFkAsBKCIKhwDWr4mkBIeJCPxBzNMPti9xxOY+YBAIDTGNQlwmSF+Hm5y8p9x2TAx//KjoTj1h4WADgdgiCoFHWDfOSnB7tIoxBfiUvJlFsmLpNt8anMPgAAcKquMTMe7mouDMUePSE3fLxE/tqeaO1hAYBTIQiCShPq7y1T7+8skTX9JSktS279dJlsOJDMTwAAADiNRiF+8vPD3UwnvbSsXLl38kr5YvFeCqYCQCUhCIJKVd3XS76/v7O0CQ+U5IwcuX3Sclm57yg/BQAA4DSCqnrKN/d2klva15F8i8grv22RN2dvIxACAJWAIAgqXUAVD/n63k7SucHJKyB3fb5c/tl5mJ8EAABwGp7urvLWja3lmSubmfsTF+2RF37eJPkaFQEAVBiCILAKXy93mTyko1zWtIZk5uTLvZNXyfcrYrgCAgAAnIaLi4sMu7ShvHF9K3FxEfl2eYw88dN6yc3Lt/bQAMBhEQSB1Xh7uMnEu9rLVS3DJDsvX0ZO3yhDJq+UhNRMfioAAMBp3N4pXN4fGG1a6M5Ye1Ae/m6NZOXmWXtYAOCQbCIIMn78eImIiBBvb2/p1KmTrFix4qzPnT59urRv314CAwOlatWqEh0dLV9//XWljhflmwo6/va28kK/5ub2wu2Hpc9//5Zf1h9imgEAgNPoH11bJtzZTjzdXGXO5gS5b8oqycjOtfawAMDhWD0IMnXqVBkxYoSMHj1a1qxZI1FRUdK3b19JTCy5XVhQUJA8//zzsnTpUtmwYYMMGTLEHHPmzKn0saN8uLq6yH3dG8jvj14irWoHSMqJHHns+7XmKsjR9GymGQAAOIXekaHyxd0dpIqHm/yzM0kGf7FCUjNzrD0sAHAoLhaLxarVlzTzo0OHDvLRRx+Z+/n5+VK3bl159NFH5dlnny3Va7Rt21b69esnr7766nmfm5qaKgEBAZKSkiL+/v4XPX6Ur5y8fBn/1y756M9dkptvkWBfL3nrxlZyRfNQphoA7AznXOYBZbN6/1G5+8uVcjwz11wgmnJPR9NRBgBw8esOq2aCZGdny+rVq6VXr17/PyBXV3NfMz3OR+M3CxYskO3bt0uPHj0qeLSoDB5urvKfXk1kxkPdpHGIrySlZcm9U1bJ09PWy3GuhAAAACfQrl6QfD+0swl8bDyYIgMnLjU103Ttm5mTJ8fSs+Vg8gnZlXhcNhxIlmV7jshf2xPlwLEMaw8dAGyeuzXfPCkpSfLy8iQ0tPhVfr2/bdu2s36dRnZq164tWVlZ4ubmJh9//LH07t27xOfqc/QoGh2C7WtVJ0B+ffQSGTtvh0z6Z4/8uOqASQu9s3M9ubFtHQkL8Lb2EAEAACpMy9oB8uMDXeTOz5bLzsQ06fbmn5Jvsci5OugGVPGQeSN6SIgf6yQAsNmaIGXh5+cn69atk5UrV8rrr79uaoosXLiwxOeOGTPGpMQUHLrVBvbTPea5q5vL1Pu7SHiQj8SlZMo7c7ZL1zcXyN1frpDfN8RROR0AADisRiG+8tODXaR+cFWzTbhoAEQLymvQo2aAtzSoUdVkjWhdtdd+22rNIQOAzbNqTRDdDuPj4yPTpk2TAQMGFD4+ePBgSU5OlpkzZ5bqde677z6JjY0tsThqSZkgGgihJoh9OZGdJ79uOCTTVh2QFfuOFj4e6OMhA6Jry03t6pgrJgAA20FNEOYB5SMv3yIHj50Qbw9XqeLpZgqnursVv5a58UCK9B+/2ARKvr63o3RvXIPpB+BUUu2hJoinp6e0a9fO1PUooIVR9X6XLl1K/Tr6NUUDHUV5eXmZCSh6wP7oCf+W9nXlxwe7yF9PXioPX9ZQwvy9JTkjRyYv2SfXjFssV33wj3yzbL9ZKAAAADgKN1cXCa/uIyH+3uLn7XFGAKRgK/GgLhHm9os/bzK1QwAANrgdRreyTJo0SaZMmSJbt26VYcOGSXp6uml7qwYNGiQjR44str1l3rx5smfPHvP89957T77++mu58847rfhdoDJpSuhTfZvJv89eLpOHdJB+rWuKp5urbI1LlRd+3mSKh+0/ks4PBQAAOJURfZpIiJ+X7DuSIZ8s3G3t4QCATbJqYVQ1cOBAOXz4sIwaNUri4+MlOjpaZs+eXVgsNSYmxnSMKaABkoceekgOHDggVapUkWbNmsk333xjXgfOd1Xk0qYh5kjOyJZpqw/If+ftkFX7j5mskBf6RcptHeuKi4uLtYcKAABQ4fy9PWT0tS3k4e/WmCDIddG1pGENX2YeAGylJog1sD/ZscUezZAnflovK/aerBtyWdMa8taNrU36KACgcnHOZR5Q+XRpf/eXK2XRjsPStWF1+fa+TlwQAuAUUu2hJghQ3uoG+cgPQzvL81c3N1tk/tp+WPq8/7fpJAMAAODoNAP2lf4txMvdVZbsPiIz1x2y9pAAwKYQBIHDcXV1kaE9Gsivj14iLWr5m+Kpmhb6nx/WSkpGjrWHBwCwsvHjx0tERIR4e3tLp06dZMWKFWd97vTp06V9+/YSGBgoVatWNdt2tRYZYMvqVa8qj17eyNx+7fctrH8AoAiCIHBYTcP8ZMZD3cwiwNVF5Od1h6Tv+3/L3M3xkk8HGQBwSlOnTjVF2UePHi1r1qyRqKgo6du3ryQmJpb4/KCgIHn++edl6dKlsmHDBlO4XY85c+ZU+tiBC3F/j4bSKMRXktKy5a0525g8ADiFmiBwCmtijskTP66XvUknu8bUq+4jd3aqJze3ryOBPp7WHh4AOCRbrAmimR8dOnSQjz76yNzPz8+XunXryqOPPirPPvtsqV6jbdu20q9fP3n11Vftdh7gHJbtOSK3frrM3P7fsK7Srl41aw8JACoMNUGAItqGV5PfH7tEHujZQPy83WX/kQx5/Y+t0nnMAnl62nrZdDCF+QIAB5ednS2rV6+WXr16FT6mHej0vmZ6lKbg5IIFC2T79u3So0ePsz4vKyvLLMSKHoA1dG5QXW5sW8fcfn7GRsnNy+cHAcDpsR0GTsPH011GXtVclj93hbxxfStpFuYnmTn58uOqA3LNuMVy/cf/yoy1ByQrN8/aQwUAVICkpCTJy8uT0NDQYo/r/fj4+LN+nWZw+Pr6iqenp8kAGTdunPTu3fuszx8zZozJ/Cg4NNMEsJbnrm4mgT4esi3+uExeso8fBACnRxAEThkMub1TuMwa3l1+erCLXBtVSzzcXGRtTLI8PnW9dB3zp/x33g5Jzsi29lABADbAz89P1q1bJytXrpTXX3/d1BRZuHDhWZ8/cuRIEzgpOGJjYyt1vEBR1X29ZORVzcztsfN2yMHkE0wQAKfmbu0BANZsIdchIsgciceby9QVsfLt8hiJT82UDxbslM8X75VBXerJfd0bSFBV6oYAgL0LDg4WNzc3SUhIKPa43g8LCzvr1+mWmUaNTnba0O4wW7duNdkel156aYnP9/LyMgdgK25uV1d+WnVAVu0/JteOWyyt6wRIZE1/iazlbz5qNxk3rSIPAE6AIAggIiF+3vLoFY1l2KUNZfbmePnoz10mbfTjhbtN6uidnevJ0O4NpIYfi1oAsFe6naVdu3amrseAAQMKC6Pq/UceeaTUr6Nfo3U/AHvh6uoib9zQSm6ftMx0i1m4/bA5ClTxcJNmNf0KAyOXNwuRmgFVrDpmAKgoBEGAov9DuLnKNa1rydUta8q8rQky7s+dsulgqnz69x6ZsmSf2UbzYM+GEurvzbwBgB3SrSyDBw+W9u3bS8eOHeX999+X9PR00/ZWDRo0SGrXrm0yPZR+1Oc2bNjQBD7++OMP+frrr+WTTz6x8ncCXJgmoX7y99OXyda4VNkSd1y2HNKPqbItLlVO5OSZbcF6KE0KuaxpiNzWMVwubVrDrI8AwFEQBAHOcsWkb4sw6RMZaq6U6PaYdbHJ8uW/+8yWmYHt60q/1jWlZe0A8fXifyMAsBcDBw6Uw4cPy6hRo0wxVN3eMnv27MJiqTExMWb7SwENkDz00ENy4MABqVKlijRr1ky++eYb8zqAvdG6aO3qBZmjQF6+RfYmpZuAiAZGVu47Kqv3H5MF2xLNEervZdY9t3SoK3Wq+Vh1/ABQHlws2u/NiZS2dzBQlP5vsnhXkny4YKes3Hes8HEXF5FGNXwlqm6gRNUJkNZ1Ak06qZe7GxMIwOlxzmXtAfu0KzFNpq6MkWmrD8ixjJzCNU+PxjVMdsgVzUPEg+wQAHa67iAIAlxgMGTZnqPy9bJ9JmU0LiXzjOd4urmaQEjb8GpyX/f6XDUB4LQIgjAPsG9ZuXkyd3OCfL8iRpbsPlL4eIifl/x3YLR0axRs1fEBZRFzJMM0QuhY//8zouAYCIJc5MQApZGYminrD6TIhgPJhR+TT10xUf7e7vLWja3lqlY1mVAATodzLvMAx7EvKV1+WBkr01bHmuKq3h6u8tU9nfhDEnan99hFsutwmvzy8CXSqk6AtYeDckQQ5CInBihrpkjs0ROy/kCyfLZ4r6yPPVlgTAuqjromUrw92CYDwHlwzmUe4JjZIQ98vdrUTNO6aN/e18lsCwbs5QJmxzcWmNvaFfKZK5tZe0iwwrqDUs9AOXJxcZHw6j5ybVQtmfZgF9NJRn23PEau+2ixbI8/znwDAAC7pXXPJtzZTjo3CJK0rFwZ9MUK03EG9ik/36nKQ8qamP+v7Tdnc7xVxwLrIQgCVBAtGPbsVc3k63s7Sg0/L9mRkGYCId8s228yRgAAAOyRZrZ+NriDtAkPlJQTOXLX58tNMVXYlxd/3iSRo2fL2iKBAUdX0AZa7Tmczu+tkyIIAlSw7o1ryKzh3aVnkxqSlZsvL/y8SR76do2kFKkdAgAAYE90K8zkIR2lRS1/UyPkzs+WS+zRjEodg7b3/WX9If6QLQPt/PP1sv2SmZMvY/7Y5jQX6AoyQbSRgZq7hWwQZ0QQBKgEwb5e8uXdHeSFfs3Fw81FZm2Kl6s++FtW7jvK/AMAALsUUMVDvr63kzQO8TXdNm7/bJnEpZyotADIUz+tl8e+Xys3T1giyRnZlfK+jkCzdjQLpMCKfUfln51J4uiyc/Nlw4EUc/uuLvXMR+1+BOdDEASorP/ZXF3kvu4N5H/DukpEdR85lJIpN09YKv3H/ysTF+027boAAADsSVBVT1MctV51H1Mc/o7PlktSWlaFB0Ce/Gm9TF970Nw/lpEjY+ftqND3dBSZOXnyyHdr5EROnnRtWF3u7hphHn9v7naHzwbZFp9qsrI1eHd/jwbi4iKyLjZZElIzrT00VDKCIEAla10nUH57rLvc2LaO+cdXO8iMmbVNerzzl1z9wT/y0Z87SesEAAB2I8Tf2wRCagV4mzoLujWmojIzNADyxI/rZMbag+Lu6iIP9GhgHteaa5sPnbzKj7N75bctsi3+uAT7esr7A6PlkcsbSRUPN1l/IEXmb0106Klbs//kVhitZRPq7y1tTnU1mruFbBBnQxAEsNI+2vduiZLlz10hrw5oKd0aVRc3VxfZEpcq787dIb3GLjI9zMfO3S4bDiSb9D0AAABbVaeaj3w7tLMpBq9/ZGtGyKS/95gOHHoFPiM796LfIzcvX0b8uE5+XnfIBEA+ur2NjLy6ufRrXVO0yclLv2x2+GyGi/HbhkOmY6Eae0u0CV7plu0h3f4/G8SRu8WsOVUUtU3dauZjnxZh5uNcusQ4HXdrDwBwZiF+3nJX53rmOJqeLfO2xJt6If/uSpKdiWmy889d8uGfu0zxpqZhftKytr+0rB0grWoHmPvapg4AAMAW1A+uKt/c20lu/XSpbD6Uao6iNEBSL8hHwqv7SL2gqqaoas+mNUxHvdIEQB7/cb38ur4gANJWrmx58o/Y569uLn9uTZSV+47JzHWHZECb2uX6fR1Jy5LnZ2wyRTWn3NNRmtf0F3uj265H/m+juf3QpQ2lR5MahZ/TrSFfL91vgld/bIqTa1rXEke0NvZkJkjbeiczQPpEhsqbs7bJ0t1HTJcj3SYD50AQBLChPbUDO4SbQ/8hXrA1wQREVuw9au5vPJhiDpFY83wtsNok1E9a1gqQy5rVkD6RYabuCAAAgLXoRZoZD3Uz3Uf2HUmXmKMZsv9IhlnLHD6eZY5Vp7YlqFB/L7mtY7jc3jHcZCaUJgAy/o620vfUVXxVK7CK2dbxzpzt8vofW+WK5iHi510+f9Au3plksk8Sj5+sc/L+/B0y8a72Yk80o/iR79fI8axcaV+vmozo3aTY5wN9PE3duv/O32Fqq1zZIkzcSxGYsif6e6c1a3QretSpbTANavhKoxBfsw194fZE6R9dvsEz2C6CIIAN0kj0DW3rmEPTOg8cO1EYBNl06mNyRk7hVZapq2KldZ0AGXlVc+nSsLq1hw8AAJxYRHBVebJv02KPpWTkyP6j6SYgooGRvUnp5g/PhNQseX/+Tvnoz10msKFdOzrVDxIX/Wv1VABk+NR18vuGOHMBaPztbQu3MRR1X/f68tOqWNl3JEPG/blLnru6+UUHDnR7yMS/9xRmueiYtX7EnsNp5g9oe/HW7G2mK4quLz+4rU2JAY57LomQL5fsNTVdNJvmxnZ1xBFb42onI/8iAbK+LUJNEER/rgRBnAdBEMDG6SKgbpCPOa5uVdM8VhAY0YDI6v3H5PsVMebkdtukZXJZ0xry7FXNzZUYAAAAWxDg4yGtfQJNgfgCWbl5MntTvNmKodkhv2+MM0eTUF+zVfi6qNry3IyN5jENgHx8RzvpHRla4uvrFuHR17aQIZNXyheL98ot7etIo5CyrYU0yDH8h3WnMnBF7ugULi/0i5RHv19jiodO+mevjLmhldiD+VsS5PPFe83td2+OktqBVUp8nmbOPNizodke8v6CHXJddK1SbVOyF2tP1QNpG36yHkgBzaQe/9duWbgt0XTO8fZgq7kzcJzfbMAJAyNXtaopL1wTKYuevkwGdalnUkT/2n5Yrvrgb3l62nqJSzlh7aECAACcNXChV9+nDesqfzzW3WyL0U4lOxLS5MWZm6Xta/MKAyCfnCMAUuCyZiHSq3mI5OZb5KVftlxwkVR9/o+rYuWacYtNACTQx0Mm3NlOXr++lVTxdJMHejY0z/vfmgOSeNz226oeSj4hT05bb27f063+eedP15JaKFW3jfy06oA4YibI6UEQrbMX5u8t6dl5pjYInANBEMAB6Anrlf4tZd6InnJ1qzBTIf3HVQfk0ncWytuzt0lqZo61hwgAAHBWkbX8TXbF8uevkNHXRkqDGlVNO1wtDq+BiF7n+QO+wIvXRIqnu6ss3pVkOtOUltYsefT7tfL0tA2SkZ0nnRsEyazh3QuLryqtp9E2PNBslZmyZJ9N/zR1G9Fj368126f1D/1nriq+PakkPp7u8vBlJwM94/7caTIjHEFOXr7ptljQHrcoradXEByau6X0vy+wbwRBAAei+1U1VXT6Q12lQ0Q1ycrNl48X7paeb/9l2sZNXRkj62KTy6VNHQAAQHnTeg1DutWXBSN6yrQHu8ivj14iVzQvXQBE1ateVR7o0cDcfvW3rXIi+9x/yGug5Y+NcXL1B//IbxvixM3VRZ7q21S+va+z1AyockYm7v09TgYJdAtPWpbtrqc+WbjbbDHy9XI3rYRL21FQs3FqBnhLXEqm2W7tCLbHH5fMnHzx93aXhiXUcunT4uTv17wtCeb3AY6PmiCAA9JUvx8f6GL2rb45a6vsPpwuk4tcsdBaY9qiTuuGNA3zl+ZhftKspr9EVPcpLEQGAABgLboeaR8RVKavfejSRjJ9zUE5mHxCPlm4S0b0OTMLQrMctIPNpH/2mGKtKjzIRz64NVranLZloijNGmgQXFX2JKXL1JWxcu8l9cXW7EtKl3F/7TK3XxvQ0gSGSktrYjx6eWNTi0VrZQzsUNdkiDjCVpjo8GoldlLsVL+6+Hm7S1JatqyLPSbt6pXt9w72w75/owGcc/GgJ2otlDp7c7wpCKWR8G3xqeYfea2erseczQmFX6N7Ii9vHiJXNAuRrg2Dzf7X0krOyJa1scmSlZNvWtM5UjEtAABgP3T98ny/5vLQt2tkwt975KZ2dSW8uk/hekWzOPTi0JH0bPOY1v4Y1LmeDO3R4LytdTVTRJ83cvpG+fyfPaaOhi2tebSuyahfNpstO90bB0v/6FoX/Bo3t68jExbtNl18vlq63xRMtWdrTrVkbnOqNe7pdPuUrn1/XndI5m5OIAjiBAiCAA5O26Bd07qWOQokpWWZgMjWuFTzcXvCcfMxPjVTvlseYw4vd1fp1ijYBDQubxZSLCVUUwV3Jh6XNfuTTXRdD22pVkD3y350e1updZYK5AAAABXpqpZh0q1Rdfl31xF55bct8nL/FvLZP3tM9obW/FDaKWVo9/pyywVmO1zfpra8N3eHHErJlN82HJLr29hOO9lZm+Ll7x2HTS2Vl69rUaYMXw3qDL+isTzx03oTDNHuOOcLDtkyvUin2tY7e4aPtl3WIIjWkXn2qmZkRjs4giCAkxZSDW7kZYIcRdNCl+05In9uS5QFWxNNCqne1kNF1vSX9hHVZPfhNFkfm1LiPlitSaIBljUxydLvw3/k/VvbSM8mNSr1ewMAANA//l+6toVc9cE/Mn9rgvy1PbGw3kPzmv7yYM8G0q9VTXOx6ELplpEh3SLknTnbZeKiPTIgurZN/NGsa7NXft1ibj94aUNpUEL9i9Ia0Ka2fLxwl9lS/cXifTK8V2OxR7ouLdjuFH2WTBDVo0kNkxGiWdI7E9OkSWjZ2ivDPhAEAVB4Qr+0aYg5Xr7OYrJDNBiyYGuCiaBviUs1R4Gqnm4SVTfQ1B9pWy9Q2tStJtWqekrMkQx56LvVsulgqtz95Qp55LJG8p9eTUz6KAAAQGVpHOpnghWT/tlrAiCaGfJAj4Zmm8jFBi3u7FRPxv+1S7bFH5e/dybZxEWfD+bvMFm9WtvkoUsvbguLrtse791EHvlurcmgubNzuFT39RJ7sy7mZBZIoxBfCahy9mwWLSB7SaNgc/Fv7uZ4giAOjiAIgDPowqBZmL85Hr6skRxJy5KF2w/LpkMppqq2Bj60qGpJgQ3dczvtwa7y2u9b5JtlMTLuz12yat8x+eC2aAnx82a2AQBApXmqbzPzB3BkzQBpVSeg3F43wMfDdFL5fPFembhot9WDILrF+Yt/TxbB160/enHrYl3dsqZE1txtLoK9+tsWk+Frr0VRdav2+fSJDD0ZBNmSII9cbp+ZLygdgiAAzksj/ze2q2OO0tAT72sDWkmHiCBTOGzpniPS78PFMu62NtK5QfVSvUZ+vsUULEtIzTRt2vTKRkLKydv6mKY39mxaQ57s09SmCpIBAADboVscBnYIr5DXvueS+qbA6pLdR2TjgZRyDbJcCF0zvfDzJpPtorVQLmsaUi6vq51UxtzQSq7/+F9TL+O66FpyebPStyu2rSDI2euBFOgVGSouMzbKhgMpcij5BLXtHBhBEAAVpn90bWlRy99UZ9+RkCa3T1omT/RpKsN6NjQn1uOZOWafZuzRDNl/NMNUIdftNPuPpkt8Sqbk5J27V7umoG45lCof39HWrgt2AQAA+6OFVa+LqiUz1h6UiX/vNkXhrUFb/a7ef0x8PN1k1LWR5frauvVZ2wDrlqIXZmySOY8H2c2aKzcv3wQ01LnaHhetmde+XjVZue+YzNuSIIO7RlTCKGENBEEAVKhGIX7y88PdzBWK6WsOmiJiP62KldTMXDl6qjXd2eh23Rq+XhIW4G3a9+rHUH9vqRngLVm5+ab41z87k+TmCUvli7s72G3EPvF4pszZFC8LtiVKy1oB8ugVjcTL/eLTWAEAQMW6v0cDEwT5Y2OcuZBT0Iq3LHLy8k0B+p0JaWbbcWmKcx5Lz5Yxs7aa24/3alKsm195GdG7qczZnGAuVr09e7u8OqCl2AOtb6edgPy83KVxSOmKxPaJDDNBkLlb4gmCODCCIAAqnLade+/mKOkYEWR612vl7QJBVT1NAa961X2kXpCPhFevau7XqVZFavh5nXOriwYM7pmy0mSEDBj/r3w+uIPVUlEvlG7pmbUxTv7YFC8r9x0Vy6mkF629ohXsP7i1jdnDDAAAbJd2mtHOItqW9rPFe+SV/qULEGg27NY4zWhNKSw+vyM+TbLz8gsvBPWPqmUCEOcKrLw1e5scy8iRZmF+cne3islcqOLpJm/e0Epu/2y5fL1sv1wbVUs61g8SW6fdClV0eKDJQC6N3pGh8vofW2XZnqOSkpFjar/A8RAEAVBpxVZv7Rhu2vJq8a7a1aqYYMfFpFRqwEOzTO75cqWJ9t8ycampO6J7Om2R7i+dtSneBD9W7T+5R7WAtm3TqvXfLY+RzYdS5Zpx/8iL10TK7R3DbaLtHgAAKNmDPRqYIMiPq2JNRzy9wFNUZk6ebDqYImtjkmVt7DHTQU+zKkqiWQsa9NC1gNbh+H1jnFkLaKFOvThUlG6B+WFlrLn92oCWFVojrWujYBnYvq5MXRUrz/5vg/wxvHu5FF+tSGtP1QNpc47WuKeLCK4qTUP9zLryz+0Jcn2b0tXDg30hCAKgUtUN8jFHee7H/WlYF3n42zVma8z9X6+SUddEyt3d6out0Jonz83YaMZXVLt61UwBs6ta1TTfhxrcJUKe+Gm9ee7zMzaZzJC3bmx9xoLKUWgRN21Fp3MR4k/3IACA/enSsLq0qh0gGw+myJQl+2RAm9rmD/B1sckm8KEXf3Lzz6xzVivAWyJr+UtkTf9THwOkblAVc/FDgyaa5aHrgSlL98tPqw/IfZfUl6E9GpgLSFrvQrcaq1va15H2ERWfmfFcv+YmW3VPUrqM+3On6bxjy3TuVZt6568HUlTfFqEmCDJ3M0EQR+VisRQkYTuH1NRUCQgIkJSUFPH397f2cACUE91H++LPmwqviAzpFiEv9IsssY1vZdF/XrUOyuhfNktaVq5Jbe1QL0iuahUmV7YMO+u+Xa3y/sW/e82+W02LDfHzkvduiZLuja3bfq8i6ALvk4W7Tc2XacO6SJ1q5Rcgg/VxzmUeAGfx6/pD8uj3a8/6ec3i0IwE3ZoRVSfQBD6qleICx5JdSeZcuf5UgU+9KPLwZY0kOzffPB7o4yF/PnFppV0smb0pXh78ZrVZX/3ySDdpUcs2tyFr3bm2r84zt9eN6i2BPqWfHw1AXTNusXi5u8qPD3QxxWHhWOsOgiAAHIYGHT5ZtNsED1Sv5qHyRJ8mUt3XU4J8PMW9ElvpJmdkm0wOTWNVWm383ZujTJplaW0+lCLDf1gnuxLTzH29AvTUlU0dpmiqLjL6j//XZIOo+sFV5acHu5jq7HAMBEGYB8BZaGbGlR/8Y87Z2pa3ZS1/05GkTXig2fKqGZ9l3d6q6xsNPmhxec3CKEprdeh248r00Ler5Y+N8dKytr/8/FC3Sl1fldaf2xLknsmrpEGNqiZIdKHzfcdny03rYz9vd/n63k7mZwjbRxDkIicGgP36bcMhGfHjenOVpKiAKh5SvarnyaBIVT28JKiqhyncWsXDzbSW0+JfusdV7+tt/ahXajRltbSLl8U7k+SJn9ZJQmqWuLu6yOO9m8iDPRuWKSvlRHaevP7HFvlmWUxhAbYPbo0uVcV4W8/cue6jf02K8GVNa5gWygeTT5grYz880Fn87aT9Hs6Ncy7zADgTvQCi57LGIX4mEFIRgRbdFvP+/B1mjdE2PFCmPdi11EU/y7OrXe+xf0vKiRx59qpmZo1ja96ds10++muX3NSujrkIdaHSs3JlyJcrZcW+o6ZOy1f3dixVm11YF0GQi5wYAPZt9f6j8spvW009jmMZ2YXdV8pKi7j2bFLDHLr3t6rXmSWVtPCZXqX5fPFec79BcFV5/9ZoaV3n4q8ezN+SIE//b4NJ7/R0c5XhvRrLAz0a2OTVl9L46M+d8u7cHVLNx0PmjegpxzNz5eYJSyQpLdt0EdLFhq0XXMP5cc5lHgCUP11vaCHWTg2qmws81vDTqlh5atoGs2Vk9n96mGxOW3L7pGUmk+P161vKHZ3qlek1TCBk8kpZsfdkIGTKvR2lLYEQm0YQ5CInBoDj0O0WenXmSHq2HEnLNoGEo+lZ5g9ufVx7yJ/IyTOLCv2o2Rf6WMF9/ZqiBc00CNGhfrVTQZEQaRLqa9r0/ueHdaaQlrqzc7g8d3Vzk2VSnldenv3fRvlzW6K537pOgLxzU5Q0DbOvrJCdCcel34eLTb2T9wdGmwJyBdtjbvt0mRzPypUrmoXIhLvaVWile1Q8zrnMAwDHpFtGBn2xwhRu7VQ/SL4f2rnSM1LOte5r/dIcSc/Ok1nDu5ss2rLKyD6ZEbJ871Hx1UDIPR1NMXfYJoIgFzkxAFD0SsDS3Udk0Y7DsnBHosQePVFscrSopwZW9I/6YF9Pefum1nJ5s9AKW3TMWHtQXvpls6Rm5oqHm4sMv6KxPNCzoV0EDHRhctOEJaZi++XNQuTzwe2LbTPSqy13fb5csnLz5fo2teW9m6NsZlGFC8c5l3kA4Lg027bPf/82F4x0LaL1T/Q8rxeO/v9jvuTmWUxGbo8mNSQsoOI7welW26s++EeqerrJhpf6XnSRfA2E3DN5pSzbUxAI6SDt6lV8Nx5HZLFYzDaq+NRMs6VL2xGX5++EXQVBxo8fL++8847Ex8dLVFSUjBs3Tjp27FjicydNmiRfffWVbNp0siVUu3bt5I033jjr80/HggzAxdB/MvcdyZBF2xNNUGTpniOSmXOy9kiv5iHy5o2tK6WwZ2Jqpmm7O3/ryayQFrX8zZ7Xi7naURl0q9Crv20xi4i5j/eQWqdaA59ezOz+r1abxdPdXSNk9LWRZS4mB+vinMs8AHBsBef10tBONlpI9UKKxJfFt8v3m+L0XRtWl++Gdi6X19RAyL2TV5l1nwZXdNsugRA5a5fD+VsTZN+RdIlPyZKE45lm3VoQ+Chas0/Xrlq3pbLXHeWXp11GU6dOlREjRsiECROkU6dO8v7770vfvn1l+/btEhIScsbzFy5cKLfddpt07dpVvL295a233pI+ffrI5s2bpXbtkynVAFBR9I9x3fdaP7i+3N2tvtkys3LfUXOVoUuD6pX2x3qIv7dMGtReZq47ZFrwbj6UKtd9tFgeuayxPHSZbWaFxBzJMIXK1Mirm5UYAFGaRaMnxf9MXSeTl+wzi6b/9GpSyaMFAADnoxcrtsWlysaDKeLu5iJurq6mKLyui4p+1K42+49kmIyK6Q91vaCWtQWW7TkiExftlsubh8rN7eqctXaYZpuq8qzfodubv7i7g9w7ZaWpNTLo8xVma0z7CDJCTqfr0q+X7Zdz0QYFIX5eFVJAuDSsngmigY8OHTrIRx99ZO7n5+dL3bp15dFHH5Vnn332vF+fl5cn1apVM18/aNCg8z6fq1IAHI3WCnlhxiaZuyXB3G8W5mdSUrV2iZ5c9PAouO3maoqYVff1Mi2EK+vko6eaOz9fLv/uOiKdGwTJd/edf+/wlCX7zIlUvXRtpAk6wb5wzmUeAKBgrXL9+CWme45eNNIAwoWsQbTzngYgdLusCvX3kvt7NJTbO4abbn5FXf7eQtlzOF2+uLt9uW9P1rpx93210qxnNCNk8j0dpUM5B0J0i7XWT9uRmCa7Eo7LzsQ0s51IO/FE2Xir3tX7j8mNnywxt69pXdO0hg719zZHWICXhPh5S4i/l3i5V0zxe7vIBMnOzpbVq1fLyJEjCx9zdXWVXr16ydKlS0v1GhkZGZKTkyNBQSX/8mVlZZmj6MQAgCPRE8rEu9rJrxviZPTMTaZIqx7nE1HdR57vF2m28VR0BsvUlbFmweDt4Spv3tC6VHU+BneNkOSMHPnv/B3y0q9bJPbYCRl2acNK2W4EAADKd63y+d3t5aZPlpotJS/8vFHeurF1qdYf/+w8LPdNWWUCIO3rVZNDySfkUEqm2Ybz8V+75N7u9eWuzvXEz9vDFLzXAIiKrlv+BUw14PLZoA4y9KtVsnhXkvk4e3iPMte10IxirfW25VCq7Ew8LjsT0kwh/5Lc8dlyU0tNuwLZopy8fHl+xkZzu6ytiSuLVYMgSUlJJpMjNLR4hE7vb9u2rVSv8cwzz0itWrVM4KQkY8aMkZdffrlcxgsAtkoXEddF1TJXV37bcEjSMnNNoVbdd6mLBr2dc+qjPrZy3zFT20RP3pc0CpYXrmkuzcIqpp5IfEqmvP77VnP7id5NL2gv8GNXNDIFtL74d6/Zd/zd8hgTHLm/RwOTSgkAAOyDrjPG3d5G7p28Un5cdUAa1PCVB3s2POfXaCtgXavoWkYv2oy/o624iIv8b80B+XjhLlOs/u3Z22Xioj0ypFtEYate/VhR6wQTCBnc3hR633QwVR6fuk6+ua/TBRdg1doZw75ZLX9tP3zG5+oGVZHGIX7SOMRXGoX4yvQ1B03waPCXK+TTu9qbIrO25vPFe81FuGo+HqZDoi2z6naYQ4cOmToeS5YskS5duhQ+/vTTT8uiRYtk+fLl5/z6N998U95++21TJ6R169alzgTR7TZ0hwHgzNKycmX8X7vk83/2msCInrdv6xguI3o3MVtlSlMcdtW+o6Z4qbbo1ereVb3cS3zu0K9WmwJZmsI5fVjXC14k6GtoEdr/ztsh6w+kmMc0BfXubhEytHuDMu0rRuVgOwzzAADn2u464c62cmXLmiVO0qJTARC9eNM7MlTG39622Baa3Lx8+WX9Ifnor12F2R8FbmhbW8beEl2hk7/ncJpcM26xZGTnydNXNpWHLm10QV///vwd8v78nWabsq5pdC2lgY+GIVVNDZLTM0YKAia6tfmj29tInxZhYkudgnr/d5FpFvDOTa3l5vZ1rTIOu+gOo9thfHx8ZNq0aTJgwIDCxwcPHizJyckyc+bMs37tu+++K6+99prMnz9f2rdvX+r3ZEEGAMVPWmNmbZU/Nsab+37e7qbN3aAuEYULDb1SsSPxuGlfu3zvUfPx8PH/Dy4XCA/yMfVImtX0l+YaGAnzM4XShv+wzrTy/e3R7uaxstLT1Z/bEs32GL3yYsbr5S5DLqkv915SXwKqePCjtTGcc5kHACiJbt+dsnS/2Sb74wNdpHWd4rUuFm5PlPu/Xm0CIH0iQ+Wj0wIgRWk73lmb4uSjP3cVbgd+4/pWcnun8Aqf/B9XxcrT0zaY4q/ThnWV6FLW7NBOePdOWWVqfbx3c5TcWIoOKToXw39YK7M2xZsLSmNviZL+0dZvDGKxWEzBWw3QdKofJD/c39lqXf3sIghSUBhV29tqW9yCwqjh4eHyyCOPnLUwqmZ/vP766zJnzhzp3PnC2h6xIAOAkiuuv/LrFtkSl1pYL2RAm9qy6WCK2TqjW1KK0qsQUXUDTGX27fHHJbGEoEhR/+nVuNw6vOhpa96WBBk7b0fhYkeDN5oVosGQkjJSYB2cc5kHACiJZnHc99UqWbj9sNTw85KZD3cr7Br31/ZEeeCr1SZTtW+LUBl329kDICW1Zt19OF3u616/Ujrl6Zrkke/Xyu8b4qRedR/5/bHu4nuedcj+I+ly7bjFkpqZa2qZvDqg5QXNmwZdpq89KBpneOuG1nJLB+tkXRTQ7/3h79aYteEfw7ub7TvWYjdBEG2Rq5kfEydONMEQbZH7448/mpogWhtEO77olhmt7aG0Je6oUaPku+++k27duhW+jq+vrznOhwUZAMhZr6RMWx0r78zZIUlpxYMaPp5u0q5eNekYESQd6geZKx1FW9MdScsywZCTRVlTzccdCcdNWmSLWv4y46Fu5d6JRhc7czbHm8yQHQlp5jFtt/Zk36ZyY9s6F7zt5mz0NKnfx/GsHFNrRdNew6v7iL83mSf2es4dP368vPPOOxIfHy9RUVHmQoyuQUoyadIk+eqrr2TTpk3mfrt27eSNN9446/PtaR4AwJqOZ+aYQqnbE45L85r+Mu3BLibb9AHNAMnLlytbhJkaIpURzLgYeqHo6g/+MZ1vzrcNR7vLXP/xv2ad1DY8UH64v8sFr490/fPizE3y7fIYq3fQS83MkV7vLTIXwx67orHZVm1NdhMEUdretmAxEh0dLR9++KHJEFGXXnqpREREyOTJk819vb1//5l9h0ePHi0vvfTSed+LhQgAnH9RMumfvbL7cJpE1wmUjvWDJLKW/wUvQjSocvDYCXOF5/T2deVJFwO/bYyTd+dsl5ijGeaxyJr+pthr14bBpX6NZXuPyM9rD5orSBrs0LopOhfp2Xnmeymqioeb3Niuttzdtb5Vr3hcKP0+Uk/kSPKJHDmWkW2q6GsHnmMZOSaVV4vOlidbPOfqxRe9wDJhwgSz1tCLLz/99JNs375dQkJCznj+HXfcYS66dO3aVby9vc3FmBkzZsjmzZvNRRp7nQcAsAUHjmXIgPFLzMUXrR229VCqCYBc1TJMPrzN9gMgBbRO2i0Tl4ouFz64NbrEbSr6Z7cWUf153SEJ9vU024TL2lVGX0uLzn+2eK+5X5aaJOVh1MxN8tXS/aYQ7azh3YtdILMGuwqCVCYWIgDgmLJy8+SrJfvlwz93yvHMXPOYFlIbeVUzU4G+JHuT0uV/qw+Y9nR6BedcNO1UU1x1QXa0SPu6S5vWkHu61ZfujYOttgf2bHYmHJcP/9xltjVp0EOvVp3trB/m7y3LnrvC4c+5Gvjo0KGDuQBTsA1XC6Y/+uijZ92GW5R2tatWrZr5eg2m2Os8AICtWBebLAMnLjUdYNTVrcLkg1vtJwByeqFTXSv88Vh3kzVa1OR/98pLv24xmarf3tdJOl9kq1v9M/6/83fKhwt2mvtaA0WLqxYsRcwHF+2lc3INo7c0Y7ZDRJAE+HiUy89Ns1p0XfHdfZ2ka6PSXXiqSKU937JxGgDgELzc3WRojwamuNgH83fIN8tjTO2Qv7YlmkKv2m5XO8loIEDbCGvwY01McuHXa12Ra1rXkh6Ng8W/iodZxPh6u5/86OVutgRpkEMXHcv2HDVte3Xvse5n1kPb2A3pVl+ub1O7QjNfSlvwVhdiM9YeMFelTqffjxaSrVbVQ6r5eJp50YWRo9OC7KtXr5aRI0cWPubq6iq9evWSpUuXluo1MjIyJCcnR4KCgs76nJI60wEASqZbbN8fGC1P/rRe+rYIk7duam13ARD1yGWNZPHOJFm1/5gMn7rWFHwt+D5W7jsqr/2+1dzWizMXGwBRuibR7Se6Pnlz1jb57tT2mPN/nZiMWR2DHh3LEBTR2iTPTd9oAiA3tKltEwGQC0EmCADAIe1KPC5v/LHNdJRR+ke/Xv34e+dhU2FdadmQHk1qmBoimjVyoWmcWtxs8pJ98uPKWLNtRgX6eJh2w41q+Epufr7k5FnMYkHbCZsj7+RjllPZF3WDqkjdaj6mINzF1k3Rrj3a+vjb5fvNeygtKndX5wgJ8fcyYwus4lnu9VnsJQPi0KFDZgvLkiVLpEuXLoWPP/3007Jo0SJZvnz5eV/joYceMoXZdTuMbo8piW7Pffnll8943FbmAQBsUU5evl0GP07f3nPVB/+YjNRHL28kT/RpKompmdJv3GJzjr6mdU0Zd1ubcs8c1Ys7szfFm6CErjDMx6K3TeaIyJ6ktDPaCetQtH5b5/ongyKlyRT57J89Jqija6sFT/SUYF/buJDCdpiLnBgAgGP4Z+dhs2+2oJOM0nRRrekxILq2hPiXbT/u6YXBflp1QCYv2SuxR8+9reZsNCBTM6BKYVCkbpCPaTus6bT1gnwkqKrnWRdNmt3y6d+75YvF++REzslgTLdG1eWpvs1K3a7PGc65FxsEefPNN02HuoULF0rr1q0vKBNEt9zYyjwAACqOBiQe+W6tCS58fU8n+WDBDtNpr0morykUb+0udompmbJs71HTGVCP04MiSrNbtSB+23rVzMcGwVUL1yC6fViLoep6460bW8nADhXfiri0CIJc5MQAAByHFgTVoqf7j2ZIn8hQc8WjIup36PvoFhzdhnIiJ188XF3E3U0P11O3XU0BUn1Mr8jEpWSarSuxxzJMB5pz0S0sGhTRFnwnAyNVze0NB1JkwqLdhW2MtbDc032bSjcbSE21tXOubofx8fGRadOmyYABAwof1y51ycnJMnPmzLN+7bvvviuvvfaazJ8/X9q3b2/X8wAAqFhP/bReflp9wNT/0LWBn5e7/PLoJaaAqK1J0KCICYgcleUaFEk6MyhSzcejMCiydPcR+WdnktlG88P9ncW1nLrxlQeCIBc5MQAAVBatM3I4LetkQOToCdPlRm/HnDo0WHI+etVG0251+4utFGi11cKo2t5W2+IWFEYNDw+XRx555KyFUTX74/XXXzfbYDp37uwQ8wAAqDjpWblyzbjFpgC7mjSovdl2aw+OpGWZmmmr9x+TNfuPyfoDyYVFawt4uLmY4q+NQ/3EllAYFQAAO6FBixA/b3O0q3fm5zNz8sw+4/1HTh4aGNF6JJrZ4unmKkO7N5ABbWqbK044txEjRpjMD83m0GCItshNT0+XIUOGmM9rxxfdMjNmzBhzX1vijho1Sr777juJiIiQ+Ph487ivr685AAA4nW55+ej2NqZ4qJ6f7SUAoqr7epnxFoxZ66htPpRyMigSc0y2xh2XQV3q2VwA5ELQHQYAABunBVsbhfiZAxdn4MCBcvjwYRPY0IBGdHS0zJ49W0JDTy72YmJiTMeYAp988onZRnPTTTcVe53Ro0ebAqgAAJSkRa0AmfnIJXY/OZ7urtImvJo5HAXdYQAAQIVgGwjzAACAra077LsHEQAAAAAAQCkRBAEAAAAAAE6BIAgAAAAAAHAKBEEAAAAAAIBTIAgCAAAAAACcAkEQAAAAAADgFAiCAAAAAAAAp0AQBAAAAAAAOAWCIAAAAAAAwCkQBAEAAAAAAE7BXZyMxWIxH1NTU609FAAAHFrBubbg3OusWHsAAGA76w6nC4IcP37cfKxbt661hwIAgNOcewMCAsRZsfYAAMB21h0uFie7PJOfny+HDh0SPz8/cXFxKdeokwZWYmNjxd/fv9xeF8xvZeF3mPm1Z/z+2uYc6xJDFyK1atUSV1fn3YFbEWsPfucrHnPM/Nozfn+ZY3uXWoHrDqfLBNHJqFOnToW9vv6ACIJUHOa34jHHzK894/fX9ubYmTNAKmPtwe98xWOOmV97xu8vc2zv/Ctg3eG8l2UAAAAAAIBTIQgCAAAAAACcAkGQcuLl5SWjR482H1H+mN+Kxxwzv/aM31/m2NnwO88c2zt+h5lfe8fvsP3Or9MVRgUAAAAAAM6JTBAAAAAAAOAUCIIAAAAAAACnQBAEAAAAAAA4BYIg5WD8+PESEREh3t7e0qlTJ1mxYkV5vKxT+vvvv+Xaa6+VWrVqiYuLi/z888/FPq8lbEaNGiU1a9aUKlWqSK9evWTnzp1WG6+9GTNmjHTo0EH8/PwkJCREBgwYINu3by/2nMzMTHn44YelevXq4uvrKzfeeKMkJCRYbcz25JNPPpHWrVsX9jPv0qWLzJo1q/DzzG35evPNN82/E//5z3+Y43Ly0ksvmTktejRr1oz5tUGsPcoPa4+Kw7qj4rH2qFysPRxj7UEQ5CJNnTpVRowYYSrXrlmzRqKioqRv376SmJh4sS/tlNLT080c6uKuJG+//bZ8+OGHMmHCBFm+fLlUrVrVzLf+z4HzW7RokflHZNmyZTJv3jzJycmRPn36mHkv8Pjjj8uvv/4qP/30k3n+oUOH5IYbbmB6S6FOnTrm5Lh69WpZtWqVXH755dK/f3/ZvHkzc1vOVq5cKRMnTjRBp6L4/b14LVq0kLi4uMJj8eLFzK+NYe1Rvlh7VBzWHRWPtUflYe3hQGsP7Q6DsuvYsaPl4YcfLryfl5dnqVWrlmXMmDFM60XSX88ZM2YU3s/Pz7eEhYVZ3nnnncLHkpOTLV5eXpbvv/+e+S6DxMREM8+LFi0qnE8PDw/LTz/9VPicrVu3mucsXbqUOS6DatWqWT777DPmthwdP37c0rhxY8u8efMsPXv2tAwfPtw8zu/vxRs9erQlKiqqxM8xv7aDtUfFYe1RsVh3VA7WHuWPtYdjrT3IBLkI2dnZ5oqvbsko4Orqau4vXbr04qJTOMPevXslPj6+2HwHBASYLUjMd9mkpKSYj0FBQeaj/j5rdkjROdZ0tPDwcOb4AuXl5ckPP/xgrjDqthjmtvxoNlO/fv2K/Z4q5rh86BZD3ZLYoEEDueOOOyQmJob5tSGsPSoXa4/yxbqjYrH2qDisPRxr7eFeLqN2UklJSeYfm9DQ0GKP6/1t27ZZbVyOSgMgqqT5LvgcSi8/P9/UUujWrZu0bNmycI49PT0lMDCQOS6jjRs3mqCHbtHSfYszZsyQyMhIWbduHXNbDjSwpFsPNSX1dPz+XjwNKk+ePFmaNm1q0lFffvll6d69u2zatIn5tRGsPSoXa4/yw7qj4rD2qFisPRxv7UEQBHDiiLb+41J0zx0unv4DrgEPvdo1bdo0GTx4sNm/iIsXGxsrw4cPN/VstBA1yt9VV11VeFvrrejCpF69evLjjz+aYtQAUFasOyoOa4+Kw9rDMdcebIe5CMHBweLm5nZGdVq9HxYWdrE/G5ymYE6Z74v3yCOPyG+//SZ//fWXKahVdI411To5ObnY8/mdLj2NVjdq1EjatWtnquJrod8PPviAuS0HmhKpRafbtm0r7u7u5tAAkxZL1tt6VYDf3/KlV16aNGkiu3bt4nfYRrD2qFysPcoH646Kxdqj4rD2cMy1B0GQi/wHR//QWbBgQbFUP72v6fAoX/Xr1ze/7EXnOzU11XSJYb5LR2u+6UJEt2j8+eefZk6L0t9nDw+PYnOsLXR1Xx5zXDb6b0JWVhZzWw6uuOIKk/KrmTYFR/v27c3e0YLb/P6Wr7S0NNm9e7dpS86/D7aBtUflYu1xcVh3WAdrj/LD2sNB1x5lLqkK44cffjDdSSZPnmzZsmWL5f7777cEBgZa4uPjmaEyVl5eu3atOfTXc+zYseb2/v37zefffPNNM78zZ860bNiwwdK/f39L/fr1LSdOnGC+S2HYsGGWgIAAy8KFCy1xcXGFR0ZGRuFzHnzwQUt4eLjlzz//tKxatcrSpUsXc+D8nn32WdNpZ+/eveb3U++7uLhY5s6dy9xWkKLdYfj9vXhPPPGE+fdBf4f//fdfS69evSzBwcGmowPzaztYe5Qv1h4Vh3VHxWPtUflYe9j/2oMgSDkYN26c+cF4enqatnXLli0rj5d1Sn/99ZcJfpx+DB48uLBN7osvvmgJDQ01wacrrrjCsn37dmsP226UNLd6fPnll4XP0YDSQw89ZNqr+fj4WK6//noTKMH53XPPPZZ69eqZfwtq1Khhfj8LAiDMbeUsRPj9vTgDBw601KxZ0/wO165d29z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+      "text/plain": [
+       "<Figure size 1100x400 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "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": 27,
+   "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",
+    "    all_velocities_avg = []\n",
+    "\n",
+    "\n",
+    "    with torch.no_grad():\n",
+    "        for batch in dataloader:\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 = 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",
+    "            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",
+    "            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),\n",
+    "            np.concatenate(all_velocities_avg, 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, 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": 28,
+   "id": "ff6c5b57",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "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",
+    "    \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, 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",
+    "    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: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"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9a9d345",
+   "metadata": {},
+   "source": [
+    "R² at step k measures how much position and velocity information survives k steps of autoregressive rollout."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "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=0.993, 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"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ace9b94",
+   "metadata": {},
+   "source": [
+    "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."
+   ]
+  },
+  {
+   "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": 30,
+   "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",
+    "    clips_np, positions_np, velocities_np = [], [], []\n",
+    "    pred_positions, pred_velocities = [], []\n",
+    "\n",
+    "    with torch.no_grad():\n",
+    "        for i in indices:\n",
+    "            clip, positions, velocities = dataset[i]\n",
+    "            clip_b = clip.unsqueeze(0).to(device)\n",
+    "\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",
+    "            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",
+    "    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 clips_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": 31,
+   "id": "a941ffbc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 3000x900 with 30 Axes>"
+      ]
+     },
+     "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",
+    "                                 num_examples=3)\n",
+    "\n",
+    "plot_predictions_with_velocity(\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",
+    "    title_prefix=\"Rollout \",\n",
+    ")"
+   ]
+  },
+  {
+   "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): 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\")"
+   ]
+  },
+  {
+   "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",
+   "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"
+   ]
+  }
+ ],
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