vae_relaxed_categorical.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YvryyD5UiqVT"
   },
   "source": [
    "# Categorical VAE with ST Gumbel-Softmax\n",
    "\n",
    "**Partial implementation of the paper [Categorical Reparameterization with Gumbel-Softmax](https://arxiv.org/abs/1611.01144) following the implementation from https://github.com/ericjang/gumbel-softmax but reorganized and translated to pure TF 2.2.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5PUK6xQMiqVi"
   },
   "source": [
    "## Imports and Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Cf1nacIdiqVo"
   },
   "outputs": [],
   "source": [
    "import copy\n",
    "\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "from tensorflow_probability import distributions as tfpd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "0w2iD0BMiqV3",
    "outputId": "a04ed99f-73b6-4646-f83b-44d86cc30ff2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('2.2.0', '0.9.0')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.__version__, tfp.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7sFBoX7-iqW1"
   },
   "outputs": [],
   "source": [
    "BATCH_SIZE=256\n",
    "NUM_ITERS=50000\n",
    "tau0=1.0 # initial temperature\n",
    "np_temp=tau0\n",
    "np_lr=0.001\n",
    "ANNEAL_RATE=0.00003\n",
    "MIN_TEMP=0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "K18in8SZiqWQ"
   },
   "source": [
    "## Gumbel softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Relaxed categorical distribution was recently added to TFP but before that sampling from it was relatively easy to achieve with the code presented below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Through the notebook, *x* denotes observed data and *y* stands for latent samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "G5HV9VIGiqWT"
   },
   "outputs": [],
   "source": [
    "@tf.function        \n",
    "def sample_gumbel(shape, eps=1e-20): \n",
    "  \"\"\"Sample from Gumbel(0, 1)\"\"\"\n",
    "  U = tf.random.uniform(shape,minval=0,maxval=1)\n",
    "  return -tf.math.log(-tf.math.log(U + eps) + eps)\n",
    "\n",
    "\n",
    "@tf.function   \n",
    "def gumbel_softmax_sample(logits, temperature): \n",
    "  \"\"\" Draw a sample from the Gumbel-Softmax distribution\"\"\"\n",
    "  y = logits + sample_gumbel(tf.shape(logits))\n",
    "  return tf.nn.softmax( y / temperature)\n",
    "\n",
    "\n",
    "@tf.function       \n",
    "def straight_through_sample(y, hard):\n",
    "  \"\"\"\n",
    "  Args:\n",
    "    y: [..., n_class] one-hot sample from the Gumbel-Softmax distribution. \n",
    "    hard: if True, take argmax, but differentiate w.r.t. soft sample y\n",
    "  Returns:\n",
    "    If hard=True, then the returned sample y will be one-hot, otherwise it will\n",
    "    be a probabilitiy distribution that sums to 1 across classes\n",
    "  \"\"\"\n",
    "  if hard:\n",
    "    K = y.shape[-1]\n",
    "    y_hard = tf.cast(tf.one_hot(tf.argmax(y,-1), K), y.dtype)\n",
    "    y = tf.stop_gradient(y_hard - y) + y  \n",
    "  return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zXgNCssWiqWd"
   },
   "source": [
    "## Model specification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two parameters configuring how the forward pass is performed:\n",
    " 1. use_tfp_distributions - switches between using TFP RelaxedOneHotCategorical and the code above\n",
    " 2. hard - turns on passing samples through straight-through (ST) estimator that converts them into 'true' one-hot encoded vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "U8bqeCYViqWg"
   },
   "outputs": [],
   "source": [
    "class CategoricalVAE(tf.Module):\n",
    "\n",
    "    def __init__(self, N=10, K=2, hard=False, use_tfp_distributions=True, name=None):\n",
    "        \"\"\"\n",
    "        \n",
    "            Args:\n",
    "                N: number of variables\n",
    "                K: number of categories for each variable\n",
    "                hard: set hard=True for ST Gumbel-Softmax \n",
    "                use_tfp_distributions: set True to represent q_y with RelaxedOneHotCategorical object \n",
    "                                        otherwise \n",
    "        \"\"\"\n",
    "        super(CategoricalVAE, self).__init__(name=name)\n",
    "\n",
    "        self.N = N # number of categorical distributions\n",
    "        self.K = K # number of classes\n",
    "        self.hard = hard # set hard=True for ST Gumbel-Softmax \n",
    "        # represent q_y with RelaxedOneHotCategorical object\n",
    "        self.use_tfp_distributions = use_tfp_distributions \n",
    "\n",
    "        self.calc_logits_y = tf.keras.Sequential([ # encoder\n",
    "                tf.keras.layers.Flatten(name=\"encoder0\"),\n",
    "                tf.keras.layers.Dense(512, activation=\"relu\", \n",
    "                    input_shape=(None, 784), name=\"encoder1\"),\n",
    "                tf.keras.layers.Dense(256, activation=\"relu\", name=\"encoder2\"),\n",
    "                tf.keras.layers.Dense(K*N, activation=None, name=\"encoder3\"),\n",
    "                tf.keras.layers.Reshape( [N,K] , name=\"encoder4\")\n",
    "                ], name=\"encoder\")\n",
    "\n",
    "        self.calc_logits_x = tf.keras.Sequential([ # decoder\n",
    "                tf.keras.layers.Flatten(name=\"decoder0\"),\n",
    "                tf.keras.layers.Dense(256, activation=\"relu\", name=\"decoder1\"),\n",
    "                tf.keras.layers.Dense(512, activation=\"relu\", name=\"decoder2\"),\n",
    "                tf.keras.layers.Dense(784, activation=None, name=\"decoder3\"),\n",
    "                ], name=\"decoder\") \n",
    "            \n",
    "    def __call__(self, x, temperature=5.0):\n",
    "        tau = tf.constant(temperature, name=\"temperature\", dtype=tf.float32)                        \n",
    "        \n",
    "        # variational posterior q(y|x), i.e. the encoder \n",
    "        # unnormalized logits for N separate K-categorical distributions \n",
    "        # (shape=(batch_size,N,K))\n",
    "        logits_y = self.calc_logits_y(x)\n",
    "        if self.use_tfp_distributions:\n",
    "            q_y = tfpd.RelaxedOneHotCategorical(tau, logits=logits_y)\n",
    "            y = q_y.sample()\n",
    "        else:\n",
    "            q_y = tf.nn.softmax(logits_y)                        \n",
    "            y = gumbel_softmax_sample(logits_y, tau)  \n",
    "        y = straight_through_sample(y, self.hard) # set hard=True for ST Gumbel-Softmax\n",
    "\n",
    "        # generative model p(x|y)\n",
    "        logits_x = self.calc_logits_x(y)    \n",
    "        p_x = tfpd.Bernoulli(logits=logits_x)\n",
    "        \n",
    "        return p_x, q_y, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "S9RoEpEYn5SR"
   },
   "source": [
    "## ELBOs with KL approximated in different ways"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several issues that need to be considered when calculating KL term in ELBO for relaxed categorical distributions. This is because:\n",
    " 1. Samples from the distribution (unless passed through ST) are not valid one-hot encoded vectors\n",
    " 2. We cannot evaluate probability mass for categorical distribution - we get only probability density of its relaxed version\n",
    " \n",
    "In consequence, certain decisions need to be made:\n",
    " 1. How the priors should look like so they would make sense with relaxed latent samples *y*\n",
    " 2. Do we try to estimate q(y) or do we approximate KL with MC as KL = y * (log q(y)-log p(y))\n",
    "\n",
    "Finally, implementations differ between using TFP Relaxed Categorical distribution or the above code.\n",
    "\n",
    "Below, we present three versions of the loss (-ELBO) with different choices regarding the issues.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lxnu7XXdiqWp"
   },
   "outputs": [],
   "source": [
    "def loss_analytical_relaxed_vs_categorical_notfp(x, p_x, q_y, *args, **kwargs):\n",
    "    \"\"\" For KL uses densities q_y coming from concrete distribution. \n",
    "        that compares to categorical prior. \n",
    "        \n",
    "        Based on\n",
    "        https://github.com/ericjang/gumbel-softmax/blob/master/Categorical%20VAE.ipynb\n",
    "    \"\"\"\n",
    "    batch_size, K = p_x.logits.shape[0], q_y.shape[-1]\n",
    "    N = int(tf.reduce_prod(q_y.shape)//K//batch_size)\n",
    "\n",
    "    log_p_y = tf.math.log(1.0/K) * tf.ones_like(q_y) # compare to categorical\n",
    "    log_q_y = tf.math.log(q_y+1e-20)        \n",
    "    kl_tmp = q_y*(log_q_y-log_p_y)\n",
    "    KL = tf.reduce_sum(kl_tmp, [1, 2])\n",
    "\n",
    "    elbo = tf.reduce_sum(p_x.log_prob(x), 1) - KL        \n",
    "    return tf.reduce_mean(-elbo) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "4pMxT6Q82gag"
   },
   "outputs": [],
   "source": [
    "def loss_MC_relaxed_vs_relaxed(x, p_x, q_y, y): \n",
    "    \"\"\" For KL uses Monte Carlo KL with Relaxed (concrete) prior. \n",
    "    \n",
    "        Based on\n",
    "        https://github.com/ericjang/gumbel-softmax/blob/master/gumbel_softmax_vae_v2.ipynb\n",
    "    \"\"\"\n",
    "    (batch_size, N), K = q_y.batch_shape, q_y.event_shape[0]\n",
    "    \n",
    "    tau = q_y.temperature # use the same temperature for prior as for posterior # TODO\n",
    "    probs_py = tf.ones_like(q_y.logits) * 1./K  \n",
    "    p_y = tfpd.RelaxedOneHotCategorical(tau, probs=probs_py) # compare to Relaxed (concrete)\n",
    "\n",
    "    KL_qp = q_y.log_prob(y) - p_y.log_prob(y) #MC estimate\n",
    "    KL = tf.reduce_sum(KL_qp, 1)\n",
    "\n",
    "    elbo = tf.reduce_sum(p_x.log_prob(x), 1) - KL        \n",
    "    return tf.reduce_mean(-elbo) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bx8LL9omii-T"
   },
   "outputs": [],
   "source": [
    "def loss_analytical_relaxed_vs_categorical(x, p_x, q_y, *args, **kwargs):\n",
    "    \"\"\" For KL uses Relaxed (concrete) distribution q_y \n",
    "        that compares to categorical prior. \"\"\"\n",
    "    (batch_size, N), K = q_y.batch_shape, q_y.event_shape[0]\n",
    "\n",
    "    probs_py = tf.ones_like(q_y.logits) * 1./K  \n",
    "    p_cat_y = tfpd.OneHotCategorical(probs=probs_py) # compare to categorical\n",
    "\n",
    "    #KL_qp = tfpd.kl_divergence(q_y, p_cat_y) #not defined between Relaxed and OneHotCategorical\n",
    "    #KL = tf.reduce_sum(KL_qp, 1)\n",
    "    KL = tf.reduce_sum(q_y.probs_parameter() * (tf.math.log(q_y.probs_parameter()) - tf.math.log(p_cat_y.probs)), [2,1])\n",
    "\n",
    "    elbo = tf.reduce_sum(p_x.log_prob(x), 1) - KL        \n",
    "    return tf.reduce_mean(-elbo) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "2AC1b8njiqWy"
   },
   "source": [
    "## Training"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use MNIST data from Keras."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "S0K0W_U7iqW9"
   },
   "outputs": [],
   "source": [
    "# get data\n",
    "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data(path='mnist.npz')\n",
    "frmt = lambda images: tf.cast(tf.reshape(images,(-1, 784)), tf.float32)/255.0\n",
    "x_train, x_test = frmt(x_train), frmt(x_test)\n",
    "\n",
    "train_ds = tf.data.Dataset.from_tensor_slices((x_train, y_train)).batch(BATCH_SIZE)\n",
    "test_ds = tf.data.Dataset.from_tensor_slices((x_test, y_test)).batch(BATCH_SIZE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create VAE and choose appropriate loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tloGJnJpf6aa"
   },
   "outputs": [],
   "source": [
    "#loss = loss_MC_relaxed_vs_relaxed\n",
    "#loss = loss_analytical_relaxed_vs_categorical\n",
    "loss = loss_analytical_relaxed_vs_categorical_notfp\n",
    "\n",
    "vae = CategoricalVAE(hard=True, use_tfp_distributions=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "l8qA4dnZiqXP"
   },
   "outputs": [],
   "source": [
    "optimizer = tf.optimizers.Adam(learning_rate=0.001)\n",
    "dat=[]\n",
    "losses = []\n",
    "best_loss, best_vae = float(\"inf\"), None\n",
    "i = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "-bi8Uc8iiqXV",
    "outputId": "29b7c1df-8a26-45e7-fe1b-8d89084c54dc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0. loss=545.85 temp=1.00\n",
      "100. loss=238.24 temp=1.00\n",
      "200. loss=218.05 temp=1.00\n",
      "300. loss=208.51 temp=1.00\n",
      "400. loss=202.13 temp=1.00\n",
      "500. loss=196.32 temp=1.00\n",
      "600. loss=190.99 temp=1.00\n",
      "700. loss=186.03 temp=1.00\n",
      "800. loss=181.93 temp=1.00\n",
      "900. loss=178.51 temp=1.00\n",
      "1000. loss=175.52 temp=1.00\n",
      "1100. loss=173.05 temp=0.97\n",
      "1200. loss=170.86 temp=0.97\n",
      "1300. loss=169.00 temp=0.97\n",
      "1400. loss=167.34 temp=0.97\n",
      "1500. loss=165.89 temp=0.97\n",
      "1600. loss=164.58 temp=0.97\n",
      "1700. loss=163.35 temp=0.97\n",
      "1800. loss=162.28 temp=0.97\n",
      "1900. loss=161.28 temp=0.97\n",
      "2000. loss=160.39 temp=0.97\n",
      "2100. loss=159.57 temp=0.94\n",
      "2200. loss=158.78 temp=0.94\n",
      "2300. loss=158.09 temp=0.94\n",
      "2400. loss=157.40 temp=0.94\n",
      "2500. loss=156.80 temp=0.94\n",
      "2600. loss=156.21 temp=0.94\n",
      "2700. loss=155.68 temp=0.94\n",
      "2800. loss=155.17 temp=0.94\n",
      "2900. loss=154.68 temp=0.94\n",
      "3000. loss=154.23 temp=0.94\n",
      "3100. loss=153.78 temp=0.91\n",
      "3200. loss=153.39 temp=0.91\n",
      "3300. loss=153.00 temp=0.91\n",
      "3400. loss=152.63 temp=0.91\n",
      "3500. loss=152.30 temp=0.91\n",
      "3600. loss=151.95 temp=0.91\n",
      "3700. loss=151.63 temp=0.91\n",
      "3800. loss=151.32 temp=0.91\n",
      "3900. loss=151.04 temp=0.91\n",
      "4000. loss=150.76 temp=0.91\n",
      "4100. loss=150.49 temp=0.89\n",
      "4200. loss=150.24 temp=0.89\n",
      "4300. loss=149.98 temp=0.89\n",
      "4400. loss=149.74 temp=0.89\n",
      "4500. loss=149.50 temp=0.89\n",
      "4600. loss=149.28 temp=0.89\n",
      "4700. loss=149.07 temp=0.89\n",
      "4800. loss=148.86 temp=0.89\n",
      "4900. loss=148.67 temp=0.89\n",
      "5000. loss=148.46 temp=0.89\n",
      "5100. loss=148.27 temp=0.86\n",
      "5200. loss=148.07 temp=0.86\n",
      "5300. loss=147.90 temp=0.86\n",
      "5400. loss=147.73 temp=0.86\n",
      "5500. loss=147.56 temp=0.86\n",
      "5600. loss=147.41 temp=0.86\n",
      "5700. loss=147.24 temp=0.86\n",
      "5800. loss=147.08 temp=0.86\n",
      "5900. loss=146.92 temp=0.86\n",
      "6000. loss=146.78 temp=0.86\n",
      "6100. loss=146.64 temp=0.84\n",
      "6200. loss=146.50 temp=0.84\n",
      "6300. loss=146.37 temp=0.84\n",
      "6400. loss=146.23 temp=0.84\n",
      "6500. loss=146.10 temp=0.84\n",
      "6600. loss=145.97 temp=0.84\n",
      "6700. loss=145.85 temp=0.84\n",
      "6800. loss=145.73 temp=0.84\n",
      "6900. loss=145.60 temp=0.84\n",
      "7000. loss=145.49 temp=0.84\n",
      "7100. loss=145.36 temp=0.81\n",
      "7200. loss=145.26 temp=0.81\n",
      "7300. loss=145.15 temp=0.81\n",
      "7400. loss=145.05 temp=0.81\n",
      "7500. loss=144.95 temp=0.81\n",
      "7600. loss=144.84 temp=0.81\n",
      "7700. loss=144.75 temp=0.81\n",
      "7800. loss=144.64 temp=0.81\n",
      "7900. loss=144.55 temp=0.81\n",
      "8000. loss=144.46 temp=0.81\n",
      "8100. loss=144.37 temp=0.79\n",
      "8200. loss=144.28 temp=0.79\n",
      "8300. loss=144.19 temp=0.79\n",
      "8400. loss=144.10 temp=0.79\n",
      "8500. loss=144.01 temp=0.79\n",
      "8600. loss=143.93 temp=0.79\n",
      "8700. loss=143.85 temp=0.79\n",
      "8800. loss=143.77 temp=0.79\n",
      "8900. loss=143.70 temp=0.79\n",
      "9000. loss=143.62 temp=0.79\n",
      "9100. loss=143.54 temp=0.76\n",
      "9200. loss=143.46 temp=0.76\n",
      "9300. loss=143.39 temp=0.76\n",
      "9400. loss=143.32 temp=0.76\n",
      "9500. loss=143.25 temp=0.76\n",
      "9600. loss=143.18 temp=0.76\n",
      "9700. loss=143.11 temp=0.76\n",
      "9800. loss=143.04 temp=0.76\n",
      "9900. loss=142.97 temp=0.76\n",
      "10000. loss=142.91 temp=0.76\n",
      "10100. loss=142.84 temp=0.74\n",
      "10200. loss=142.78 temp=0.74\n",
      "10300. loss=142.72 temp=0.74\n",
      "10400. loss=142.65 temp=0.74\n",
      "10500. loss=142.59 temp=0.74\n",
      "10600. loss=142.52 temp=0.74\n",
      "10700. loss=142.47 temp=0.74\n",
      "10800. loss=142.41 temp=0.74\n",
      "10900. loss=142.36 temp=0.74\n",
      "11000. loss=142.30 temp=0.74\n",
      "11100. loss=142.24 temp=0.72\n",
      "11200. loss=142.19 temp=0.72\n",
      "11300. loss=142.13 temp=0.72\n",
      "11400. loss=142.08 temp=0.72\n",
      "11500. loss=142.03 temp=0.72\n",
      "11600. loss=141.97 temp=0.72\n",
      "11700. loss=141.92 temp=0.72\n",
      "11800. loss=141.87 temp=0.72\n",
      "11900. loss=141.82 temp=0.72\n",
      "12000. loss=141.77 temp=0.72\n",
      "12100. loss=141.72 temp=0.70\n",
      "12200. loss=141.67 temp=0.70\n",
      "12300. loss=141.62 temp=0.70\n",
      "12400. loss=141.58 temp=0.70\n",
      "12500. loss=141.53 temp=0.70\n",
      "12600. loss=141.48 temp=0.70\n",
      "12700. loss=141.44 temp=0.70\n",
      "12800. loss=141.40 temp=0.70\n",
      "12900. loss=141.35 temp=0.70\n",
      "13000. loss=141.31 temp=0.70\n",
      "13100. loss=141.27 temp=0.68\n",
      "13200. loss=141.22 temp=0.68\n",
      "13300. loss=141.18 temp=0.68\n",
      "13400. loss=141.14 temp=0.68\n",
      "13500. loss=141.10 temp=0.68\n",
      "13600. loss=141.06 temp=0.68\n",
      "13700. loss=141.02 temp=0.68\n",
      "13800. loss=140.98 temp=0.68\n",
      "13900. loss=140.94 temp=0.68\n",
      "14000. loss=140.91 temp=0.68\n",
      "14100. loss=140.87 temp=0.66\n",
      "14200. loss=140.83 temp=0.66\n",
      "14300. loss=140.80 temp=0.66\n",
      "14400. loss=140.76 temp=0.66\n",
      "14500. loss=140.72 temp=0.66\n",
      "14600. loss=140.68 temp=0.66\n",
      "14700. loss=140.65 temp=0.66\n",
      "14800. loss=140.61 temp=0.66\n",
      "14900. loss=140.58 temp=0.66\n",
      "15000. loss=140.55 temp=0.66\n",
      "15100. loss=140.51 temp=0.64\n",
      "15200. loss=140.48 temp=0.64\n",
      "15300. loss=140.44 temp=0.64\n",
      "15400. loss=140.41 temp=0.64\n",
      "15500. loss=140.38 temp=0.64\n",
      "15600. loss=140.35 temp=0.64\n",
      "15700. loss=140.32 temp=0.64\n",
      "15800. loss=140.29 temp=0.64\n",
      "15900. loss=140.26 temp=0.64\n",
      "16000. loss=140.22 temp=0.64\n",
      "16100. loss=140.19 temp=0.62\n",
      "16200. loss=140.16 temp=0.62\n",
      "16300. loss=140.13 temp=0.62\n",
      "16400. loss=140.10 temp=0.62\n",
      "16500. loss=140.07 temp=0.62\n",
      "16600. loss=140.04 temp=0.62\n",
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      "16800. loss=139.98 temp=0.62\n",
      "16900. loss=139.96 temp=0.62\n",
      "17000. loss=139.93 temp=0.62\n",
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      "17200. loss=139.87 temp=0.60\n",
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      "17400. loss=139.82 temp=0.60\n",
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      "17600. loss=139.77 temp=0.60\n",
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      "18000. loss=139.66 temp=0.60\n",
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      "18200. loss=139.61 temp=0.58\n",
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      "19900. loss=139.21 temp=0.57\n",
      "20000. loss=139.19 temp=0.57\n",
      "20100. loss=139.17 temp=0.55\n",
      "20200. loss=139.15 temp=0.55\n",
      "20300. loss=139.12 temp=0.55\n",
      "20400. loss=139.10 temp=0.55\n",
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      "25500. loss=138.26 temp=0.50\n",
      "25600. loss=138.25 temp=0.50\n",
      "25700. loss=138.23 temp=0.50\n",
      "25800. loss=138.22 temp=0.50\n",
      "25900. loss=138.21 temp=0.50\n",
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      "26100. loss=138.18 temp=0.50\n",
      "26200. loss=138.17 temp=0.50\n",
      "26300. loss=138.16 temp=0.50\n",
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      "26900. loss=138.09 temp=0.50\n",
      "27000. loss=138.08 temp=0.50\n",
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      "27300. loss=138.05 temp=0.50\n",
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      "27500. loss=138.03 temp=0.50\n",
      "27600. loss=138.02 temp=0.50\n",
      "27700. loss=138.01 temp=0.50\n",
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      "27900. loss=137.99 temp=0.50\n",
      "28000. loss=137.98 temp=0.50\n",
      "28100. loss=137.98 temp=0.50\n",
      "28200. loss=137.97 temp=0.50\n",
      "28300. loss=137.96 temp=0.50\n",
      "28400. loss=137.96 temp=0.50\n",
      "28500. loss=137.95 temp=0.50\n",
      "28600. loss=137.94 temp=0.50\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28700. loss=137.93 temp=0.50\n",
      "28800. loss=137.92 temp=0.50\n",
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      "49500. loss=138.32 temp=0.50\n",
      "49600. loss=138.33 temp=0.50\n",
      "49700. loss=138.34 temp=0.50\n",
      "49800. loss=138.35 temp=0.50\n",
      "49900. loss=138.36 temp=0.50\n",
      "50000. loss=138.37 temp=0.50\n"
     ]
    }
   ],
   "source": [
    "while i<NUM_ITERS:\n",
    "\n",
    "    for np_x, labels in train_ds:\n",
    "        \n",
    "        with tf.GradientTape() as tape:        \n",
    "            p_x, q_y, y = vae(np_x, temperature=np_temp)\n",
    "            l = loss(np_x, p_x, q_y, y)\n",
    "            losses.append(float(l)); \n",
    "        g = tape.gradient(l, vae.trainable_variables)\n",
    "        optimizer.apply_gradients(zip(g, vae.trainable_variables))\n",
    "        \n",
    "        if i % 1000 == 1:\n",
    "            np_temp = np.maximum(tau0*np.exp(-ANNEAL_RATE*i),MIN_TEMP)\n",
    "            \n",
    "        ########################################################################\n",
    "\n",
    "        dat.append([i,np_temp,l])\n",
    "    \n",
    "        if i%100==0: \n",
    "            print(\"%i. loss=%.2f temp=%.2f\" % (i, np.mean(losses), np_temp) )\n",
    "            \n",
    "            if np.mean(losses)<best_loss: # track the best over 100 iterations\n",
    "                best_loss = np.mean(losses)\n",
    "                best_vae = copy.deepcopy(vae)                        \n",
    "        i += 1\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the best from observed\n",
    "vae = best_vae            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "H3AWzRqFiqYV"
   },
   "source": [
    "## Training Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7cvJaiSNiqYX"
   },
   "outputs": [],
   "source": [
    "dat=np.array(dat).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "DUHQi-0giqYc",
    "outputId": "cf23f4a4-cc46-4b1f-c41b-866ed060a06e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90, 185)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f,axarr=plt.subplots(1,2)\n",
    "axarr[0].plot(dat[0],dat[1])\n",
    "axarr[0].set_ylabel('Temperature')\n",
    "axarr[1].plot(dat[0],dat[2])\n",
    "axarr[1].set_ylabel('-ELBO')\n",
    "axarr[1].set_ylim((90,185))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "eyR7mEediqX2"
   },
   "outputs": [],
   "source": [
    "import matplotlib.animation as animation\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xyYdoTHNiqXg"
   },
   "outputs": [],
   "source": [
    "np_x1 = x_train[-BATCH_SIZE:]\n",
    "p_x, q_y, y = vae(np_x1)\n",
    "np_x2 = p_x.mean()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HZYEk+AQdkARhB5Ig7EAShB1IgrADSRB2IAnCDiTxfxB2IpncNZnWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Gz/pe9ybpIY1c1g1r5IroKknHSlop6YXG7UAf9faApOckPauRYM3sUW/na+RPw2clrW38XNbr567QV1eeN94uCyTBO+iAJAg7kARhB5Ig7EAShB1IgrADSRB2IIn/Ba3VO6rXHmjyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAANFUlEQVR4nO3dbYxc5XnG8euKWZvW4MoG21jGKYSAWkRap9qYtFSUihAZS5WJEpK4SmQikkURbpMoTYtom6CqlehLQlFekDbBiokSJ1FiwB9IG8tCQlEThwUZbDCuCbKD7a0X5Eo4RTV+ufthD9Vidp5Zz5yZM/b9/0mjmTn3mXNujfbyOTPPGT+OCAE4+72l6QYA9AdhB5Ig7EAShB1IgrADSZzTz53N9pw4V3P7uUsglf/V/+i1OOrpal2F3fZKSfdKmiXpGxFxd2n9czVXV/v6bnYJoGBbbG1Z6/g03vYsSV+VdKOkKyWtsX1lp9sD0FvdfGZfIen5iHghIl6T9F1Jq+tpC0Ddugn7UkkvTnm+v1r2BrZHbI/ZHjumo13sDkA3ugn7dF8CvOna24gYjYjhiBge0pwudgegG92Efb+kZVOeXyzpYHftAOiVbsL+uKTLbV9qe7akD0vaXE9bAOrW8dBbRBy3vU7Sv2ty6G19RDxTW2cAatXVOHtEPCLpkZp6AdBDXC4LJEHYgSQIO5AEYQeSIOxAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEl3N4go0ac+97y7Wd3/gqy1rV/zotuJrr/j4WEc9DbKuwm57r6Qjkk5IOh4Rw3U0BaB+dRzZ/zgiXq5hOwB6iM/sQBLdhj0k/dj2E7ZHplvB9ojtMdtjx3S0y90B6FS3p/HXRMRB24skbbH9XEQ8NnWFiBiVNCpJ87wgutwfgA51dWSPiIPV/YSkByWtqKMpAPXrOOy259o+//XHkt4raWddjQGoVzen8YslPWj79e18JyL+rZaukILf9Y5i/U+/9aNiffV59xTrJwt/3jtWfqX42ms/+ZlifeF9Py3WB1HHYY+IFyT9bo29AOghht6AJAg7kARhB5Ig7EAShB1Igp+4ojG7b5tTrH/o/PE2W+j8z3fIs4r1k0PueNuDiiM7kARhB5Ig7EAShB1IgrADSRB2IAnCDiTBODt66i2/81staz+4/mttXl0e6952dKhYX/vox1vWzt03u/jaSzfuKdZPFKuDiSM7kARhB5Ig7EAShB1IgrADSRB2IAnCDiTBODt6at+fLGhZu2p2d78Z/9f9NxTrV9za+bTLZ+I4ejsc2YEkCDuQBGEHkiDsQBKEHUiCsANJEHYgCcbZ0ZVZb7+0WP/Ih7b2bN97v/P2Yn2hXurZvs9EbY/sttfbnrC9c8qyBba32N5T3c/vbZsAujWT0/hvSlp5yrI7JG2NiMslba2eAxhgbcMeEY9JOnzK4tWSNlSPN0i6qea+ANSs0y/oFkfEuCRV94tarWh7xPaY7bFjOtrh7gB0q+ffxkfEaEQMR8TwkMoT+QHonU7Dfsj2Ekmq7ifqawlAL3Qa9s2S1laP10p6uJ52APRK23F22xslXSfpQtv7JX1B0t2Svm/7Vkm/lHRzL5vE4HrPQ08V67fP393xtlc++4FifclDLxTrxzve89mpbdgjYk2L0vU19wKgh7hcFkiCsANJEHYgCcIOJEHYgST4iSuKXh75/WL9z+Z/pVg/WagdPF6+fPrcv/j1Yv34f+0r1vFGHNmBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnG2ZObtXBhsf6eT/60Z/u++e8+V6xf8FTv9p0RR3YgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSIJx9uSe++e3FusPLnqkzRbKx4s/P3Bty9qiTc8VX3uizZ5xejiyA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EASjLOf5SbW/UGxvvuGL7fZQvl4MORZxfqLN/5ay9qJ/z7cZt+oU9sju+31tids75yy7C7bB2xvr26retsmgG7N5DT+m5JWTrP8nohYXt3aXWYFoGFtwx4Rj0nifAs4w3XzBd06209Xp/nzW61ke8T2mO2xYyrP7QWgdzoN+32SLpO0XNK4pC+2WjEiRiNiOCKGhzSnw90B6FZHYY+IQxFxIiJOSvq6pBX1tgWgbh2F3faSKU/fJ2lnq3UBDIa24+y2N0q6TtKFtvdL+oKk62wvlxSS9kq6rYc9oo1zLlrcsvZHH/t58bUnizOotzf8+XXF+gWHf9bV9lGftmGPiDXTLL6/B70A6CEulwWSIOxAEoQdSIKwA0kQdiAJfuJ6Bjjn4qXF+m9879WWtX+8qLtpjz8/8a5i/YJvMK3ymYIjO5AEYQeSIOxAEoQdSIKwA0kQdiAJwg4kwTj7GWD8a+cV65sueajjbX9uvPxfTf9i9cI2WzjY8b7RXxzZgSQIO5AEYQeSIOxAEoQdSIKwA0kQdiAJxtkHwDlLLirWV7312Y63ffhEecqtn315uFiff4Dfq58tOLIDSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKMs/dBaUplSXr1gTnF+t8ufLJYP1QYS185+pfF1y7b8B/FOs4ebY/stpfZftT2LtvP2P5UtXyB7S2291T383vfLoBOzeQ0/rikz0bEb0t6t6TbbV8p6Q5JWyPicklbq+cABlTbsEfEeEQ8WT0+ImmXpKWSVkvaUK22QdJNvWoSQPdO6ws625dIeqekbZIWR8S4NPkPgqRFLV4zYnvM9tgxla/TBtA7Mw677fMk/VDSpyPilZm+LiJGI2I4IoaHVP4iCkDvzCjstoc0GfRvR8SmavEh20uq+hJJE71pEUAd2g692bak+yXtiogvTSltlrRW0t3V/cM96fAssG/tZcX6E1fe29X2/+bAqpa1ZX/P0BomzWSc/RpJH5W0w/b2atmdmgz5923fKumXkm7uTYsA6tA27BHxE0luUb6+3nYA9AqXywJJEHYgCcIOJEHYgSQIO5AEP3Gtwax584r1z9yyqVhvZ+ORpcX6y7dMe6VyZcYXO+Isx5EdSIKwA0kQdiAJwg4kQdiBJAg7kARhB5JgnL0GBz52VbH+kXlbu9r+Pzz8/mL9bbuZVhntcWQHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQYZ6/B4rFXi/VtR4eK9avnHCtv/+cnT7sn4FQc2YEkCDuQBGEHkiDsQBKEHUiCsANJEHYgCUdEeQV7maQHJF0k6aSk0Yi41/Zdkj4h6aVq1Tsj4pHStuZ5QVxtJn4FemVbbNUrcXjaWZdnclHNcUmfjYgnbZ8v6QnbW6raPRHxL3U1CqB3ZjI/+7ik8erxEdu7JJWnKAEwcE7rM7vtSyS9U9K2atE620/bXm97fovXjNgesz12TEe7ahZA52YcdtvnSfqhpE9HxCuS7pN0maTlmjzyf3G610XEaEQMR8TwkObU0DKATswo7LaHNBn0b0fEJkmKiEMRcSIiTkr6uqQVvWsTQLfaht22Jd0vaVdEfGnK8iVTVnufpJ31twegLjP5Nv4aSR+VtMP29mrZnZLW2F4uKSTtlXRbTzoEUIuZfBv/E0nTjdsVx9QBDBauoAOSIOxAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiTR9r+SrnVn9kuS9k1ZdKGkl/vWwOkZ1N4GtS+J3jpVZ2+/GRELpyv0Nexv2rk9FhHDjTVQMKi9DWpfEr11ql+9cRoPJEHYgSSaDvtow/svGdTeBrUvid461ZfeGv3MDqB/mj6yA+gTwg4k0UjYba+0vdv287bvaKKHVmzvtb3D9nbbYw33st72hO2dU5YtsL3F9p7qfto59hrq7S7bB6r3brvtVQ31tsz2o7Z32X7G9qeq5Y2+d4W++vK+9f0zu+1Zkv5T0g2S9kt6XNKaiHi2r420YHuvpOGIaPwCDNvXSvqVpAci4qpq2T9JOhwRd1f/UM6PiL8akN7ukvSrpqfxrmYrWjJ1mnFJN0m6RQ2+d4W+Pqg+vG9NHNlXSHo+Il6IiNckfVfS6gb6GHgR8Zikw6csXi1pQ/V4gyb/WPquRW8DISLGI+LJ6vERSa9PM97oe1foqy+aCPtSSS9Oeb5fgzXfe0j6se0nbI803cw0FkfEuDT5xyNpUcP9nKrtNN79dMo04wPz3nUy/Xm3mgj7dFNJDdL43zUR8XuSbpR0e3W6ipmZ0TTe/TLNNOMDodPpz7vVRNj3S1o25fnFkg420Me0IuJgdT8h6UEN3lTUh16fQbe6n2i4n/83SNN4TzfNuAbgvWty+vMmwv64pMttX2p7tqQPS9rcQB9vYntu9cWJbM+V9F4N3lTUmyWtrR6vlfRwg728waBM491qmnE1/N41Pv15RPT9JmmVJr+R/4Wkv26ihxZ9vU3SU9XtmaZ7k7RRk6d1xzR5RnSrpAskbZW0p7pfMEC9fUvSDklPazJYSxrq7Q81+dHwaUnbq9uqpt+7Ql99ed+4XBZIgivogCQIO5AEYQeSIOxAEoQdSIKwA0kQdiCJ/wOy1tF3Ayn0CwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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r6NYu93W5n//XS8t4T7fMuHrguevm8ufdCPvDklbYPtP2HElXS9rYhT7exfb82gcnsj1f0uXqvaWoN0q6pnb9Gkl3d7GXn9Iry3hXLTOuLj93XV/+PCI6/iPpSk1+Iv+spM92o4eKvpZL+nHt5/Fu9ybpdk2+rBvV5CuitZJOkrRF0s7a5aIe6u3rkrZJekyTwVrSpd4+rMm3ho9J2lr7ubLbz12hr448b3xdFkiCb9ABSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBL/BwoAahuuqC7TAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rM3rI6esCSb/KfrY0uzdJD6r/sK5X/UdE10k6R9IqSduz27Et1Nt3JD0r6Rn1B6uzSb39qfo/Gj4jaVP2M6fZ712ir4a8b1wuCwTBFXRAEIQdCIKwA0EQdiAIwg4EQdiBIAg7EMT/Aw6ONS9iMZEGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kezTysm5II6+IrpB0vKR1kp6pXU/vod6+ImmjpKc0EqxZXertvRp5a/iUpA21y6JuP3eFvjryvHG6LJAEZ9ABSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBL/C8wWQH6UJhiYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    plt.imshow(np_x1[i].numpy().reshape((28,28))); plt.show()\n",
    "    plt.imshow(np_x2[i].numpy().reshape((28,28))); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7xmiYkdEiqYn"
   },
   "source": [
    "## Unconditional generation\n",
    "\n",
    "This consists of sampling from the prior $p_\\theta(y)$ and passing it through decoder of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x460.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "ys = []\n",
    "for _ in range(10):\n",
    "    xs = []\n",
    "    for _ in range(10):\n",
    "        np_y = np.zeros((N,K))\n",
    "        np_y[range(N),np.random.choice(K,N)] = 1\n",
    "        np_y = np.reshape(np_y,[1,N,K])\n",
    "\n",
    "        logits_x = vae.calc_logits_x(tf.constant(np_y, dtype=tf.float32)) \n",
    "        p_x = tfp.distributions.Bernoulli(logits=logits_x)\n",
    "        np_x = p_x.mean().numpy()[0].reshape((28,28))\n",
    "        xs.append(np_x)\n",
    "    ys.append(np.hstack(xs))\n",
    "img = np.vstack(ys)   \n",
    "\n",
    "fig = plt.figure(figsize=(6.4, 6.4), dpi=72)\n",
    "plt.imshow(img, cmap=plt.cm.gray,interpolation='none')\n",
    "plt.xticks([],{})\n",
    "plt.yticks([],{})\n",
    "plt.savefig(\"vae_concrete.pdf\", bbox_inches = 'tight', pad_inches =0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "name": "CategoricalVAE_TF2.ipynb",
   "provenance": []
  },
  "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}