VAE-MNIST.ipynb

{
 "cells": [
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-21T07:26:07.273891Z",
     "start_time": "2024-05-21T07:26:05.848338Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import math\n",
    "import torch.optim as optim\n",
    "import torchvision.datasets as datasets\n",
    "import matplotlib.pyplot as plt\n",
    "import torchvision.transforms as transforms\n",
    "\n",
    "device = \"cpu\"\n",
    "if torch.cuda.is_available():\n",
    "    device = \"cuda\"\n",
    "elif torch.backends.mps.is_available():\n",
    "    device = \"mps\""
   ],
   "id": "a6328efd03cb976",
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Load data from MNIST",
   "id": "dcf875a912726d44"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-21T18:03:54.189999Z",
     "start_time": "2024-05-21T18:03:53.927127Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# download the MNIST dataset\n",
    "train = datasets.MNIST(root='./data', train=True, transform=transforms.ToTensor(), download=True)\n",
    "test = datasets.MNIST(root='./data', train=False, transform=transforms.ToTensor(), download=True)\n",
    "# binarize the data\n",
    "train.data = torch.where(train.data > 128, 1, 0)\n",
    "test.data = torch.where(test.data > 128, 1, 0)\n",
    "# plot samples\n",
    "sample_train = train.data[:2]\n",
    "sample_test = test.data[:2]\n",
    "for sample in sample_train:\n",
    "    plt.figure()\n",
    "    plt.imshow(sample.numpy(), cmap='gray')\n",
    "for sample in sample_test:\n",
    "    plt.figure()\n",
    "    plt.imshow(sample.numpy(), cmap='gray')"
   ],
   "id": "3ae94d2a87539cf6",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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vPydOyohGowoEAtbTeKSk2CmAFMDCokgEz/OUm5s77HbWggMAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAICJMf1FVAATjxWqkWm4AgIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATLAYKSZ0kUvn3IS91kRhkVBgbLgCAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMsBgpJhQLdwL4GldAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwMSoAlRTU6NFixYpJydHhYWFWr16tZqamuL2eemll+Tz+eLG5s2bEzppAED6G1WAGhoaFA6HdfbsWZ04cUJ3797V8uXL1dPTE7ffpk2b1NHRERt79+5N6KQBAOlvVH8R9fjx43EfHzhwQIWFhTp//ryWLl0ae3zq1KkKBoOJmSEAICON6z0gz/MkSfn5+XGPf/TRRyooKND8+fO1c+dO3bp1a9jn6OvrUzQajRsAgEeAG6P+/n73/e9/3y1ZsiTu8d///vfu+PHj7tKlS+7//u//3NNPP+3WrFkz7PPs2bPHSWIwGAxGhg3P8x7YkTEHaPPmza60tNS1t7c/cL+6ujonyTU3Nw+5vbe313meFxvt7e3mB43BYDAY4x8jBWhU7wF9bevWrTp27JjOnDmjGTNmPHDfiooKSVJzc7Nmz55933a/3y+/3z+WaQAA0tioAuSc05tvvqna2lrV19errKxsxM+5ePGiJKm4uHhMEwQAZKZRBSgcDuvgwYM6evSocnJyFIlEJEmBQEBTpkxRS0uLDh48qO9973uaNm2aLl26pO3bt2vp0qVasGBBUr4AAECaGs37Phrm53z79+93zjnX1tbmli5d6vLz853f73dz5sxxb7/99og/B/xfnueZ/9ySwWAwGOMfI33v9/0nLCkjGo0qEAhYTwMAME6e5yk3N3fY7awFBwAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwkXIBcs5ZTwEAkAAjfT9PuQB1d3dbTwEAkAAjfT/3uRS75BgYGNC1a9eUk5Mjn88Xty0ajaqkpETt7e3Kzc01mqE9jsMgjsMgjsMgjsOgVDgOzjl1d3crFApp0qThr3Mem8A5PZRJkyZpxowZD9wnNzf3kT7BvsZxGMRxGMRxGMRxGGR9HAKBwIj7pNyP4AAAjwYCBAAwkVYB8vv92rNnj/x+v/VUTHEcBnEcBnEcBnEcBqXTcUi5mxAAAI+GtLoCAgBkDgIEADBBgAAAJggQAMBE2gRo3759euaZZ/T444+roqJCn332mfWUJtw777wjn88XN+bNm2c9raQ7c+aMVq1apVAoJJ/PpyNHjsRtd85p9+7dKi4u1pQpU1RVVaUrV67YTDaJRjoOr7322n3nR3V1tc1kk6SmpkaLFi1STk6OCgsLtXr1ajU1NcXt09vbq3A4rGnTpunJJ5/UunXr1NnZaTTj5HiY4/DSSy/ddz5s3rzZaMZDS4sAffLJJ9qxY4f27NmjL774QuXl5VqxYoWuX79uPbUJ9/zzz6ujoyM2/vznP1tPKel6enpUXl6uffv2Dbl97969+uCDD/Thhx/q3LlzeuKJJ7RixQr19vZO8EyTa6TjIEnV1dVx58ehQ4cmcIbJ19DQoHA4rLNnz+rEiRO6e/euli9frp6entg+27dv16effqrDhw+roaFB165d09q1aw1nnXgPcxwkadOmTXHnw969e41mPAyXBhYvXuzC4XDs4/7+fhcKhVxNTY3hrCbenj17XHl5ufU0TElytbW1sY8HBgZcMBh07733Xuyxrq4u5/f73aFDhwxmODHuPQ7OObdhwwb38ssvm8zHyvXr150k19DQ4Jwb/LfPyspyhw8fju3z5ZdfOkmusbHRappJd+9xcM657373u+7HP/6x3aQeQspfAd25c0fnz59XVVVV7LFJkyapqqpKjY2NhjOzceXKFYVCIc2aNUuvvvqq2trarKdkqrW1VZFIJO78CAQCqqioeCTPj/r6ehUWFmru3LnasmWLbty4YT2lpPI8T5KUn58vSTp//rzu3r0bdz7MmzdPM2fOzOjz4d7j8LWPPvpIBQUFmj9/vnbu3Klbt25ZTG9YKbcY6b2++uor9ff3q6ioKO7xoqIi/f3vfzealY2KigodOHBAc+fOVUdHh9599129+OKLunz5snJycqynZyISiUjSkOfH19seFdXV1Vq7dq3KysrU0tKin//851q5cqUaGxs1efJk6+kl3MDAgLZt26YlS5Zo/vz5kgbPh+zsbOXl5cXtm8nnw1DHQZJ++MMfqrS0VKFQSJcuXdLPfvYzNTU16U9/+pPhbOOlfIDwXytXroz994IFC1RRUaHS0lL98Y9/1MaNGw1nhlTwgx/8IPbfL7zwghYsWKDZs2ervr5ey5YtM5xZcoTDYV2+fPmReB/0QYY7Dq+//nrsv1944QUVFxdr2bJlamlp0ezZsyd6mkNK+R/BFRQUaPLkyffdxdLZ2algMGg0q9SQl5en5557Ts3NzdZTMfP1OcD5cb9Zs2apoKAgI8+PrVu36tixYzp9+nTcn28JBoO6c+eOurq64vbP1PNhuOMwlIqKCklKqfMh5QOUnZ2thQsXqq6uLvbYwMCA6urqVFlZaTgzezdv3lRLS4uKi4utp2KmrKxMwWAw7vyIRqM6d+7cI39+XL16VTdu3Mio88M5p61bt6q2tlanTp1SWVlZ3PaFCxcqKysr7nxoampSW1tbRp0PIx2HoVy8eFGSUut8sL4L4mF8/PHHzu/3uwMHDri//e1v7vXXX3d5eXkuEolYT21C/eQnP3H19fWutbXV/eUvf3FVVVWuoKDAXb9+3XpqSdXd3e0uXLjgLly44CS5999/3124cMH961//cs4596tf/crl5eW5o0ePukuXLrmXX37ZlZWVudu3bxvPPLEedBy6u7vdW2+95RobG11ra6s7efKk++Y3v+meffZZ19vbaz31hNmyZYsLBAKuvr7edXR0xMatW7di+2zevNnNnDnTnTp1yn3++eeusrLSVVZWGs468UY6Ds3Nze4Xv/iF+/zzz11ra6s7evSomzVrllu6dKnxzOOlRYCcc+63v/2tmzlzpsvOznaLFy92Z8+etZ7ShFu/fr0rLi522dnZ7umnn3br1693zc3N1tNKutOnTztJ940NGzY45wZvxd61a5crKipyfr/fLVu2zDU1NdlOOgkedBxu3brlli9f7qZPn+6ysrJcaWmp27RpU8b9n7Shvn5Jbv/+/bF9bt++7d544w331FNPualTp7o1a9a4jo4Ou0knwUjHoa2tzS1dutTl5+c7v9/v5syZ495++23neZ7txO/Bn2MAAJhI+feAAACZiQABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAw8f+/eThc2yBfbAAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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rYPRwBgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmOBmpMhKo3VTUQAjxxkQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYGJYAYpEIpo/f77y8vJUXFys5cuXq6WlJWGbl156ST6fL2GtX78+qUMDADLfsALU1NSkcDisU6dO6ejRo7pz544WL16svr6+hO3WrVunzs7O+Nq1a1dShwYAZL4Jw9n4yJEjCR/v3btXxcXFOnPmjBYtWhR/fNKkSQoGg8mZEACQlR7re0Ce50mSCgsLEx7/+OOPVVRUpDlz5mjr1q26cePGkK8Ri8UUjUYTFgAg+w3rDOj/6+/v16ZNm7Rw4ULNmTMn/virr76q8vJyhUIhnT9/Xu+++65aWlr02WefDfo6kUhEO3fuHOkYAIAM5XPOuZH8wg0bNujPf/6zvvjiC02dOnXI7Y4fP66amhq1trZqxowZA56PxWKKxWLxj6PRqMrKykYyEhA3wsN61Ph8PusRgJTzPE/5+flDPj+iM6CNGzfq8OHDOnny5APjI0lVVVWSNGSA/H6//H7/SMYAAGSwYQXIOae33npL9fX1amxsVEVFxUN/zblz5yRJpaWlIxoQAJCdhhWgcDisffv26dChQ8rLy1NXV5ckKRAIaOLEiWpra9O+ffv04x//WJMnT9b58+e1efNmLVq0SHPnzk3JJwAAyFBuGCQNuvbs2eOcc66jo8MtWrTIFRYWOr/f72bOnOneeecd53neI7+H53lDvg+L9agr3VnvHxZrNNbDvvaP+CKEVIlGowoEAtZjIMOl2WE9ABchYCxIyUUIAP6HmAAjw81IAQAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAAT3IwUWYkbhALpjzMgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJtIuQM456xEAAEnwsK/naReg3t5e6xEAAEnwsK/nPpdmpxz9/f26cuWK8vLyBtzROBqNqqysTJcuXVJ+fr7RhPbYD/ewH+5hP9zDfrgnHfaDc069vb0KhUIaN27o85y0+3EM48aN09SpUx+4TX5+/pg+wP6L/XAP++Ee9sM97Id7rPdDIBB46DZp91dwAICxgQABAExkVID8fr927Nghv99vPYop9sM97Id72A/3sB/uyaT9kHYXIQAAxoaMOgMCAGQPAgQAMEGAAAAmCBAAwETGBGj37t165pln9MQTT6iqqkpffvml9Uij7r333pPP50tYs2fPth4r5U6ePKlly5YpFArJ5/Pp4MGDCc8757R9+3aVlpZq4sSJqq2t1cWLF22GTaGH7YfXX399wPFRV1dnM2yKRCIRzZ8/X3l5eSouLtby5cvV0tKSsM2tW7cUDoc1efJkPfXUU1q1apW6u7uNJk6NR9kPL7300oDjYf369UYTDy4jAvTpp59qy5Yt2rFjh77++mtVVlZqyZIlunr1qvVoo+75559XZ2dnfH3xxRfWI6VcX1+fKisrtXv37kGf37Vrlz788EN99NFHOn36tJ588kktWbJEt27dGuVJU+th+0GS6urqEo6P/fv3j+KEqdfU1KRwOKxTp07p6NGjunPnjhYvXqy+vr74Nps3b9bnn3+uAwcOqKmpSVeuXNHKlSsNp06+R9kPkrRu3bqE42HXrl1GEw/BZYAFCxa4cDgc//ju3bsuFAq5SCRiONXo27Fjh6usrLQew5QkV19fH/+4v7/fBYNB9/7778cf6+npcX6/3+3fv99gwtFx/35wzrk1a9a4l19+2WQeK1evXnWSXFNTk3Pu3u99Tk6OO3DgQHybb775xklyzc3NVmOm3P37wTnnfvSjH7mf/exndkM9grQ/A7p9+7bOnDmj2tra+GPjxo1TbW2tmpubDSezcfHiRYVCIU2fPl2vvfaaOjo6rEcy1d7erq6uroTjIxAIqKqqakweH42NjSouLtasWbO0YcMGXbt2zXqklPI8T5JUWFgoSTpz5ozu3LmTcDzMnj1b06ZNy+rj4f798F8ff/yxioqKNGfOHG3dulU3btywGG9IaXcz0vt9++23unv3rkpKShIeLykp0d///nejqWxUVVVp7969mjVrljo7O7Vz5069+OKLunDhgvLy8qzHM9HV1SVJgx4f/31urKirq9PKlStVUVGhtrY2/fKXv9TSpUvV3Nys8ePHW4+XdP39/dq0aZMWLlyoOXPmSLp3POTm5qqgoCBh22w+HgbbD5L06quvqry8XKFQSOfPn9e7776rlpYWffbZZ4bTJkr7AOF/li5dGv/vuXPnqqqqSuXl5frTn/6ktWvXGk6GdPCTn/wk/t8vvPCC5s6dqxkzZqixsVE1NTWGk6VGOBzWhQsXxsT3QR9kqP3wxhtvxP/7hRdeUGlpqWpqatTW1qYZM2aM9piDSvu/gisqKtL48eMHXMXS3d2tYDBoNFV6KCgo0HPPPafW1lbrUcz89xjg+Bho+vTpKioqysrjY+PGjTp8+LBOnDiR8ONbgsGgbt++rZ6enoTts/V4GGo/DKaqqkqS0up4SPsA5ebmat68eWpoaIg/1t/fr4aGBlVXVxtOZu/69etqa2tTaWmp9ShmKioqFAwGE46PaDSq06dPj/nj4/Lly7p27VpWHR/OOW3cuFH19fU6fvy4KioqEp6fN2+ecnJyEo6HlpYWdXR0ZNXx8LD9MJhz585JUnodD9ZXQTyKTz75xPn9frd37173t7/9zb3xxhuuoKDAdXV1WY82qn7+85+7xsZG197e7v7yl7+42tpaV1RU5K5evWo9Wkr19va6s2fPurNnzzpJ7oMPPnBnz551//rXv5xzzv3mN79xBQUF7tChQ+78+fPu5ZdfdhUVFe7mzZvGkyfXg/ZDb2+ve/vtt11zc7Nrb293x44dc9/73vfcs88+627dumU9etJs2LDBBQIB19jY6Do7O+Prxo0b8W3Wr1/vpk2b5o4fP+6++uorV11d7aqrqw2nTr6H7YfW1lb3q1/9yn311Veuvb3dHTp0yE2fPt0tWrTIePJEGREg55z7/e9/76ZNm+Zyc3PdggUL3KlTp6xHGnWrV692paWlLjc3133nO99xq1evdq2trdZjpdyJEyecpAFrzZo1zrl7l2Jv27bNlZSUOL/f72pqalxLS4vt0CnwoP1w48YNt3jxYjdlyhSXk5PjysvL3bp167Luf9IG+/wluT179sS3uXnzpnvzzTfd008/7SZNmuRWrFjhOjs77YZOgYfth46ODrdo0SJXWFjo/H6/mzlzpnvnnXec53m2g9+HH8cAADCR9t8DAgBkJwIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADAxP8BGZp8+y7/ZSMAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 156
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Define Loss",
   "id": "6a6603d00a8b3c37"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-23T07:55:22.821963Z",
     "start_time": "2024-05-23T07:55:22.818878Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def elbo(x_hat, x, mu, std):\n",
    "    bce_loss = nn.BCELoss(reduction='sum')\n",
    "    kl_divergence = 0.5 * torch.sum(mu ** 2 + std ** 2 - torch.log(std ** 2))\n",
    "    return bce_loss(x_hat, x) + 5 * kl_divergence"
   ],
   "id": "dcc1300d107055a",
   "outputs": [],
   "execution_count": 695
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Define Model",
   "id": "39b59f7505d218a6"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-23T07:55:40.324897Z",
     "start_time": "2024-05-23T07:55:40.319882Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class VAE(nn.Module):\n",
    "    def __init__(self, input_dim):\n",
    "        super(VAE, self).__init__()\n",
    "        self.input_dim = input_dim\n",
    "        self.latent_dim = 12\n",
    "        self.encoder = nn.Sequential(\n",
    "            nn.Linear(self.input_dim, 512),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(512, 64),\n",
    "            nn.ReLU(),\n",
    "        )\n",
    "        self.mu = nn.Sequential(\n",
    "            nn.Linear(64, self.latent_dim ),\n",
    "            nn.Tanh()\n",
    "        )\n",
    "        self.std = nn.Sequential(\n",
    "            nn.Linear(64, self.latent_dim ),\n",
    "            nn.Tanh()\n",
    "        )\n",
    "        self.decoder = nn.Sequential(\n",
    "            nn.Linear(self.latent_dim ,64),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(64, 512),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(512, self.input_dim,),\n",
    "            nn.Sigmoid()\n",
    "        )\n",
    "        \n",
    "    def get_latent_distribution(self, x):\n",
    "        mu = self.mu(self.encoder(x))\n",
    "        std = self.std(self.encoder(x))\n",
    "        return mu, std\n",
    "    \n",
    "    def sample_latent_distribution(self, mu, std):\n",
    "        return std * torch.randn(std.shape[0]).unsqueeze(-1).to(device) + mu\n",
    "    \n",
    "    def encode(self, x):\n",
    "        mu, std = self.get_latent_distribution(x)\n",
    "        return self.sample_latent_distribution(mu, std), mu, std\n",
    "    \n",
    "    def decode(self, z):\n",
    "        return self.decoder(z)\n",
    "    \n",
    "    def forward(self, x):\n",
    "        x_hat, mu, std = self.encode(x)\n",
    "        return self.decode(x_hat), mu, std\n",
    "    \n",
    "    def generate(self):\n",
    "        z = self.sample_latent_distribution(torch.zeros(self.latent_dim ).to(device), torch.ones\n",
    "        (self.latent_dim).to(device))\n",
    "        size = int(math.sqrt(self.input_dim))\n",
    "        return self.decode(z).reshape(z.shape[0], size, size)\n",
    "    "
   ],
   "id": "f4198745a15326c6",
   "outputs": [],
   "execution_count": 697
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Training Loop",
   "id": "64b68b760567d75a"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-23T08:00:19.791042Z",
     "start_time": "2024-05-23T07:55:58.421347Z"
    }
   },
   "cell_type": "code",
   "source": [
    "vae = VAE(28**2).to(device)\n",
    "optimizer = optim.Adam(vae.parameters(), lr=1e-3)\n",
    "batch_size = 32\n",
    "train_loader = torch.utils.data.DataLoader(train.data, batch_size=batch_size, shuffle=True)\n",
    "test_loader = torch.utils.data.DataLoader(test.data, batch_size=100, shuffle=True)\n",
    "\n",
    "epochs = 15\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    epoch_loss = 0\n",
    "    for batch_idx, x in enumerate(train_loader):\n",
    "        optimizer.zero_grad()\n",
    "        x = torch.flatten(x.float(), start_dim=1).to(device)\n",
    "        x_hat, mu, std = vae(x)\n",
    "        loss = elbo(x_hat, x, mu, std)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        epoch_loss += loss.item()\n",
    "    print('Epoch: {}, Loss: {}'.format(epoch + 1, epoch_loss / len(train_loader)))\n",
    "\n",
    "    \n",
    "\n",
    "\n"
   ],
   "id": "b4c233850df41190",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss: 5194.737702734375\n",
      "Epoch: 2, Loss: 3753.293591015625\n",
      "Epoch: 3, Loss: 3470.616396614583\n",
      "Epoch: 4, Loss: 3324.9196298177085\n",
      "Epoch: 5, Loss: 3230.832218359375\n",
      "Epoch: 6, Loss: 3166.2898897135415\n",
      "Epoch: 7, Loss: 3114.7548666666667\n",
      "Epoch: 8, Loss: 3074.804042447917\n",
      "Epoch: 9, Loss: 3040.181546875\n",
      "Epoch: 10, Loss: 3013.182621875\n",
      "Epoch: 11, Loss: 2988.044172005208\n",
      "Epoch: 12, Loss: 2966.87210546875\n",
      "Epoch: 13, Loss: 2947.650641796875\n",
      "Epoch: 14, Loss: 2929.304574869792\n",
      "Epoch: 15, Loss: 2914.27051015625\n"
     ]
    }
   ],
   "execution_count": 698
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Decode Test Data",
   "id": "96c498a44da67f7c"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-23T08:01:57.467141Z",
     "start_time": "2024-05-23T08:01:56.887222Z"
    }
   },
   "cell_type": "code",
   "source": [
    "i = 0\n",
    "limit = 5\n",
    "for batch_idx, x in enumerate(test_loader):\n",
    "    if i < limit:\n",
    "        fig = plt.figure()\n",
    "        x = torch.flatten(x.float(), start_dim=1).to(device)\n",
    "        x_hat, _, _ = vae(x)\n",
    "        size = int(math.sqrt(vae.input_dim))\n",
    "        \n",
    "        fig.add_subplot(1, 2, 1)\n",
    "        plt.imshow(x[0].reshape(size, size).detach().cpu(), cmap='gray')\n",
    "      \n",
    "        fig.add_subplot(1, 2, 2)\n",
    "        plt.imshow(x_hat[0].reshape(size, size).detach().cpu(), cmap='gray')\n",
    "        \n",
    "    i += 1\n",
    "    "
   ],
   "id": "d97e7522451095cc",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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/fsf6iBHOY/+///2vYz0UCiXcUyp9/etfd6x/4QtfSOr1m5qaHOvvvvtuUq+P2zjyAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAq7vOBYWGMSev7ezyetL4/kC6x7kMxZcoUx/rkyZMd65/97Gcd66dPn3asx/rdfP755x3rmzdvdqzH0tnZ6VhfsGBBUq+P+CR05KOurk6zZs1SUVGRysrKtHz5crW0tERt093drUAgoHHjxmns2LFauXKl2tvbU9o0gMzC7AAwUELho6mpSYFAQM3NzTp48KB6e3u1cOFCdXV1RbbZuHGj3nzzTe3du1dNTU26cuWKnnzyyZQ3DiBzMDsADJTQn10aGhqift61a5fKysp08uRJzZs3T8FgUL/+9a+1e/duPfbYY5Kk+vp6Pfjgg2pubtbnP//51HUOIGMwOwAMlNQJp8FgUJJUWloqSTp58qR6e3tVW1sb2Wbq1KmqqqrSsWPHBn2NcDisUCgUtQBkN2YHkNuGHD76+/u1YcMGzZ07V9OmTZMktbW1qaCgQCUlJVHblpeXq62tbdDXqaurk8/ni6zKysqhtgQgAzA7AAw5fAQCAZ09e1Z79uxJqoEtW7YoGAxGVmtra1KvB8DdmB0AhnSp7bp16/TWW2/p6NGjmjhxYuRxv9+vnp4edXR0RH2CaW9vl9/vH/S1vF6vvF7vUNoAkGGYHQCkBMOHMUbr16/Xvn37dOTIEVVXV0fVZ86cqZEjR6qxsVErV66UJLW0tOjSpUuqqalJXddIWrrvw5Es7uORWZgd9rzxxhuO9WXLljnWx44d61j/4x//6Fj/4IMPHOsPPvigY33kyJGO9fz8fMd6rNlWVlaW1PORGgmFj0AgoN27d+vAgQMqKiqK/C3W5/OpsLBQPp9Pzz77rDZt2qTS0lIVFxdr/fr1qqmp4Wx1IIcxOwAMlFD42LlzpyRp/vz5UY/X19frmWeekST99Kc/VV5enlauXKlwOKxFixbp5ZdfTkmzADITswPAQB7jsmNMoVBIPp8v3W2kncv+WVyHP7vYEQwGVVxcnO424sLsuO1LX/qSY3337t1Jvf7Hl0nfjdv/7DJ69GjHend3t2MdscUzN/hiOQAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABg1ZDucIrhF+tqjmy/GoarWYChOXDggGO9p6fHsV5YWOhY//jLAIdajyXWbLt586Zj/ZM3sPskrmZxB458AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK+3xkKLffB4T7dADpEQ6HHevz5s1zrD///POO9SeeeMKxHutbafv6+hzrjz76qGO9ubnZsY7MwJEPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFZ5TLpvCPEJoVBIPp8v3W0AkBQMBlVcXJzuNuLC7ADcIZ65wZEPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYlFD7q6uo0a9YsFRUVqaysTMuXL1dLS0vUNvPnz5fH44laa9asSWnTADILswPAQAmFj6amJgUCATU3N+vgwYPq7e3VwoUL1dXVFbXdc889p6tXr0bW9u3bU9o0gMzC7AAw0IhENm5oaIj6edeuXSorK9PJkyc1b968yOOjR4+W3+9PTYcAMh6zA8BASZ3zEQwGJUmlpaVRj//ud7/T+PHjNW3aNG3ZskU3b96862uEw2GFQqGoBSC7MTuAHGeGqK+vzzzxxBNm7ty5UY//8pe/NA0NDebMmTPmt7/9rfnUpz5lVqxYcdfX2bZtm5HEYrFcuILB4FBHBLODxcrRFc/cGHL4WLNmjZk0aZJpbW113K6xsdFIMufPnx+03t3dbYLBYGS1tramfcexWKzbazjCB7ODxcruNWzhIxAImIkTJ5r3338/5rY3btwwkkxDQ0Ncrx0MBtO+41gs1u2V6vDB7GCxsn/FMzcSOuHUGKP169dr3759OnLkiKqrq2M+5/Tp05KkCRMmJPJWALIIswPAQAmFj0AgoN27d+vAgQMqKipSW1ubJMnn86mwsFAXLlzQ7t279cUvflHjxo3TmTNntHHjRs2bN0+f+9znhuV/AAD3Y3YAiBLX8cz/0V0OsdTX1xtjjLl06ZKZN2+eKS0tNV6v10yZMsV885vfTOjQLYdOWSz3rFT92eVur8/sYLGyb8Xze+v532BwjVAoJJ/Pl+42AOj2JbHFxcXpbiMuzA7AHeKZG3y3CwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrXhQ+Xfc8dkNMy6fcxk3oFslk8v4uuCx+dnZ3pbgHA/2TS72Mm9Qpks3h+Fz3GZR8X+vv7deXKFRUVFcnj8SgUCqmyslKtra0Z89XebsM+TE4u7j9jjDo7O1VRUaG8PNd9RhkUsyO12H/Jy7V9mMjcGGGpp7jl5eVp4sSJdzxeXFycE/94w4l9mJxc238+ny/dLSSE2TE82H/Jy6V9GO/cyIyPNAAAIGsQPgAAgFWuDx9er1fbtm2T1+tNdysZi32YHPZfZuLfLTnsv+SxD+/OdSecAgCA7Ob6Ix8AACC7ED4AAIBVhA8AAGAV4QMAAFhF+AAAAFa5Pnzs2LFDn/70pzVq1CjNmTNHf/vb39LdkmsdPXpUS5cuVUVFhTwej/bv3x9VN8Zo69atmjBhggoLC1VbW6tz586lp1kXqqur06xZs1RUVKSysjItX75cLS0tUdt0d3crEAho3LhxGjt2rFauXKn29vY0dYy7YW7Ej7mRHObG0Lg6fLzxxhvatGmTtm3bpr///e+aPn26Fi1apGvXrqW7NVfq6urS9OnTtWPHjkHr27dv10svvaRXXnlFx48f15gxY7Ro0SJ1d3db7tSdmpqaFAgE1NzcrIMHD6q3t1cLFy5UV1dXZJuNGzfqzTff1N69e9XU1KQrV67oySefTGPX+CTmRmKYG8lhbgyRcbHZs2ebQCAQ+bmvr89UVFSYurq6NHaVGSSZffv2RX7u7+83fr/f/OQnP4k81tHRYbxer3n99dfT0KH7Xbt2zUgyTU1Nxpjb+2vkyJFm7969kW3++c9/Gknm2LFj6WoTn8DcGDrmRvKYG/Fx7ZGPnp4enTx5UrW1tZHH8vLyVFtbq2PHjqWxs8x08eJFtbW1Re1Pn8+nOXPmsD/vIhgMSpJKS0slSSdPnlRvb2/UPpw6daqqqqrYhy7B3Egt5kbimBvxcW34+PDDD9XX16fy8vKox8vLy9XW1pamrjLXx/uM/Rmf/v5+bdiwQXPnztW0adMk3d6HBQUFKikpidqWfegezI3UYm4khrkRvxHpbgBwo0AgoLNnz+qdd95JdysAMgRzI36uPfIxfvx45efn33FGcHt7u/x+f5q6ylwf7zP2Z2zr1q3TW2+9pcOHD2vixImRx/1+v3p6etTR0RG1PfvQPZgbqcXciB9zIzGuDR8FBQWaOXOmGhsbI4/19/ersbFRNTU1aewsM1VXV8vv90ftz1AopOPHj7M//8cYo3Xr1mnfvn06dOiQqquro+ozZ87UyJEjo/ZhS0uLLl26xD50CeZGajE3YmNuDFG6z3h1smfPHuP1es2uXbvMe++9Z1avXm1KSkpMW1tbultzpc7OTnPq1Clz6tQpI8m8+OKL5tSpU+aDDz4wxhjzox/9yJSUlJgDBw6YM2fOmGXLlpnq6mrz0Ucfpblzd1i7dq3x+XzmyJEj5urVq5F18+bNyDZr1qwxVVVV5tChQ+bEiROmpqbG1NTUpLFrfBJzIzHMjeQwN4bG1eHDGGN+/vOfm6qqKlNQUGBmz55tmpub092Sax0+fNhIumOtWrXKGHP7srkXXnjBlJeXG6/Xax5//HHT0tKS3qZdZLB9J8nU19dHtvnoo4/M1772NXPPPfeY0aNHmxUrVpirV6+mr2kMirkRP+ZGcpgbQ+Mxxhh7x1kAAECuc+05HwAAIDsRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGDV/wFyTT/2FFOHFwAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 699
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Generate New Digits",
   "id": "7299001915dfbd44"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-23T17:01:08.810360Z",
     "start_time": "2024-05-23T17:01:08.225771Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import math\n",
    "num_images = 16\n",
    "num_columns = 4\n",
    "f, axs = plt.subplots(4, num_images // num_columns)\n",
    "axs = axs.flatten()\n",
    "for i, ax in enumerate(axs):\n",
    "    size = int(math.sqrt(vae.input_dim))\n",
    "    ax.imshow(vae.generate().detach().cpu()[0], cmap='gray')\n",
    "plt.show()"
   ],
   "id": "4d9cb24c75dcb785",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 16 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 702
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "d48715c103c44d0f"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}