Normalizing_Flow_for_Embedding_Generation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using a Normalizing Flow to generate image embeddings\n",
    "## A simple demo of RealNVP in pure PyTorch\n",
    "### Authors: Jary Pomponi & Simone Scardapane"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we want to show how a Normalizing Flow (NF) can be used to learn a prior over the embeddings of an autoencoder, allowing fast sampling of real looking images.\n",
    "\n",
    "### A (very brief) primer on NFs\n",
    "\n",
    "A NF is a method that allows the construction of flexible posterior distributions starting from a simpler one defined by a collection of continuous random variables. Given a vector $\\mathbf{x}$, we want to express it as transformations $T(\\cdot)$ from a real vector $\\mathbf{u}$ sampled from a prior $p(\\mathbf{u})$: \n",
    "\n",
    "$$\\mathbf{x} = T(\\mathbf{u})$$\n",
    "\n",
    "The key property of the transformation $T(\\cdot)$ is that it must be invertible and both the transformation and its inverse must be differentiable. Under these conditions, $p(\\mathbf{x})$ is well defined and can be obtained via the change of variables: \n",
    "\n",
    "$$p(\\mathbf{x}) = p(\\mathbf{u}) \\vert \\text{det}J_T(\\mathbf{u}) \\vert^{-1} \\, \\, \\text{with} \\, \\, \\mathbf{u} = T^{-1}(\\mathbf{x})$$\n",
    "\n",
    "Another property of these transformations is that they be composed: \n",
    "\n",
    "$$ \\mathbf{x} = T_k \\circ T_{k-1} \\dots \\circ T_1(\\mathbf{u}) $$\n",
    "$$ \\mathbf{u} = (T_k \\circ T_{k-1} \\dots \\circ T_1)^{-1}(\\mathbf{x}) = (T_1 \\circ T_{2} \\dots \\circ T_k)(\\mathbf{x}) $$\n",
    "\n",
    "and the Jacobians of the resulting transformation are simply the product of the components' Jacobians.\n",
    "\n",
    "Using these properties we can build a complex transofrmation which is a combination of simpler ones, leading to a more complex distribution $\\mathbf{x}$, provided the networks can be inverted and the determinant of the base Jacobian are tractable.\n",
    "\n",
    "### What we do in this notebook\n",
    "\n",
    "In this notebook we use a model proposed in [RealNVP](https://arxiv.org/abs/1605.08803). Each transformation can either be an affine coupling layer (see the code below), a permutation, or a batch normalization layer. For more informations on each layer we refer to the original paper or the other references in the README file.\n",
    "\n",
    "To generate samples from the MNIST dataset and make the problem tractable, we train the model on embeddings generated by a separate autoencoder instead of the raw pixels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "import rnvp\n",
    "import numpy as np\n",
    "from torchvision import datasets, transforms\n",
    "import itertools\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyper-parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "EMBEDDING_DIM = 20 # The dimension of the embeddings\n",
    "FLOW_N = 9 # Number of affine coupling layers\n",
    "RNVP_TOPOLOGY = [200] # Size of the hidden layers in each coupling layer\n",
    "AE_EPOCHS = 10 # Epochs for training the autoencoder\n",
    "NF_EPOCHS = 20 # Epochs for training the normalizing flow\n",
    "SEED = 0 # Seed of the random number generator\n",
    "BATCH_SIZE = 100 # Batch size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the random seeds\n",
    "torch.manual_seed(0)\n",
    "np.random.seed(0)\n",
    "\n",
    "torch.backends.cudnn.deterministic = True\n",
    "torch.backends.cudnn.benchmark = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autoencoder definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class AutoEncoder(nn.Module):\n",
    "    \"\"\"\n",
    "    A simple autoencoder for images. \n",
    "    self.linear1 generates the intermediate embeddings that we use for the normalizing flow.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        \n",
    "        # Encoding layers\n",
    "        self.conv1 = nn.Conv2d(in_channels=1, out_channels=32, stride=2, kernel_size=3, bias=False, padding=1)\n",
    "        self.conv2 = nn.Conv2d(in_channels=32, out_channels=64, stride=2, kernel_size=3, bias=False, padding=1)\n",
    "        self.linear1 = nn.Linear(in_features=3136, out_features=EMBEDDING_DIM)\n",
    "        \n",
    "        # Decoding layers\n",
    "        self.linear2 = nn.Linear(in_features=EMBEDDING_DIM, out_features=3136)\n",
    "        self.convt1 = nn.ConvTranspose2d(in_channels=64, out_channels=32, stride=2, kernel_size=3, padding=1, output_padding=1)\n",
    "        self.convt2 = nn.ConvTranspose2d(in_channels=32, out_channels=1, stride=2, kernel_size=3, padding=1, output_padding=1)\n",
    "\n",
    "\n",
    "    def forward(self, x):\n",
    "        \n",
    "        emb = self.encoder(x)\n",
    "        _x = self.decoder(emb)\n",
    "        \n",
    "        return _x, emb\n",
    "    \n",
    "    def decoder(self, emb):\n",
    "\n",
    "        _x = torch.relu(self.linear2(emb))\n",
    "        _x = _x.view(-1, 64, 7, 7)\n",
    "        _x = torch.relu(self.convt1(_x))\n",
    "        _x = self.convt2(_x)\n",
    "        \n",
    "        return _x\n",
    "    \n",
    "    def encoder(self, x):\n",
    "        _x = torch.relu(self.conv1(x))\n",
    "        _x = torch.relu(self.conv2(_x))\n",
    "        sh = _x.shape\n",
    "\n",
    "        _x = torch.relu(torch.flatten(_x, 1))\n",
    "        \n",
    "        emb = self.linear1(_x)\n",
    "        \n",
    "        return emb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autoencoder training on MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the dataset\n",
    "train_set = datasets.MNIST('./data', train=True, download=True,\n",
    "                       transform=transforms.Compose([\n",
    "                           transforms.ToTensor()\n",
    "                       ]))\n",
    "train_loader = torch.utils.data.DataLoader(train_set, BATCH_SIZE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch #1\n",
      "Epoch #2\n",
      "Epoch #3\n",
      "Epoch #4\n",
      "Epoch #5\n",
      "Epoch #6\n",
      "Epoch #7\n",
      "Epoch #8\n",
      "Epoch #9\n",
      "Epoch #10\n"
     ]
    }
   ],
   "source": [
    "# We use a binary cross-entropy loss for the reconstruction error\n",
    "loss_f = nn.BCELoss()\n",
    "\n",
    "# Build the autoencoder\n",
    "autoencoder = AutoEncoder()\n",
    "autoencoder = autoencoder.to(device)\n",
    "\n",
    "optimizer = torch.optim.Adam(itertools.chain(autoencoder.parameters()),\n",
    "                             lr=1e-3, weight_decay=1e-5)\n",
    "\n",
    "for i in range(AE_EPOCHS):\n",
    "    print('Epoch #{}'.format(i+1))\n",
    "\n",
    "    losses = []\n",
    "    for batch_idx, data in enumerate(train_loader):\n",
    "\n",
    "        x, _ = data\n",
    "        x = x.to(device)\n",
    "\n",
    "        # Run the autoencoder\n",
    "        _x, emb = autoencoder(x)\n",
    "        _x = torch.sigmoid(_x)\n",
    "\n",
    "        # Compute loss\n",
    "        rec_loss = loss_f(_x, x)\n",
    "\n",
    "        autoencoder.zero_grad()\n",
    "        rec_loss.backward()\n",
    "        optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a new dataset containing the embeddings and the associated labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We replace the original x with the corresponding embedding from the trained autoencoder\n",
    "\n",
    "embs = []\n",
    "for batch_idx, data in enumerate(train_loader):\n",
    "\n",
    "    with torch.no_grad():\n",
    "        x, y = data\n",
    "\n",
    "        x = x.to(device)\n",
    "\n",
    "        _, emb = autoencoder(x)\n",
    "        for i in range(len(emb)):\n",
    "            embs.append((emb[i], y[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "embs_loader = torch.utils.data.DataLoader(embs, BATCH_SIZE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normalizing Flow training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# See the file realmvp.py for the full definition\n",
    "nf_model = rnvp.LinearRNVP(input_dim=EMBEDDING_DIM, coupling_topology=RNVP_TOPOLOGY, flow_n=FLOW_N, batch_norm=True,\n",
    "                      mask_type='odds', conditioning_size=10, use_permutation=True, single_function=True)\n",
    "nf_model = nf_model.to(device)\n",
    "\n",
    "optimizer1 = torch.optim.Adam(itertools.chain(nf_model.parameters()), lr=1e-4, weight_decay=1e-5)\n",
    "\n",
    "nf_model.train()\n",
    "for i in range(NF_EPOCHS):\n",
    "    print('Epoch #{}'.format(i+1))\n",
    "\n",
    "    losses = []\n",
    "    for batch_idx, data in enumerate(embs_loader):\n",
    "\n",
    "        emb, y = data\n",
    "        emb = emb.to(device)\n",
    "        y = y.to(device)\n",
    "        y = torch.nn.functional.one_hot(y, 10).to(device).float()\n",
    "        \n",
    "        # Get the inverse transformation and the corresponding log determinant of the Jacobian\n",
    "        u, log_det = nf_model.forward(emb, y=y) \n",
    "\n",
    "        # Train via maximum likelihood\n",
    "        prior_logprob = nf_model.logprob(u)\n",
    "        log_prob = -torch.mean(prior_logprob.sum(1) + log_det)\n",
    "\n",
    "        nf_model.zero_grad()\n",
    "\n",
    "        log_prob.backward()\n",
    "\n",
    "        optimizer1.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the NF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1440x1440 with 100 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_n = 10\n",
    "f, axs = plt.subplots(nrows=10, ncols=sample_n, figsize=(20, 20))\n",
    "\n",
    "nf_model.eval()\n",
    "with torch.no_grad():\n",
    "    for j in range(10):\n",
    "\n",
    "        y = torch.nn.functional.one_hot(torch.tensor([j]*sample_n), 10).to(device).float()\n",
    "        emb, d = nf_model.sample(sample_n, y=y, return_logdet=True)\n",
    "        z = autoencoder.decoder(emb)\n",
    "\n",
    "        d_sorted = d.sort(0)[1].flip(0)\n",
    "        z = z[d_sorted]\n",
    "        z = torch.sigmoid(z).cpu()\n",
    "        \n",
    "        for i in range(sample_n):\n",
    "            axs[j][i].imshow(z[i].reshape(28, 28), cmap='gray')\n",
    "\n",
    "for ax in axs:\n",
    "    for a in ax:\n",
    "        a.set_xticklabels([])\n",
    "        a.set_yticklabels([])\n",
    "        a.set_aspect('equal')\n",
    "\n",
    "f.subplots_adjust(wspace=0, hspace=0)\n",
    "plt.show()\n",
    "plt.close('all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}