jvanvugt/vae.ipynb

## vae.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "from torch import nn\n",
    "import torch.nn.functional as F\n",
    "from torchvision import datasets, transforms\n",
    "import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "PROBA_OUT = False  # Output gaussians over pixel values\n",
    "SSE_RECON_LOSS = False  # only if not PROBA_OUT: use SSE loss, otherwise BCE\n",
    "DO_SIGMOID = not(PROBA_OUT or SSE_RECON_LOSS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class VAE(nn.Module):\n",
    "    def __init__(self, z_dim=2, hidden_dim=512, probabilistic_output=False):\n",
    "        super().__init__()\n",
    "        self.encoder = nn.Sequential(\n",
    "            nn.Linear(28*28, hidden_dim),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(hidden_dim, z_dim*2),\n",
    "        )\n",
    "        self.decoder = nn.Sequential(\n",
    "            nn.Linear(z_dim, hidden_dim),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(hidden_dim, (bool(probabilistic_output)+1)*28*28),\n",
    "        )\n",
    "        self.z_dim = z_dim\n",
    "\n",
    "    def forward(self, x):\n",
    "        z_mu_sigma = self.encoder(x).view(x.shape[0], 2, self.z_dim)\n",
    "        z_mu, z_sigma = z_mu_sigma[:, 0], z_mu_sigma[:, 1]\n",
    "        z_sigma = torch.exp(z_sigma)\n",
    "        z_sample = torch.randn(x.shape[0], self.z_dim).cuda()\n",
    "        z_sample = z_sample * z_sigma + z_mu\n",
    "        return self.decoder(z_sample), (z_mu, z_sigma)\n",
    "\n",
    "\n",
    "def gaussian_log_prob(x, mu, sigma):\n",
    "    return torch.log(1 / torch.sqrt(2*math.pi*sigma)) - (x-mu)**2/(2*sigma)\n",
    "\n",
    "vae = VAE(probabilistic_output=PROBA_OUT).cuda()\n",
    "optim = torch.optim.Adam(vae.parameters())\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('data', train=True, download=True, transform=transforms.ToTensor()),\n",
    "    batch_size=128, shuffle=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c65c9d62b2e54fb29247e64071545e78",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=50), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 0; last KL=334.67828369140625; last RL=15596.2646484375\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2933a0a5ef0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 10; last KL=334.7369689941406; last RL=13866.205078125\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2932eca9518>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20; last KL=342.6477355957031; last RL=13823.6806640625\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2930ac3c048>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 30; last KL=326.5901794433594; last RL=13260.6181640625\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2930aebe358>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 40; last KL=340.5096740722656; last RL=14156.3173828125\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2930ae24898>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "for epoch in tqdm.tqdm_notebook(range(50)):\n",
    "    for images, _ in train_loader:\n",
    "        images = images.view(-1, 28*28)\n",
    "        images = images.cuda()\n",
    "        predicted_images, (z_mu, z_sigma) = vae(images)\n",
    "        if PROBA_OUT:\n",
    "            predicted_images = predicted_images.view(images.shape[0], 2, -1)\n",
    "            mus, stds = predicted_images[:, 0], torch.exp(predicted_images[:, 1])\n",
    "            predicted_images = mus\n",
    "            reconstruction_loss = -torch.sum(gaussian_log_prob(images, mus, stds))\n",
    "        elif SSE_RECON_LOSS:\n",
    "            reconstruction_loss = torch.sum((predicted_images - images)**2)\n",
    "        else:\n",
    "            reconstruction_loss = F.binary_cross_entropy_with_logits(\n",
    "                predicted_images,images, reduction=\"sum\")\n",
    "        kl_loss = -0.5 * torch.sum(torch.sum(1 + torch.log(z_sigma) - z_mu*z_mu - z_sigma, dim=1))\n",
    "        loss = kl_loss + reconstruction_loss\n",
    "        loss.backward()\n",
    "        optim.step()\n",
    "        vae.zero_grad()\n",
    "\n",
    "    if epoch % 10 == 0:\n",
    "        print(f\"epoch {epoch}; last KL={kl_loss.item()}; last RL={reconstruction_loss.item()}\")\n",
    "        images = images.view(images.shape[0], 1, 28, 28)\n",
    "        if DO_SIGMOID:\n",
    "            predicted_images = torch.sigmoid(predicted_images)\n",
    "        predicted_images = predicted_images.view(images.shape[0], 1, 28, 28)\n",
    "        plt.subplot(121)\n",
    "        plt.imshow(images[0, 0].cpu().numpy(), cmap=\"gray\")\n",
    "        plt.subplot(122)\n",
    "        plt.imshow(predicted_images[0, 0].cpu().detach().numpy(), cmap=\"gray\")\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling in latent space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2933a079080>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2930aefab38>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = images.view(-1, 28 * 28)\n",
    "image_a = images[0].unsqueeze(0)\n",
    "image_b = images[1].unsqueeze(0)\n",
    "plt.subplot(121)\n",
    "plt.imshow(image_a.view(28, 28).cpu().numpy(), cmap=\"gray\")\n",
    "plt.subplot(122)\n",
    "plt.imshow(image_b.view(28, 28).cpu().numpy(), cmap=\"gray\")\n",
    "plt.show()\n",
    "z_a = vae(image_a)[1][0]\n",
    "z_b = vae(image_b)[1][0]\n",
    "\n",
    "# linearly interpolate from image_a to image_b (inclusive)\n",
    "n_interps = 5\n",
    "interps_z = z_a + (z_b - z_a) * torch.linspace(0, 1, n_interps).view(n_interps, 1).cuda()\n",
    "interps_images = vae.decoder(interps_z).detach()\n",
    "if DO_SIGMOID:\n",
    "    interps_images = torch.sigmoid(interps_images)\n",
    "interps_images = interps_images.view(n_interps, bool(PROBA_OUT)+1, 28, 28)\n",
    "_, axs = plt.subplots(1, n_interps)\n",
    "for ax, image in zip(axs, interps_images):\n",
    "    ax.imshow(image[0].cpu().numpy(), cmap=\"gray\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}