experiment_04_feature_visualization.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature visualization\n",
    "\n",
    "Let's experiment with visualising some of the features in the neural network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch.utils.data import DataLoader\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CellPredictorNeuralNetwork(nn.Module):\n",
    "    \"\"\"Predicts the next state of the cells.\n",
    "\n",
    "    Inputs:\n",
    "        x: Tensor of shape (batch_size, channels, width+2, height+2), where channels=1. width and height are the dimensions of the entire game grid.\n",
    "           We add one cell of padding on each side to ensure that predictions can be made for the boundary cells.\n",
    "    \n",
    "    Returns: Tensor of shape (batch_size, width, height), the logits of the predicted states.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.conv0 = nn.Conv2d(1, 85, 3)\n",
    "        self.conv1 = nn.Conv2d(85, 10, 1)\n",
    "        self.conv2 = nn.Conv2d(10, 1, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = F.relu(self.conv0(x))\n",
    "        x = F.relu(self.conv1(x))\n",
    "        logits = self.conv2(x)\n",
    "        logits = torch.squeeze(logits, 1) # Remove channels dimension\n",
    "        return logits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<All keys matched successfully>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = CellPredictorNeuralNetwork()\n",
    "model.load_state_dict(torch.load(\"model_weights.pth\"))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `conv0` layer\n",
    "\n",
    "Since the `conv0` layer is just a 3 x 3 2D convolution and takes its input straight from the input data, we can visualise the layers as 3 x 3 grids. The values in the grid are just the weights, ignoring the bias, because that's what we would obtain if we did gradient ascent on the input space. (This is due to the Cauchy-Schwarz inequality)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([85, 1, 3, 3])\n",
      "torch.Size([85])\n"
     ]
    }
   ],
   "source": [
    "print(model.conv0.weight.shape)\n",
    "print(model.conv0.bias.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.8724248  0.         0.950449  ]\n",
      " [0.07223934 0.74881715 0.06117183]\n",
      " [0.38132328 0.5775547  0.3574369 ]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x21e1eaf7ca0>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize a single feature\n",
    "\n",
    "feature = 0\n",
    "\n",
    "with torch.no_grad():\n",
    "    feature_viz = model.conv0.weight[feature, 0, :, :]\n",
    "    feature_viz = feature_viz.numpy().copy() # For some reason we need this to avoid overwriting the model weights\n",
    "feature_viz /= np.max(np.abs(feature_viz)) # Scale to [-1, 1]\n",
    "feature_viz -= np.min(feature_viz) # Shift to [0, 2]\n",
    "feature_viz /= 2.0 # Scale to [0, 1]\n",
    "print(feature_viz)\n",
    "\n",
    "plt.imshow(feature_viz, interpolation=\"nearest\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualize multiple features\n",
    "\n",
    "with torch.no_grad():\n",
    "    feature_viz = model.conv0.weight[:, 0, :, :]\n",
    "    feature_viz = feature_viz.numpy().copy()\n",
    "feature_viz /= np.abs(feature_viz).max(axis=(1, 2), keepdims=True) # Scale to [-1, 1]\n",
    "feature_viz -= np.min(feature_viz, axis=(1,2), keepdims=True) # Shift to [0, 2]\n",
    "feature_viz /= 2.0 # Scale to [0, 1]\n",
    "\n",
    "\n",
    "def plot_features(i):\n",
    "    fig, axs = plt.subplots(3, 6, constrained_layout=True, figsize=(10, 5))\n",
    "    axs = axs.flatten()\n",
    "\n",
    "    for j in range(18):\n",
    "        feature = 18*i + j\n",
    "        ax: plt.Axes = axs[j]\n",
    "\n",
    "        if feature >= 85:\n",
    "            ax.set_visible(False)\n",
    "            continue\n",
    "\n",
    "        ax.imshow(feature_viz[feature], interpolation=\"nearest\",)\n",
    "        ax.set_title(f\"Feature {feature}\")\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_features(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_features(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_features(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dPXv2mGuvvda0atXKZGZmmuHDh5u9e/dGvLS8Mcbcf//95pRTTjEJCQlhL1VfWlpqfvzjH5vMzEyTnp5uRowYYQ4cOFDny9MfPHiw1nmXLFli+vfvb9LS0kxaWpo588wzTUFBgdm6dWu9t/Pxxx83vXv3Nm3atDFJSUmmQ4cO5oYbbjDbt2+v9+Nq7iPxa7o8Q5vhnLa5Y8cOM3z4cNO5c2eTkpJiWrRoYfLy8sxTTz1lgsFgvceAM7QZzu15c/369SY/P9+kpaWZ9PR08/3vf99s27at3mOgYXQZzm2Xy5YtM5LME088Ue/nhXu0Gc5Nm6Wlpea+++4zZ511lklNTTWZmZnm6quvNhs3bqz3GHCGNsO5afPBBx80Z555pklJSTGtW7c211xzTUy6DBhz3PfmAQAAAACAa3HxM9gAAAAAAPiNBRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwQFKsDxgMBrV3716lp6crEAjE+vA4QcYYHT58WDk5OUpIiJ+vz9Bl00ebsFG8dinRZlMXr23SZdNHm7CRmy5jvmDv3btXubm5sT4sPLZ792517NjR7zE8Q5fxgzZho3jrUqLNeBFvbdJl/KBN2MhJlzFfsNPT0yVJn23orIyWdn1VKv//3eL3CBHSX/7A7xHCVKpCf9WfQv8d40XN7ely12QlJKf4PE24hTc+7vcIEX7R93t+jxCh0pRr1eGX47bNUx77LyWkJvs8TbiEg3bNI0nTr1ro9whhjpZUaexFW+KuS+nrNk+/bbISLTtvVvUq9nuECJ0eCvo9QpjKqjKt3vJ43LVZc3tO/cUk6x7Pu/7qU79HiFRV6fcEESpNuVYVLYrbNvvrSiWpmc/ThPvZ3zb7PUKEJ/J6+j1CmEpTober/uioy5gv2DVPichomaCMdLsW7MRmdp2IJSkpYNdfQJnq/4m3p7bU3J6E5BTr/qHY0rK/J5KUFGju9wh1its2U5OVkGpXmwkp9i3YLdIT/R6hVvHWpfT1bUq08LypFuV+TxAhKbHK7xFqFW9tfvPxPCHFri6TEix87Aza92+MGvHaZpKaWffv+zQLHzttu49qOOnS3r9VAAAAAAA0ISzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOCBRi3Ys2fPVufOnZWSkqI+ffro/fff93ouoFFoEzaiS9iKNmEr2oSN6BJOuF6wFy1apAkTJmjKlCnasGGDevbsqUGDBunAgQPRmA9wjDZhI7qErWgTtqJN2Igu4ZTrBfuRRx7RmDFjdPPNN+uss87SU089pRYtWui5556r9fplZWUqLi4OewOiwU2bdIlY4ZwJW9EmbMXjOWzEORNOuVqwy8vLtX79euXn53/9CRISlJ+fr3fffbfWj5k1a5YyMzNDb7m5uSc2MVALt23SJWKBcyZsRZuwFY/nsBHnTLjhasH+8ssvVVVVpaysrLDLs7KyVFhYWOvHTJw4UUVFRaG33bt3N35aoA5u26RLxALnTNiKNmErHs9hI86ZcCMp2gdITk5WcnJytA8DuEKXsBVtwla0CRvRJWxFmycvV9/Bbtu2rRITE7V///6wy/fv36/s7GxPBwPcoE3YiC5hK9qErWgTNqJLuOFqwW7evLny8vK0YsWK0GXBYFArVqxQ3759PR8OcIo2YSO6hK1oE7aiTdiILuGG66eIT5gwQaNHj1avXr3Uu3dvPfbYYzpy5IhuvvnmaMwHOEabsBFdwla0CVvRJmxEl3DK9YL9wx/+UAcPHtTkyZNVWFioc845R8uWLYv4oX8g1mgTNqJL2Io2YSvahI3oEk416kXOxo0bp3Hjxnk9C3DCaBM2okvYijZhK9qEjegSTrj6GWwAAAAAAFA7FmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAeS/Dpw3vwfKyElxa/D16riwqDfI0RI39nT7xHCmMpj0vuv+j1G1JTllish1a6vOw1ePc7vESL84+9z/R4hQvHhoFp/2+8poue0n/xNSYFmfo8RJv3ttn6PEGHB/j5+jxCm4ki5pI/9HiOqytoaJaQYv8cI0/W6TX6PECHQurXfI4QJmHK/R4iqitZVSkit8nuMMLt+cobfI0TYUvBrv0eIEO+P51/8vI8Sk+3agaYXnO/3CBGu+2iZ3yOEOVpSqZUO7ya7NgkAAAAAAJooFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAA64X7NWrV2vIkCHKyclRIBDQH/7whyiMBbhDl7AVbcJWtAkb0SVsRZtwyvWCfeTIEfXs2VOzZ8+OxjxAo9AlbEWbsBVtwkZ0CVvRJpxKcvsBgwcP1uDBg6MxC9BodAlb0SZsRZuwEV3CVrQJp1wv2G6VlZWprKws9H5xcXG0Dwk0iC5hK9qErWgTNqJL2Io2T15Rf5GzWbNmKTMzM/SWm5sb7UMCDaJL2Io2YSvahI3oEraizZNX1BfsiRMnqqioKPS2e/fuaB8SaBBdwla0CVvRJmxEl7AVbZ68ov4U8eTkZCUnJ0f7MIArdAlb0SZsRZuwEV3CVrR58uL3YAMAAAAA4AHX38EuKSnRp59+Gnp/586d+vDDD9WmTRt16tTJ0+EAp+gStqJN2Io2YSO6hK1oE065XrDXrVunSy+9NPT+hAkTJEmjR4/WvHnzPBsMcIMuYSvahK1oEzaiS9iKNuGU6wV7wIABMsZEYxag0egStqJN2Io2YSO6hK1oE07xM9gAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4IEkvw5899ClSm3p2+FrNfXNH/g9QoR/dW/h9whhqsoTpPf9niJ6bsn7q1JaNvN7jDArD37b7xEiDMo5x+8RIlSaCkk7/B4jagrH9VFicorfY4T5v9N+7fcIES748Dq/RwhTdaTM7xGiruuiQ0pKTPZ7jDBv7P3Q7xEi9PvZT/weIUxlxTFpqd9TRM+3f7lFSYHmfo8RJlha6vcIEcpur/B7hAhlJuj3CFH1/k9+o4x0u77H+XJJpt8jRHjjXz38HiFMeUm54+va9V8XAAAAAIAmigUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8ICrBXvWrFk6//zzlZ6ervbt22vo0KHaunVrtGYDHKNN2IguYSvahK1oEzaiS7jhasFetWqVCgoKtHbtWi1fvlwVFRUaOHCgjhw5Eq35AEdoEzaiS9iKNmEr2oSN6BJuJLm58rJly8Lenzdvntq3b6/169fr4osv9nQwwA3ahI3oEraiTdiKNmEjuoQbrhbs4xUVFUmS2rRpU+d1ysrKVFZWFnq/uLj4RA4JONJQm3QJP3DOhK1oE7bi8Rw24pyJ+jT6Rc6CwaDGjx+vfv36qXv37nVeb9asWcrMzAy95ebmNvaQgCNO2qRLxBrnTNiKNmErHs9hI86ZaEijF+yCggJt2rRJCxcurPd6EydOVFFRUeht9+7djT0k4IiTNukSscY5E7aiTdiKx3PYiHMmGtKop4iPGzdOr732mlavXq2OHTvWe93k5GQlJyc3ajjALadt0iViiXMmbEWbsBWP57AR50w44WrBNsbojjvu0NKlS/XWW2+pS5cu0ZoLcIU2YSO6hK1oE7aiTdiILuGGqwW7oKBACxYs0Kuvvqr09HQVFhZKkjIzM5WamhqVAQEnaBM2okvYijZhK9qEjegSbrj6Gew5c+aoqKhIAwYMUIcOHUJvixYtitZ8gCO0CRvRJWxFm7AVbcJGdAk3XD9FHLARbcJGdAlb0SZsRZuwEV3CjUa/ijgAAAAAAPgaCzYAAAAAAB5gwQYAAAAAwAMs2AAAAAAAeIAFGwAAAAAAD7BgAwAAAADgARZsAAAAAAA8wIINAAAAAIAHWLABAAAAAPAACzYAAAAAAB5gwQYAAAAAwANJsT6gMUaSdLSkKtaHblDw6DG/R4hQVW7X10Cqyqvvo5r/jvGi5vaUHan0eZJIlUfK/B4hgjEVfo8QoVLVM8VrmzV/92xSfDjo9wgRqiz7+1JVWj1PvHUpfX2bKqvsus8lO9usrLDr73BVRXw/nlda+DgVtHAmG/+uHC6pnile2ywuse8+L7VwLysvKfd7hDAVR5z/OzNgYlzvnj17lJubG8tDIgp2796tjh07+j2GZ+gyftAmbBRvXUq0GS/irU26jB+0CRs56TLmC3YwGNTevXuVnp6uQCDQ6M9TXFys3Nxc7d69WxkZGR5OGH+8vK+MMTp8+LBycnKUkGDXd9dPhFddSrTpBm02jDZjjy6d4fE89mizYZwz/UGbDaPN2POry5g/RTwhIcHTr0ZlZGQQlkNe3VeZmZkeTGMXr7uUaNMN2qwbbfqHLuvH47l/aLNunDP9RZt1o03/xLrL+PmyEAAAAAAAPmLBBgAAAADAA012wU5OTtaUKVOUnJzs9yjW476KLe5v57ivYov72xnup9ji/naO+yq2uL+d476KLe5vZ/y6n2L+ImcAAAAAAMSjJvsdbAAAAAAAbMKCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeaLIL9uzZs9W5c2elpKSoT58+ev/99/0eyTqzZs3S+eefr/T0dLVv315Dhw7V1q1b/R4rrtFlw+jSH7TZMNr0B202jDZjjy4bRpf+oM2G+d1mk1ywFy1apAkTJmjKlCnasGGDevbsqUGDBunAgQN+j2aVVatWqaCgQGvXrtXy5ctVUVGhgQMH6siRI36PFpfo0hm6jD3adIY2Y482naHN2KJLZ+gy9mjTGd/bNE1Q7969TUFBQej9qqoqk5OTY2bNmuXjVPY7cOCAkWRWrVrl9yhxiS4bhy6jjzYbhzajjzYbhzajiy4bhy6jjzYbJ9ZtNrnvYJeXl2v9+vXKz88PXZaQkKD8/Hy9++67Pk5mv6KiIklSmzZtfJ4k/tBl49FldNFm49FmdNFm49Fm9NBl49FldNFm48W6zSa3YH/55ZeqqqpSVlZW2OVZWVkqLCz0aSr7BYNBjR8/Xv369VP37t39Hifu0GXj0GX00Wbj0Gb00Wbj0GZ00WXj0GX00Wbj+NFmUkyOAt8VFBRo06ZN+utf/+r3KEAIXcJWtAlb0SZsRJewlR9tNrkFu23btkpMTNT+/fvDLt+/f7+ys7N9mspu48aN02uvvabVq1erY8eOfo8Tl+jSPbqMDdp0jzZjgzbdo83oo0v36DI2aNM9v9psck8Rb968ufLy8rRixYrQZcFgUCtWrFDfvn19nMw+xhiNGzdOS5cu1V/+8hd16dLF75HiFl06R5exRZvO0WZs0aZztBk7dOkcXcYWbTrne5sxeSk1jy1cuNAkJyebefPmmS1btpixY8eaVq1amcLCQr9Hs8pPf/pTk5mZad566y2zb9++0Ftpaanfo8UlunSGLmOPNp2hzdijTWdoM7bo0hm6jD3adMbvNpvkgm2MMU8++aTp1KmTad68uendu7dZu3at3yNZR1Ktb3PnzvV7tLhFlw2jS3/QZsNo0x+02TDajD26bBhd+oM2G+Z3m4F/DwEAAAAAAE5Ak/sZbAAAAAAAbMSCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeaBIL9rx58xQIBGp9+8UvfhGVY65Zs0ZTp07VoUOHovL5vbBhwwZdc801atOmjVq0aKHu3bvriSeeiLjemjVr1L9/f7Vo0ULZ2dm68847VVJS4sPE8Yc2a+ekzTfffFM//vGP1b17dyUmJqpz587+DBunaLN2DbVZWlqq2bNna+DAgerQoYPS09N17rnnas6cOaqqqvJx8vhAl7Vzcs6cOXOmLrjgArVr104pKSnq1q2bxo8fr4MHD/o0dXyhzdo5/bdmjUOHDql9+/YKBAL6/e9/H8NJ4xdt1s5JmwMGDKj1frviiiuiOltSVD+7x+677z516dIl7LLu3btH5Vhr1qzRtGnTdNNNN6lVq1ZROcaJePPNNzVkyBCde+65mjRpklq2bKl//OMf2rNnT9j1PvzwQ11++eX6zne+o0ceeUR79uzRf//3f2v79u164403fJo+/tDm15y2uWDBAi1atEjnnXeecnJyfJo2/tHm15y0uWPHDt1xxx26/PLLNWHCBGVkZOj//u//dPvtt2vt2rV6/vnnfbwF8YMuv+b0nLl+/Xqdc845GjlypNLT0/XJJ5/o2Wef1euvv64PP/xQaWlpPt2C+EKbX3Pa5jdNnjxZpaWlMZzy5EGbX3PTZseOHTVr1qywy6L9784mtWAPHjxYvXr18nuME3LkyJETfhAsLi7Wj370I1111VX6/e9/r4SEup+I8Mtf/lKtW7fWW2+9pYyMDElS586dNWbMGL355psaOHDgCc2CarRZzU2bM2fO1LPPPqtmzZrp6quv1qZNm07o2KgdbVZz2mZ2drY+/vhjnX322aHLfvKTn+iWW27R3LlzNWnSJJ1++uknNAvosoabc+aSJUsiLuvbt6+uu+46/e///q9Gjhx5QrOgGm1Wc9NmjU2bNmnOnDmaPHmyJk+efELHRyTarOa2zczMTN1www0ndEy3msRTxJ164403dNFFFyktLU3p6em66qqrtHnz5rDrfPTRR7rpppvUtWtXpaSkKDs7W7fccov++c9/hq4zdepU3XPPPZKkLl26hJ5OsGvXLu3atUuBQEDz5s2LOH4gENDUqVPDPk8gENCWLVt0/fXXq3Xr1urfv3/oz1944QXl5eUpNTVVbdq00ciRI7V79+4Gb+eCBQu0f/9+zZgxQwkJCTpy5IiCwWDE9YqLi7V8+XLdcMMNoeVakn70ox+pZcuWevnllxs8FrxBm5FycnLUrFmzBj8noos2w7Vt2zZsua5x7bXXSpI++eSTBo+FE0eXztT8aI3NT+OMN7RZt5/97Ge69tprddFFFzX4+eE92qxbZWVlTH88tkl9B7uoqEhffvll2GVt27aVJM2fP1+jR4/WoEGD9OCDD6q0tFRz5sxR//79tXHjxtCD0PLly7Vjxw7dfPPNys7O1ubNm/XMM89o8+bNWrt2rQKBgIYNG6Zt27bppZde0qOPPho6Rrt27Rr1s07Dhw9Xt27dNHPmTBljJEkzZszQpEmTNGLECN166606ePCgnnzySV188cXauHFjvU/H+POf/6yMjAx98cUXGjp0qLZt26a0tDTdeOONevTRR5WSkiJJ+vjjj1VZWRnx1a7mzZvrnHPO0caNG13fFtSONqs5bROxQ5vVTrTNwsLCsPsOJ4Yuq7nt0hijf/7zn6qsrNT27dv1i1/8QomJiRowYIDr24La0WY1t20uXrxYa9as0SeffKJdu3a5nh8No81qbtus+fPy8nJlZWVpzJgxmjx5cnS/yWOagLlz5xpJtb4ZY8zhw4dNq1atzJgxY8I+rrCw0GRmZoZdXlpaGvH5X3rpJSPJrF69OnTZww8/bCSZnTt3hl13586dRpKZO3duxOeRZKZMmRJ6f8qUKUaSGTVqVNj1du3aZRITE82MGTPCLv/4449NUlJSxOXH69Gjh2nRooVp0aKFueOOO8ySJUvMHXfcYSSZkSNHhq63ePHiiNtVY/jw4SY7O7ve46BhtBnOaZvHu+qqq8ypp55a7+eGO7QZrrFtGmNMWVmZOeuss0yXLl1MRUVFvddF/egynNsu9+3bF3afdezY0SxatKjeY8AZ2gznps3S0lLTqVMnM3HiRGOMMStXrjSSzOLFi+s9BpyhzXBu2rzlllvM1KlTzZIlS8zvfvc7c8011xhJZsSIEfUe40Q1qe9gz549W9/+9rcjLl++fLkOHTqkUaNGhX1lJzExUX369NHKlStDl6Wmpob+/7Fjx1RSUqILLrhAUvWr0UXjaS233XZb2PuvvPKKgsGgRowYETZvdna2unXrppUrV+qXv/xlnZ+vpKREpaWluu2220Kvljds2DCVl5fr6aef1n333adu3brp6NGjkqTk5OSIz5GSkhL6c5w42qzmtE3EDm1WO5E2x40bpy1btuj1119XUlKTeti0Fl1Wc9tlmzZttHz5ch07dkwbN27UK6+8wm8F8RhtVnPT5gMPPKCKiop6Px9OHG1Wc9Pmb3/727CPvfHGGzV27Fg9++yzuuuuu0K33WtN6l8KvXv3rvWH+7dv3y5Juuyyy2r9uG/+/PG//vUvTZs2TQsXLtSBAwfCrldUVOThtF87/hX/tm/fLmNMnf+Ya+gpCzV/OUaNGhV2+fXXX6+nn35a7777rrp16xa6XllZWcTnOHbsWNhfMpwY2qzmtE3EDm1Wa2ybDz/8sJ599lndf//9uvLKK93cBNSDLqu57bJ58+bKz8+XJF199dW6/PLL1a9fP7Vv315XX32169uDSLRZzWmbu3bt0sMPP6zZs2erZcuWJ3AL0BDarHai/9b8+c9/rmeffVZ//vOfWbDrU/OD7fPnz1d2dnbEn3/zOw4jRozQmjVrdM899+icc85Ry5YtFQwGdcUVVzh6YZFAIFDr5fX9ftTjF9lgMKhAIKA33nhDiYmJEddv6ASVk5OjzZs3KysrK+zy9u3bS5K++uorSVKHDh0kSfv27Yv4HPv27eNXI8UAbVY7vk34jzar1dfmvHnz9F//9V+67bbb9P/+3/+r9/PDG3RZzek588ILL1SHDh304osvsmBHGW1WO77NyZMn65RTTtGAAQNCP3td85oVBw8e1K5du9SpUydHr0KOxqHNak7Pm7m5uZKqv9gQLXGxYJ922mmSqu/Ymq/s1uarr77SihUrNG3atLBfH1DzlZ9vqiug1q1bS4p8xc7PPvvM1bzGGHXp0qXWp3o0JC8vT8uXL9cXX3yhM844I3T53r17JVW/CIFU/bvxkpKStG7dOo0YMSJ0vfLycn344YdhlyE6aLPa8W3Cf7RZra42X331Vd16660aNmyYZs+e7fp4aBy6rObmnHns2LGofecJX6PNase3+fnnn+vTTz9V165dIz7H7bffLqn6PrHxdynHC9qs5vS8uWPHDkfXOxFx8eWkQYMGKSMjQzNnzlRFRUXEn9e84l3NV0nMv1/BrsZjjz0W8TE1v6Pt+IAyMjLUtm1brV69OuzyX//6147nHTZsmBITEzVt2rSIWcy/XyG0PjWL8fE/V/Cb3/xGSUlJoVcTzczMVH5+vl544QUdPnw4dL358+erpKREw4cPdzwzGoc2qx3fJvxHm9Vqa3P16tUaOXKkLr74Yr344ot85yWG6LLa8V0eOXJEpaWlER+/ZMkSffXVV03+d+M2BbRZ7fg2p0+frqVLl4a93X///ZKk//zP/9TSpUtP+Pceo360We34NouLiyN+TNYYo+nTp0uqvt+iJS6+g52RkaE5c+boxhtv1HnnnaeRI0eqXbt2+vzzz/X666+rX79++tWvfqWMjAxdfPHFeuihh1RRUaFTTjlFb775pnbu3BnxOfPy8iRJ9957r0aOHKlmzZppyJAhSktL06233qoHHnhAt956q3r16qXVq1dr27Ztjuc97bTTNH36dE2cOFG7du3S0KFDlZ6erp07d2rp0qUaO3as7r777jo//txzz9Utt9yi5557TpWVlbrkkkv01ltvafHixZo4cWLYU79nzJihCy+8UJdcconGjh2rPXv26H/+5380cOBAXXHFFS7uZTQGbdbd5kcffaQ//vGPkqRPP/1URUVFoZNez549NWTIEMdzwz3arL3Nzz77TNdcc40CgYCuu+46LV68OOzz9OjRQz169HA8N9yhy9q73L59u/Lz8/XDH/5QZ555phISErRu3Tq98MIL6ty5s372s5+5vKfhFm3W3uY3f69xjZrvVp9//vkaOnSo45nROLRZe5sbNmzQqFGjNGrUKJ1++uk6evSoli5dqnfeeUdjx47Veeed5/KediGqr1HukZqXp//ggw/qvd7KlSvNoEGDTGZmpklJSTGnnXaauemmm8y6detC19mzZ4+59tprTatWrUxmZqYZPny42bt3b8RLyxtjzP33329OOeUUk5CQEPZS9aWlpebHP/6xyczMNOnp6WbEiBHmwIEDdb48/cGDB2udd8mSJaZ///4mLS3NpKWlmTPPPNMUFBSYrVu3NniflJeXm6lTp5pTTz3VNGvWzJx++unm0UcfrfW6b7/9trnwwgtNSkqKadeunSkoKDDFxcUNHgMNo81ITtus79dOjB49usHjoH60GclJmzW/Xqaut+NvL9yhy0hOujx48KAZO3asOfPMM01aWppp3ry56datmxk/fnydM8Ed2ozk5t+ax99H4td0eYY2Izlpc8eOHWb48OGmc+fOJiUlxbRo0cLk5eWZp556ygSDwQaPcSICxhz3vXkAAAAAAOAaP1gGAAAAAIAHWLABAAAAAPAACzYAAAAAAB5gwQYAAAAAwAMs2AAAAAAAeCDmvwc7GAxq7969Sk9PVyAQiPXhcYKMMTp8+LBycnKUkBA/X5+hy6aPNmGjeO1Sos2mLl7bpMumjzZhIzddxnzB3rt3r3Jzc2N9WHhs9+7d6tixo99jeIYu4wdtwkbx1qVEm/Ei3tqky/hBm7CRky5jvmCnp6dLknIe+KUSUlJiffh6nTH9M79HiLDnibZ+jxCmqrRMn976WOi/Y7youT3dxk5WYnO7uixvZd+vqm+1zb6ZqiqO6W9Lp8dtmx2n/T/rzpl/u/Y5v0eIcOlHQ/0eIUxVaZk+/tHsuOtS+rrNHj+YpMRmdrX51Xf8niBS5ynv+z1CmEpV6K/6U9y1WXN7NnzQTi1b2vXdz9sv/b7fI0T48lct/R4hQryeN0M70EMTlZBq1zlTFfZ9R/3jq+f5PUKY4pKgTj1vl6MuY75g1zwlIiElxbq4khKa+z1ChMQWyX6PUKt4e2pLze1JbJ6ixGS7ukxIsW+ZTWxu30w14rXNhJQU6xbsjHS7/vEqcc6MpdB5s1mKdV+YTLBrHElSUqCZ3yOE+/dpPN7arLk9LVsmKN2ycxT/znQnXttMSLVvB1KSffe1jf/GkJx1aefkAAAAAAA0MSzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOCBRi3Ys2fPVufOnZWSkqI+ffro/fff93ouoFFoEzaiS9iKNmEr2oSN6BJOuF6wFy1apAkTJmjKlCnasGGDevbsqUGDBunAgQPRmA9wjDZhI7qErWgTtqJN2Igu4ZTrBfuRRx7RmDFjdPPNN+uss87SU089pRYtWui5556LxnyAY7QJG9ElbEWbsBVtwkZ0CadcLdjl5eVav3698vPzv/4ECQnKz8/Xu+++W+vHlJWVqbi4OOwN8JrbNukSscA5E7aiTdiKx3PYiHMm3HC1YH/55ZeqqqpSVlZW2OVZWVkqLCys9WNmzZqlzMzM0Ftubm7jpwXq4LZNukQscM6ErWgTtuLxHDbinAk3ov4q4hMnTlRRUVHobffu3dE+JNAguoStaBO2ok3YiC5hK9o8eSW5uXLbtm2VmJio/fv3h12+f/9+ZWdn1/oxycnJSk5ObvyEgANu26RLxALnTNiKNmErHs9hI86ZcMPVd7CbN2+uvLw8rVixInRZMBjUihUr1LdvX8+HA5yiTdiILmEr2oStaBM2oku44eo72JI0YcIEjR49Wr169VLv3r312GOP6ciRI7r55pujMR/gGG3CRnQJW9EmbEWbsBFdwinXC/YPf/hDHTx4UJMnT1ZhYaHOOeccLVu2LOKH/oFYo03YiC5hK9qErWgTNqJLOOV6wZakcePGady4cV7PApww2oSN6BK2ok3YijZhI7qEE1F/FXEAAAAAAE4GLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4IEkvw582sJyJSXZtd+/tPGPfo8QYeitd/o9QpjKikS/R4iqZqVGiZXG7zHCfHT3HL9HiHDlpdf5PUKEyqoyv0eIqm9/d7eapTX3e4wwZzz3U79HiNBxZbnfI4SprDzm9whRd+Pdryu1pW//nKjVE/OG+j1ChORV2X6PECbhSLk02O8poufK536mxOQUv8cIs3Hd436PEKHfVLv+nSlJwfL4Pm8uu3y20tPt2oFeLu7h9wgRfltk1znzaEmlpB2OrmvXf10AAAAAAJooFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAA64X7NWrV2vIkCHKyclRIBDQH/7whyiMBbhDl7AVbcJWtAkb0SVsRZtwyvWCfeTIEfXs2VOzZ8+OxjxAo9AlbEWbsBVtwkZ0CVvRJpxKcvsBgwcP1uDBgx1fv6ysTGVlZaH3i4uL3R4SaBBdwla0CVvRJmxEl7AVbcKpqP8M9qxZs5SZmRl6y83NjfYhgQbRJWxFm7AVbcJGdAlb0ebJK+oL9sSJE1VUVBR62717d7QPCTSILmEr2oStaBM2okvYijZPXq6fIu5WcnKykpOTo30YwBW6hK1oE7aiTdiILmEr2jx58Wu6AAAAAADwAAs2AAAAAAAecP0U8ZKSEn366aeh93fu3KkPP/xQbdq0UadOnTwdDnCKLmEr2oStaBM2okvYijbhlOsFe926dbr00ktD70+YMEGSNHr0aM2bN8+zwQA36BK2ok3YijZhI7qErWgTTrlesAcMGCBjTDRmARqNLmEr2oStaBM2okvYijbhFD+DDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeSPLrwH/43QJlpNu13w/K6ev3CBGSkz/ye4QwiabC7xGiqv9N65TcspnfY4QZlHOO3yNESGz9T79HiGTK/Z4gqoZmbVRqS99O2bV6uLSL3yNESFqx3u8RwsX5OVOSbs4otO7x/OGepX6PEKFbywN+jxCmTPHdZseH31NSwK7H8+QCu+aRpLYflvg9QoTKqmN+jxBV46+4TkkJyX6PEabys91+jxDB9L3I7xHCVFYek7TW0XXtekQEAAAAAKCJYsEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPOBqwZ41a5bOP/98paenq3379ho6dKi2bt0ardkAx2gTNqJL2Io2YSvahI3oEm64WrBXrVqlgoICrV27VsuXL1dFRYUGDhyoI0eORGs+wBHahI3oEraiTdiKNmEjuoQbSW6uvGzZsrD3582bp/bt22v9+vW6+OKLPR0McIM2YSO6hK1oE7aiTdiILuGGqwX7eEVFRZKkNm3a1HmdsrIylZWVhd4vLi4+kUMCjjTUJl3CD5wzYSvahK14PIeNOGeiPo1+kbNgMKjx48erX79+6t69e53XmzVrljIzM0Nvubm5jT0k4IiTNukSscY5E7aiTdiKx3PYiHMmGtLoBbugoECbNm3SwoUL673exIkTVVRUFHrbvXt3Yw8JOOKkTbpErHHOhK1oE7bi8Rw24pyJhjTqKeLjxo3Ta6+9ptWrV6tjx471Xjc5OVnJycmNGg5wy2mbdIlY4pwJW9EmbMXjOWzEORNOuFqwjTG64447tHTpUr311lvq0qVLtOYCXKFN2IguYSvahK1oEzaiS7jhasEuKCjQggUL9Oqrryo9PV2FhYWSpMzMTKWmpkZlQMAJ2oSN6BK2ok3YijZhI7qEG65+BnvOnDkqKirSgAED1KFDh9DbokWLojUf4AhtwkZ0CVvRJmxFm7ARXcIN108RB2xEm7ARXcJWtAlb0SZsRJdwo9GvIg4AAAAAAL7Ggg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8EBSrA9ojJEkFZcEY33oBlWaCr9HiBAwdn0NpOY+qvnvGC9qbk/5EfsaqDT2/V0xptzvESJU/numeG3zaEmVz5NEqio75vcIEWw7j1cqPs+Zkt2P58FS+9osK7GrzZrHu3hrs+b2VKpCsuymFR+27+9KZZV9f1cqq8okxXGbQRv/DWXX+UmSTKVdbbrpMmBiXO+ePXuUm5sby0MiCnbv3q2OHTv6PYZn6DJ+0CZsFG9dSrQZL+KtTbqMH7QJGznpMuYLdjAY1N69e5Wenq5AINDoz1NcXKzc3Fzt3r1bGRkZHk4Yf7y8r4wxOnz4sHJycpSQYNd310+EV11KtOkGbTaMNmOPLp3h8Tz2aLNhnDP9QZsNo83Y86vLmD9FPCEhwdOvRmVkZBCWQ17dV5mZmR5MYxevu5Ro0w3arBtt+ocu68fjuX9os26cM/1Fm3WjTf/Eusv4+bIQAAAAAAA+YsEGAAAAAMADTXbBTk5O1pQpU5ScnOz3KNbjvoot7m/nuK9ii/vbGe6n2OL+do77Kra4v53jvoot7m9n/LqfYv4iZwAAAAAAxKMm+x1sAAAAAABswoINAAAAAIAHWLABAAAAAPAACzYAAAAAAB5osgv27Nmz1blzZ6WkpKhPnz56//33/R7JOrNmzdL555+v9PR0tW/fXkOHDtXWrVv9Hiuu0WXD6NIftNkw2vQHbTaMNmOPLhtGl/6gzYb53WaTXLAXLVqkCRMmaMqUKdqwYYN69uypQYMG6cCBA36PZpVVq1apoKBAa9eu1fLly1VRUaGBAwfqyJEjfo8Wl+jSGbqMPdp0hjZjjzadoc3Yoktn6DL2aNMZ39s0TVDv3r1NQUFB6P2qqiqTk5NjZs2a5eNU9jtw4ICRZFatWuX3KHGJLhuHLqOPNhuHNqOPNhuHNqOLLhuHLqOPNhsn1m02ue9gl5eXa/369crPzw9dlpCQoPz8fL377rs+Tma/oqIiSVKbNm18niT+0GXj0WV00Wbj0WZ00Wbj0Wb00GXj0WV00WbjxbrNJrdgf/nll6qqqlJWVlbY5VlZWSosLPRpKvsFg0GNHz9e/fr1U/fu3f0eJ+7QZePQZfTRZuPQZvTRZuPQZnTRZePQZfTRZuP40WZSTI4C3xUUFGjTpk3661//6vcoQAhdwla0CVvRJmxEl7CVH202uQW7bdu2SkxM1P79+8Mu379/v7Kzs32aym7jxo3Ta6+9ptWrV6tjx45+jxOX6NI9uowN2nSPNmODNt2jzeijS/foMjZo0z2/2mxyTxFv3ry58vLytGLFitBlwWBQK1asUN++fX2czD7GGI0bN05Lly7VX/7yF3Xp0sXvkeIWXTpHl7FFm87RZmzRpnO0GTt06RxdxhZtOud7mzF5KTWPLVy40CQnJ5t58+aZLVu2mLFjx5pWrVqZwsJCv0ezyk9/+lOTmZlp3nrrLbNv377QW2lpqd+jxSW6dIYuY482naHN2KNNZ2gztujSGbqMPdp0xu82m+SCbYwxTz75pOnUqZNp3ry56d27t1m7dq3fI1lHUq1vc+fO9Xu0uEWXDaNLf9Bmw2jTH7TZMNqMPbpsGF36gzYb5nebgX8PAQAAAAAATkCT+xlsAAAAAABsxIINAAAAAIAHWLABAAAAAPAACzYAAAAAAB5gwQYAAAAAwAMs2AAAAAAAeIAFGwAAAAAAD7BgAwAAAADgARZsAAAAAAA8wIINAAAAAIAHWLABAAAAAPBAk1iw582bp0AgUOvbL37xi6gcc82aNZo6daoOHToUlc/vhQ0bNuiaa65RmzZt1KJFC3Xv3l1PPPFExPXKy8s1c+ZMnXnmmUpJSVFWVpauuuoq7dmzx4ep4wtt1q6hNnft2lXn/RYIBDRmzBgfp48PtFk7J+fNYDCop556Suecc45atmyprKwsDR48WGvWrPFp6vhBl7Vz0mVFRYWmTZumrl27Kjk5WV27dtX06dNVWVnp09TxhTbD3XTTTfU+Tn/xxRdh11+zZo369++vFi1aKDs7W3feeadKSkp8mj6+0GY4N22++eab+vGPf6zu3bsrMTFRnTt3jsmMSTE5ikfuu+8+denSJeyy7t27R+VYa9as0bRp03TTTTepVatWUTnGiXjzzTc1ZMgQnXvuuZo0aZJatmypf/zjHxFLc0VFha666iqtWbNGY8aMUY8ePfTVV1/pvffeU1FRkTp27OjTLYgvtPk1J222a9dO8+fPj/jYZcuW6cUXX9TAgQNjOXJco82vOT1v3nPPPXrkkUd0ww036Pbbb9ehQ4f09NNP65JLLtE777yj3r17+3QL4gddfs1plzfccIMWL16sW265Rb169dLatWs1adIkff7553rmmWd8mj7+0Ga1n/zkJ8rPzw+7zBij2267TZ07d9Ypp5wSuvzDDz/U5Zdfru985zt65JFHtGfPHv33f/+3tm/frjfeeCPWo8ct2qzmps0FCxZo0aJFOu+885STkxO7IU0TMHfuXCPJfPDBBzE75sMPP2wkmZ07d3r6eUtKSk74cxQVFZmsrCxz7bXXmqqqqnqv++CDD5pmzZqZ995774SPi0i0Gc5Nm7W5/PLLTUZGhjl69OgJz3Kyo81wTtusqKgwqamp5rrrrgu7fMeOHUaSufPOO094lpMZXYZz2uX7779vJJlJkyaFXf7zn//cBAIB87e//e2EZznZ0WbD3n77bSPJzJgxI+zywYMHmw4dOpiioqLQZc8++6yRZP7v//4vKrOcTGizYXW1+cUXX5jy8nJjjDFXXXWVOfXUU6Ny/OM1iaeIO/XGG2/ooosuUlpamtLT03XVVVdp8+bNYdf56KOPdNNNN6lr165KSUlRdna2brnlFv3zn/8MXWfq1Km65557JEldunQJPeVg165doae2zps3L+L4gUBAU6dODfs8gUBAW7Zs0fXXX6/WrVurf//+oT9/4YUXlJeXp9TUVLVp00YjR47U7t27G7ydCxYs0P79+zVjxgwlJCToyJEjCgaDEdcLBoN6/PHHde2116p3796qrKxUaWlpg58f3qPNhu3bt08rV67UsGHDlJKS4uhjcOJoM1xFRYWOHj2qrKyssMvbt2+vhIQEpaamNngsnDi6DPf2229LkkaOHBl2+ciRI2WM0aJFixo8FrxxsrRZmwULFigQCOj6668PXVZcXKzly5frhhtuUEZGRujyH/3oR2rZsqVefvnlRh0L7tFmeJuSlJOTo2bNmjXqc56IJvUU8aKiIn355Zdhl7Vt21aSNH/+fI0ePVqDBg3Sgw8+qNLSUs2ZM0f9+/fXxo0bQ8+5X758uXbs2KGbb75Z2dnZ2rx5s5555hlt3rxZa9euVSAQ0LBhw7Rt2za99NJLevTRR0PHaNeunQ4ePOh67uHDh6tbt26aOXOmjDGSpBkzZmjSpEkaMWKEbr31Vh08eFBPPvmkLr74Ym3cuLHep2P8+c9/VkZGhr744gsNHTpU27ZtU1pamm688UY9+uijoeVky5Yt2rt3r3r06KGxY8fq+eefV3l5ub773e/q8ccf16WXXur6tqB2tFnNaZu1WbhwoYLBoP7jP/7D9e1A3WizmtM2U1NT1adPH82bN099+/bVRRddpEOHDun+++9X69atNXbsWNe3BZHosprTLsvKyiQp4gs8LVq0kCStX7/e9W1B7WizdhUVFXr55Zd14YUXhv0c68cff6zKykr16tUr7PrNmzfXOeeco40bN7q+LagdbdaurjZ9FZPvk5+gmqdG1PZmjDGHDx82rVq1MmPGjAn7uMLCQpOZmRl2eWlpacTnf+mll4wks3r16tBldT01YufOnUaSmTt3bsTnkWSmTJkSen/KlClGkhk1alTY9Xbt2mUSExMjnsbw8ccfm6SkpIjLj9ejRw/TokUL06JFC3PHHXeYJUuWmDvuuMNIMiNHjgxd75VXXjGSzLe+9S3TrVs3M3fuXDN37lzTrVs307x5c55S5gHaDOe0zdrk5eWZDh06NOqp5YhEm+HctLl9+3Zz3nnnhd1nXbt2NX//+9/rPQYaRpfhnHa5ZMkSI8nMnz8/7OOfeuopI8l079693uOgYbRZv//93/81ksyvf/3rsMsXL14ccbtqDB8+3GRnZ7s6DiLRZv3qavN4sXyKeJP6Dvbs2bP17W9/O+Ly5cuX69ChQxo1alTYV3YSExPVp08frVy5MnTZN7/6e+zYMZWUlOiCCy6QVP0qnhdddJHnc992221h77/yyisKBoMaMWJE2LzZ2dnq1q2bVq5cqV/+8pd1fr6SkhKVlpbqtttuC73K6LBhw1ReXq6nn35a9913n7p16xZ69cbDhw9r48aNys3NlSRddtllOv300/XQQw/phRde8PrmnpRos5rTNo+3bds2rV+/XnfddZcSEuLqJ1d8R5vV3LSZnp6us88+W3379tXll1+uwsJCPfDAAxo6dKjefvvt0Ffz0Xh0Wc1pl1deeaVOPfVU3X333WrRooXy8vL03nvv6d5771VSUpKOHj3q+W09WdFm7RYsWKBmzZppxIgRYZfXtJecnBzxMSkpKbTpIdqsXV1t+qlJLdi9e/eOeAqKJG3fvl1S9eJYm2/+TMi//vUvTZs2TQsXLtSBAwfCrldUVOThtF87/hX/tm/fLmNMrYuGpAZ/VqDmL8eoUaPCLr/++uv19NNP691331W3bt1C1+vXr19ouZakTp06qX///vzKGQ/RZjWnbR7vxRdflCSeHh4FtFnNaZuVlZXKz8/XgAED9OSTT4aul5+fr7PPPlsPP/ywHnzwwcbcJHwDXVZz2mVKSopef/11jRgxQj/4wQ8kVS80Dz30kGbMmKGWLVs29ibhOLQZqaSkRK+++qoGDRqkb33rW2F/VtNwzY8xfNOxY8d43QoP0Wak+tr0U5NasOtS84Ig8+fPV3Z2dsSfJyV9fTNHjBihNWvW6J577gn9jtNgMKgrrrjC0YsxBQKBWi+vqqqq82OOP7kEg0EFAgG98cYbSkxMjLh+Qw+UOTk52rx5c60vwiNJX331Veh6kiKuV3Ndfi4m+miz2vFtHm/BggU644wzlJeXV+/nh3dos9rxba5evVqbNm3SI488Ena9bt266Tvf+Y7eeeedeo+DE0OX1Wo7Z5599tnatGmTtmzZoq+++kpnnXWWUlNTddddd+mSSy6p9zg4cSdbm9/0hz/8QaWlpbV+EbxDhw6Sql+o9Hj79u2L7a9GOknRZu1t+ikuFuzTTjtNUvUD0vG/F+2bvvrqK61YsULTpk3T5MmTQ5fXfOXnm+oKqHXr1pIU8YvXP/vsM1fzGmPUpUuXWp/q0ZC8vDwtX75cX3zxhc4444zQ5Xv37pVU/SIEkvTd735XzZo1C/uF69+8bs31ED20We34Nr/pvffe06effqr77rvP9fHQeLRZ7fg29+/fL6n2fyxUVFSosrLS9bHhHF1Wq+ucGQgEdPbZZ4fe/9Of/qRgMFjvfQVvnGxtftOLL76oli1b6pprron4s+7duyspKUnr1q0Le4pueXm5PvzwQ6uethuvaLP2Nv0UFz/sOGjQIGVkZGjmzJmqqKiI+POaV7yr+SqJ+fcr2NV47LHHIj4mLS1NUmRAGRkZatu2rVavXh12+a9//WvH8w4bNkyJiYmaNm1axCzGmLCXyq9Nzcnqt7/9bdjlv/nNb5SUlKQBAwZIqv45wiuvvFJr1qzR3//+99D1PvnkE61Zs0bf+973HM+MxqHNase3+U0LFiyQpIhfrYDoos1qx7dZ82C/cOHCsOtt2LBBW7du1bnnnut4ZrhHl9XqO2fWOHr0qCZNmqQOHTpEPMUc3jvZ2qxx8OBB/fnPf9a1114betX6b8rMzFR+fr5eeOEFHT58OHT5/PnzVVJSouHDhzueGY1Dm7W36ae4+A52RkaG5syZoxtvvFHnnXeeRo4cqXbt2unzzz/X66+/rn79+ulXv/qVMjIydPHFF+uhhx5SRUWFTjnlFL355pvauXNnxOesearqvffeq5EjR6pZs2YaMmSI0tLSdOutt+qBBx7Qrbfeql69emn16tXatm2b43lPO+00TZ8+XRMnTtSuXbs0dOhQpaena+fOnVq6dKnGjh2ru+++u86PP/fcc3XLLbfoueeeU2VlpS655BK99dZbWrx4sSZOnBj2dJyZM2dqxYoVuuyyy3TnnXdKkp544gm1adPG1QsIoHFos+42pervEi5atEgXXHBB6CuwiA3arL3NvLw8fe9739Pzzz+v4uJiDRw4UPv27dOTTz6p1NRUjR8/3t0dDVfosu5z5ogRI5STk6OzzjpLxcXFeu6557Rjxw69/vrrSk9Pd3EvozFOtjZrLFq0SJWVlfU+BXfGjBm68MILdckll2js2LHas2eP/ud//kcDBw7UFVdc4XhmNA5t1t3mRx99pD/+8Y+SpE8//VRFRUWaPn26JKlnz54aMmSI47ldicVLlZ+ompen/+CDD+q93sqVK82gQYNMZmamSUlJMaeddpq56aabzLp160LX2bNnj7n22mtNq1atTGZmphk+fLjZu3dvxEvLG2PM/fffb0455RSTkJAQ9lL1paWl5sc//rHJzMw06enpZsSIEebAgQN1vjz9wYMHa513yZIlpn///iYtLc2kpaWZM8880xQUFJitW7c2eJ+Ul5ebqVOnmlNPPdU0a9bMnH766ebRRx+t9brr1683+fn5Ji0tzaSnp5vvf//7Ztu2bQ0eAw2jzUhu2ly2bJmRZJ544okGPy/coc1ITtssLS019913nznrrLNMamqqyczMNFdffbXZuHFjg8dA/egyktMuH3zwQXPmmWealJQU07p1a3PNNdfQpIdos3YXXHCBad++vamsrKz3em+//ba58MILTUpKimnXrp0pKCgwxcXFjo6B+tFm7Zy0Wd+vOBs9erSj4zRGwJjjvjcPAAAAAABci4ufwQYAAAAAwG8s2AAAAAAAeIAFGwAAAAAAD7BgAwAAAADgARZsAAAAAAA8wIINAAAAAIAHkmJ9wGAwqL179yo9PV2BQCDWh8cJMsbo8OHDysnJUUJC/Hx9hi6bPtqEjeK1S4k2m7p4bZMumz7ahI3cdBnzBXvv3r3Kzc2N9WHhsd27d6tjx45+j+EZuowftAkbxVuXEm3Gi3hrky7jB23CRk66jPmCnZ6eLkk664ZJSmyeEuvD1ytz6F6/R4jwv2e+4fcIYYpLgjr1vF2h/47xoub2XNJtnJISk32eJtyxU+y7r1+b8zu/R4gQ721+tqGzMlra9ZX8ouBRv0eIUG6Cfo8QpqQkqPPOPxh3XUpft3nKffcqIcWux/PT/nOd3yNEWLrtY79HCBPv58z+ulJJaubzNOH+8dQ5fo8QKWD8niBC8GiZvhj/YNy2aePj+QNfnuH3CBHeu7C53yOEqVSF/qo/Oeoy5gt2zVMiEpunWLdgJ6XZtVhJUka6XX8Ba8TbU1tqbk9SYrJ1C3ZSkl1/TyR7u5Tit82MlgnW3e8maNc8klRm378VJcVfl9LXtykhJUUJqXadp5ICdi1Wkr3nzXhrM/R4rmbWdWDb3xNJVi7YNeK1TRsfz5OP2fV3RbLwPP7vvypOurTrvy4AAAAAAE0UCzYAAAAAAB5gwQYAAAAAwAMs2AAAAAAAeIAFGwAAAAAAD7BgAwAAAADgARZsAAAAAAA8wIINAAAAAIAHWLABAAAAAPAACzYAAAAAAB5gwQYAAAAAwAMs2AAAAAAAeKBRC/bs2bPVuXNnpaSkqE+fPnr//fe9ngtoFNqEjegStqJN2Io2YSO6hBOuF+xFixZpwoQJmjJlijZs2KCePXtq0KBBOnDgQDTmAxyjTdiILmEr2oStaBM2oks45XrBfuSRRzRmzBjdfPPNOuuss/TUU0+pRYsWeu6556IxH+AYbcJGdAlb0SZsRZuwEV3CKVcLdnl5udavX6/8/PyvP0FCgvLz8/Xuu+/W+jFlZWUqLi4OewO85rZNukQscM6ErWgTtuLxHDbinAk3XC3YX375paqqqpSVlRV2eVZWlgoLC2v9mFmzZikzMzP0lpub2/hpgTq4bZMuEQucM2Er2oSteDyHjThnwo2ov4r4xIkTVVRUFHrbvXt3tA8JNIguYSvahK1oEzaiS9iKNk9eSW6u3LZtWyUmJmr//v1hl+/fv1/Z2dm1fkxycrKSk5MbPyHggNs26RKxwDkTtqJN2IrHc9iIcybccPUd7ObNmysvL08rVqwIXRYMBrVixQr17dvX8+EAp2gTNqJL2Io2YSvahI3oEm64+g62JE2YMEGjR49Wr1691Lt3bz322GM6cuSIbr755mjMBzhGm7ARXcJWtAlb0SZsRJdwyvWC/cMf/lAHDx7U5MmTVVhYqHPOOUfLli2L+KF/INZoEzaiS9iKNmEr2oSN6BJOuV6wJWncuHEaN26c17MAJ4w2YSO6hK1oE7aiTdiILuFE1F9FHAAAAACAkwELNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAA0l+HTiYGFAgMeDX4Wv1r1c6+j1ChG4HbvJ7hDDB0mOSpvs9RtQcvKCNEpun+D1GmG89+67fI0RYUpLh9wgRSkuq/B4hql4pyVCLQKLfY4SZ+vztfo8Q4Rc3vuz3CGGOllZK2u/3GFE19MJ1Sm7ZzO8xwhxdZ9c8kvRf+8/xe4QwZSUVknb4PUbU/OOpc5SQatfj+ZnjP/V7hAgD3/nM7xEiHCup1L1+DxFF111xtZISk/0eI0zSb4/6PUKEwvFd/R4hTFXZMenXrzq6Lt/BBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdcL9irV6/WkCFDlJOTo0AgoD/84Q9RGAtwhy5hK9qErWgTNqJL2Io24ZTrBfvIkSPq2bOnZs+eHY15gEahS9iKNmEr2oSN6BK2ok04leT2AwYPHqzBgwdHYxag0egStqJN2Io2YSO6hK1oE065XrDdKisrU1lZWej94uLiaB8SaBBdwla0CVvRJmxEl7AVbZ68ov4iZ7NmzVJmZmboLTc3N9qHBBpEl7AVbcJWtAkb0SVsRZsnr6gv2BMnTlRRUVHobffu3dE+JNAguoStaBO2ok3YiC5hK9o8eUX9KeLJyclKTk6O9mEAV+gStqJN2Io2YSO6hK1o8+TF78EGAAAAAMADrr+DXVJSok8//TT0/s6dO/Xhhx+qTZs26tSpk6fDAU7RJWxFm7AVbcJGdAlb0Saccr1gr1u3Tpdeemno/QkTJkiSRo8erXnz5nk2GOAGXcJWtAlb0SZsRJewFW3CKdcL9oABA2SMicYsQKPRJWxFm7AVbcJGdAlb0Sac4mewAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADSX4duOqyQ1KLZL8OX6sPzv+d3yNEuOaU8/0eIUylqdAuv4eIooQKKSHg9xThXvtivd8jRBja6yq/R4hQGSyX9De/x4iaJ3dcpkTLzpm5l33u9wgRXjyzo98jhKk0FZLW+T1GVPVruU0t0hP9HiPMuOU/8nuECDl/sevBpbLimKRX/R4jahKbVSmheZXfY4T505ZVfo8QYdin3/N7hAgVR8olveX3GFET+FWZEtKM32OEqfoPu87hkhQc5fcE4YJB59flO9gAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAecLVgz5o1S+eff77S09PVvn17DR06VFu3bo3WbIBjtAkb0SVsRZuwFW3CRnQJN1wt2KtWrVJBQYHWrl2r5cuXq6KiQgMHDtSRI0eiNR/gCG3CRnQJW9EmbEWbsBFdwo0kN1detmxZ2Pvz5s1T+/bttX79el188cWeDga4QZuwEV3CVrQJW9EmbESXcMPVgn28oqIiSVKbNm3qvE5ZWZnKyspC7xcXF5/IIQFHGmqTLuEHzpmwFW3CVjyew0acM1GfRr/IWTAY1Pjx49WvXz917969zuvNmjVLmZmZobfc3NzGHhJwxEmbdIlY45wJW9EmbMXjOWzEORMNafSCXVBQoE2bNmnhwoX1Xm/ixIkqKioKve3evbuxhwQccdImXSLWOGfCVrQJW/F4DhtxzkRDGvUU8XHjxum1117T6tWr1bFjx3qvm5ycrOTk5EYNB7jltE26RCxxzoStaBO24vEcNuKcCSdcLdjGGN1xxx1aunSp3nrrLXXp0iVacwGu0CZsRJewFW3CVrQJG9El3HC1YBcUFGjBggV69dVXlZ6ersLCQklSZmamUlNTozIg4ARtwkZ0CVvRJmxFm7ARXcINVz+DPWfOHBUVFWnAgAHq0KFD6G3RokXRmg9whDZhI7qErWgTtqJN2Igu4Ybrp4gDNqJN2IguYSvahK1oEzaiS7jR6FcRBwAAAAAAX2PBBgAAAADAAyzYAAAAAAB4gAUbAAAAAAAPsGADAAAAAOABFmwAAAAAADzAgg0AAAAAgAdYsAEAAAAA8AALNgAAAAAAHmDBBgAAAADAA0mxPqAxRpJUVVoW60M3qPhw0O8RIlSaCr9HCFOp6nlq/jvGi1CXFcd8niSSlV0Gy/0eIULNTHHbpoXnzMoq+2YS58yYqblNpSVVPk8SKXjUvnN5ZUXA7xHC1DzexVubNbcneNS+85ONj+cVR+x7PK+ZKV7brCy17z5X0K7zkyRVldl1Hq+Zx0mXARPjevfs2aPc3NxYHhJRsHv3bnXs2NHvMTxDl/GDNmGjeOtSos14EW9t0mX8oE3YyEmXMV+wg8Gg9u7dq/T0dAUCjf9qSXFxsXJzc7V7925lZGR4OGH88fK+Msbo8OHDysnJUUJC/PyEgVddSrTpBm02jDZjjy6d4fE89mizYZwz/UGbDaPN2POry5g/RTwhIcHTr0ZlZGQQlkNe3VeZmZkeTGMXr7uUaNMN2qwbbfqHLuvH47l/aLNunDP9RZt1o03/xLrL+PmyEAAAAAAAPmLBBgAAAADAA012wU5OTtaUKVOUnJzs9yjW476KLe5v57ivYov72xnup9ji/naO+yq2uL+d476KLe5vZ/y6n2L+ImcAAAAAAMSjJvsdbAAAAAAAbMKCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADTXbBnj17tjp37qyUlBT16dNH77//vt8jWWfWrFk6//zzlZ6ervbt22vo0KHaunWr32PFNbpsGF36gzYbRpv+oM2G0Wbs0WXD6NIftNkwv9tskgv2okWLNGHCBE2ZMkUbNmxQz549NWjQIB04cMDv0ayyatUqFRQUaO3atVq+fLkqKio0cOBAHTlyxO/R4hJdOkOXsUebztBm7NGmM7QZW3TpDF3GHm0643ubpgnq3bu3KSgoCL1fVVVlcnJyzKxZs3ycyn4HDhwwksyqVav8HiUu0WXj0GX00Wbj0Gb00Wbj0GZ00WXj0GX00WbjxLrNJvcd7PLycq1fv175+fmhyxISEpSfn693333Xx8nsV1RUJElq06aNz5PEH7psPLqMLtpsPNqMLtpsPNqMHrpsPLqMLtpsvFi32eQW7C+//FJVVVXKysoKuzwrK0uFhYU+TWW/YDCo8ePHq1+/furevbvf48Qdumwcuow+2mwc2ow+2mwc2owuumwcuow+2mwcP9pMislR4LuCggJt2rRJf/3rX/0eBQihS9iKNmEr2oSN6BK28qPNJrdgt23bVomJidq/f3/Y5fv371d2drZPU9lt3Lhxeu2117R69Wp17NjR73HiEl26R5exQZvu0WZs0KZ7tBl9dOkeXcYGbbrnV5tN7inizZs3V15enlasWBG6LBgMasWKFerbt6+Pk9nHGKNx48Zp6dKl+stf/qIuXbr4PVLcokvn6DK2aNM52owt2nSONmOHLp2jy9iiTed8bzMmL6XmsYULF5rk5GQzb948s2XLFjN27FjTqlUrU1hY6PdoVvnpT39qMjMzzVtvvWX27dsXeistLfV7tLhEl87QZezRpjO0GXu06QxtxhZdOkOXsUebzvjdZpNcsI0x5sknnzSdOnUyzZs3N7179zZr1671eyTrSKr1be7cuX6PFrfosmF06Q/abBht+oM2G0absUeXDaNLf9Bmw/xuM/DvIQAAAAAAwAlocj+DDQAAAACAjViwAQAAAADwAAs2AAAAAAAeYMEGAAAAAMADLNgAAAAAAHiABRsAAAAAAA+wYAMAAAAA4AEWbAAAAAAAPMCCDQAAAACAB1iwAQAAAADwAAs2AAAAAAAe+P/M7LKN4NtFzAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x500 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_features(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x500 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_features(4)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The concepts being learnt here seem fairly entangled, but we can try to interpret the meaning nonetheless.\n",
    "\n",
    "The concept of the middle cell being alive can be somewhat seen in features 12, 30, 37, 44, 61 and 78.\n",
    "\n",
    "Features 1 and 35 seem to show 3 living neighbours. Different permutations of 3 living neighbours along with the middle cell being alive seem to be present in features 4, 23, 31, 42 and 77.\n",
    "\n",
    "2 living neighbours are shown by features 19, 28 and 47."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "In conclusion, feature visualization did not give much insight into how the model makes its predictions. This could be for multiple reasons.\n",
    "\n",
    "It is possible that the model is learning human-comprehensible features in `conv0` like \"middle cell alive\" and exact configurations of \"2 neighbours alive\" and \"3 neighbours\" alive, but that these exist only as a linear combination of the neural network units rather than within a single unit.\n",
    "\n",
    "To test this hypothesis, we could perform a linear regression to predict a meaningful concept such as \"middle cell alive\" from the `conv0` layer activations. If we can predict the concept with very high accuracy, it suggests that simple concepts exist in the network but are \"between\" the nodes rather than in any single node.\n",
    "\n",
    "Another possibility is that the model is encoding the cell states into floating-point numbers in a \"pathological\" way. There are 512 possible combinations of states in a 3 x 3 grid, since each cell can only be alive or dead. This is 9 bits of information, which can easily be encoded into a single 32-bit floating-point number. In the worst case this means the entire state of the 3 x 3 grid could be encoded in a single 3 x 3 convolutional filter, provided later layers can extract this information. The feature visualization of the filter would be misleading.\n",
    "\n",
    "To test this hypothesis, we could reduce number of filters in the `conv0` layer and see how few filters the model can have while still being able to train to 100% accuracy. We may need to increase the number of filters and/or layers after the `conv0` layer so the model can extract information from the `conv0` bottleneck.\n",
    "\n",
    "> Incidentally, the reason I chose 85 as the number of filters in the `conv0` layer was because it was an intuitive lower bound for the number of filters needed to get 100% accuracy. The cell update rule depends on the cell's current state and whether the cell has 2 or 3 living neighbours. To identify whether the current cell is alive, a single convolutional filter will do: $ [[0, 0, 0], [0, 1, 0], [0, 0, 0]] $. To identify all the states where exactly 2 neighbours are alive, we use one filter for each state where 2 neighbours are alive, for example $ [[+1, +1, -1], [-1, 0, -1], [-1, -1, -1]] $ (or similar). This gives a total of $ {8 \\choose 2} = 28 $ filters. Similarly, for the states where 3 neighbours are alive, we get $ {8 \\choose 3} = 56 $ filters. In total, this gives $ 1 + 28 + 56 = 85 $ filters.\n",
    "> \n",
    "> Thinking about it now, we could actually just count the number of alive neighbours with a single filter: $ [[1, 1, 1], [1, 0, 1], [1, 1, 1]] $. Thus, we would only need two filters at the `conv0` level, provided that later layers were able to perform the appropriate logic on those values to get the correct final result.\n",
    "\n",
    "There are a number of approaches we could take to try and instill more interpretable concepts in the model.\n",
    "\n",
    "Firstly, we could use regularization or dropout in the training process to make the model weights less complex.\n",
    "\n",
    "Secondly, we could introduce noise into the training data so that the model does not rely on the input values being exactly 0 or 1.\n",
    "\n",
    "Thirdly, we could try varying the model architecture. There is information online suggesting that deeper models are better able to disentangle concepts, however it is unclear whether this approach would be relevant to such a simple prediction task."
   ]
  }
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