MNIST - Adversarial Autoencoder - Unsupervised 2D Gaussian Latent Representation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adversarial Autoencoder\n",
    "\n",
    "Adversarial autoencoder is regularized by matching the aggregated posterior $q(z)$ to an arbitrary prior distribution $p(z)$. The generator of the adversarial network is also the encoder of the autoencoder $q(z|x)$. The encoder or generator of the network ensures the aggregated posterior distribution can fool the discriminative adversarial network into thinking that the hidden code $q(z)$ comes from the true prior distribution $p(z)$.\n",
    "\n",
    "Adversarial autoencoder is trained jointly in two phases - reconstruction phase and regularisation phase. In reconstruction phase, autoencoder updates the encoder and decoder to minimise the reconstruction error. In regularisation phase, adversarial network first updates its discriminator to tell apart true samples (generated using the prior $p(z)$) from the generated samples (generated by encoder or generator aggregrated posterior $q(z)$). The adversarial network then updates its generator to confuse the discriminator. Once training is done, decoder will define the generative model that maps the imposed prior $p(z)$ to the data distribution $p_d(x)$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pandas.__version 0.20.3\n",
      "torch.__version__: 0.2.0_3\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import tqdm\n",
    "import os\n",
    "import datetime\n",
    "import glob\n",
    "\n",
    "# pytorch\n",
    "import torch\n",
    "import torchvision\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "from torchvision import datasets, transforms\n",
    "from torch.autograd import Variable\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "print(\"pandas.__version\", pd.__version__)\n",
    "print(\"torch.__version__:\", torch.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Args (\n",
       "  train_batch_size: 1000\n",
       "  cuda: True\n",
       "  save_epoch_interval: 10\n",
       "  test_batch_size: 1000\n",
       "  epochs: 300\n",
       "  no_cuda: False\n",
       "  log_interval: None\n",
       ")"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class Args:\n",
    "    \"\"\"Dummy argument class\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        # batch size for training phase\n",
    "        self.train_batch_size = 1000\n",
    "        # batch size for testing phase\n",
    "        self.test_batch_size = 1000\n",
    "#        self.seed = 10\n",
    "        # enable or disable training using CUDA\n",
    "        self.no_cuda = False\n",
    "        # to indicate whether CUDA is used for training\n",
    "        self.cuda = not self.no_cuda and torch.cuda.is_available()\n",
    "        # randomising seed\n",
    "        self.epochs = 300\n",
    "        self.save_epoch_interval = 10\n",
    "        # number of batches to wait before logging training status\n",
    "        # None to indicate no logging of batch training status\n",
    "        self.log_interval = None\n",
    "    def __repr__(self):\n",
    "        tmpstr = self.__class__.__name__ + ' (\\n'\n",
    "        attrs = list(self.__dict__.keys())\n",
    "        for attr in attrs:\n",
    "             tmpstr = tmpstr + '  ' + attr + ': ' + self.__dict__[attr].__repr__() + '\\n'\n",
    "        tmpstr = tmpstr + ')'\n",
    "        return tmpstr\n",
    "# arguments\n",
    "args = Args()\n",
    "args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'num_workers': 4, 'pin_memory': True}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#torch.manual_seed(args.seed)\n",
    "#if args.cuda:\n",
    "#    torch.cuda.manual_seed(args.seed)\n",
    "\n",
    "kwargs = {'num_workers': 4, 'pin_memory': True} if args.cuda else {}\n",
    "kwargs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Utility Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_mnist_sample(tensor, sample_idx=None, size=10):\n",
    "    \"\"\"Plot MNIST samples from tensor.\n",
    "    \"\"\"\n",
    "    # sample from data if sample indices are not provided\n",
    "    if sample_idx is None:\n",
    "        # get sample indices\n",
    "        sample_idx = np.random.uniform(size=size) * tensor.shape[0]\n",
    "        sample_idx = sample_idx.astype(int)\n",
    "    # plot data\n",
    "    nrows = int(np.ceil(len(sample_idx)/10))\n",
    "    fig, axes = plt.subplots(nrows=nrows, ncols=10, figsize=(20,2))\n",
    "    for i,s in enumerate(sample_idx):\n",
    "        ax = axes.item(i)\n",
    "        ax.imshow(tensor[s].numpy())\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "        ax.set_title(\"Sample Index\\n{}\".format(s))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# transforms.ToTensor converts a PIL.Image or numpy.ndarray (H x W x C) \n",
    "# in the range [0, 255] to a torch.FloatTensor of shape (C x H x W) in \n",
    "# the range [0.0, 1.0]\n",
    "mnist_train = datasets.MNIST(\"../data\", train=True, download=True,\n",
    "                             transform=transforms.ToTensor())\n",
    "mnist_test = datasets.MNIST(\"../data\", train=False, download=True,\n",
    "                            transform=transforms.ToTensor())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cbc93eb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d245dddd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot first 10 samples from training data\n",
    "plot_mnist_sample(mnist_train.train_data, \n",
    "                  sample_idx=[i for i in range(10)])\n",
    "# plot 10 random samples of test data \n",
    "plot_mnist_sample(mnist_test.test_data, size=10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Check Transformation\n",
    "- Transform MNIST to [0, 1]\n",
    "- Check transformation is correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n.shape: (60000, 28, 28, 1)\n",
      "torch.Size([1, 28, 28])\n",
      "Original max values: 255\n",
      "Transformed max values: 1.0\n",
      "Reverse back to original, max values: 255\n",
      "Is original equal to reversed transformed tensor: True\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cb580a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cb5832160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = mnist_train.train_data.numpy()\n",
    "n.resize((60000, 28, 28, 1)) # Sample x Height x Width x Channel\n",
    "print(\"n.shape:\", n.shape) # Sample x Height x Width x Channel\n",
    "\n",
    "tensor_0 = mnist_train.transform(n[0]) # first sample after transformation\n",
    "print(tensor_0.size())\n",
    "# plot first training sample\n",
    "plot_mnist_sample(tensor_0, sample_idx=[0])\n",
    "plot_mnist_sample(mnist_train.train_data, sample_idx=[0])\n",
    "\n",
    "n_0_flatten = n[0, :, :, 0].reshape(784)\n",
    "print(\"Original max values:\", n_0_flatten.max())\n",
    "print(\"Transformed max values:\", tensor_0[0, :, :].numpy().max())\n",
    "tensor_0_flattern_reverse = tensor_0[0, :, :].numpy() * 255\n",
    "tensor_0_flattern_reverse = tensor_0_flattern_reverse.reshape(784).astype(int)\n",
    "print(\"Reverse back to original, max values:\", tensor_0_flattern_reverse.max())\n",
    "print(\"Is original equal to reversed transformed tensor:\",np.equal(n_0_flatten, tensor_0_flattern_reverse).sum() == 784)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST Data Loader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "train_loader = torch.utils.data.DataLoader(mnist_train, \n",
    "                        batch_size=args.train_batch_size,\n",
    "                        shuffle=True, \n",
    "                        **kwargs)\n",
    "test_loader = torch.utils.data.DataLoader(mnist_test, \n",
    "                        batch_size=args.test_batch_size,\n",
    "                        shuffle=True, \n",
    "                        **kwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Feed Forward Network as Autoencoder in AAE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_dim = 784 # input dimension to Encoder\n",
    "z_dim = 2 # latent space dimension\n",
    "\n",
    "class Encoder(nn.Module):\n",
    "    \"\"\"Encoder of AAE, it extends base class for neural network modules.\n",
    "    \n",
    "    Input values to the Encoder are in the range [0.0, 1.0].\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        super(Encoder, self).__init__()\n",
    "        # nn.Linear:\n",
    "        # Layer of weights and bias that performs linear transformation to incomming data\n",
    "        # output of each layer: y = Ax + B\n",
    "        # where A is the weight of the layer and B the bias\n",
    "        self.lin1 = nn.Linear(x_dim, 1000) # 1000 output dimension with X_dim input dimension \n",
    "        self.lin2 = nn.Linear(1000, 1000) # 1000 output dimension with 1000 input dimension\n",
    "        self.lin3 = nn.Linear(1000, z_dim) # z_dim output dimension from 1000 input dimension\n",
    "    \n",
    "    def forward(self, x):\n",
    "        \"\"\"Defines the forward computation.\n",
    "        \"\"\"\n",
    "        x = self.lin1(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.selu(x, inplace=False)\n",
    "        \n",
    "        x = self.lin2(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.selu(x, inplace=False)\n",
    "        \n",
    "        x = self.lin3(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        return x\n",
    "\n",
    "class Decoder(nn.Module):\n",
    "    \"\"\"Decoder of AAE, it extends base class for neural network modules.\n",
    "    \n",
    "    Output values of Decoder are in the range [0.0, 1.0].\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        super(Decoder, self).__init__()\n",
    "        self.lin1 = nn.Linear(z_dim, 1000)\n",
    "        self.lin2 = nn.Linear(1000, 1000)\n",
    "        self.lin3 = nn.Linear(1000, x_dim)\n",
    "    \n",
    "    def forward(self, x):\n",
    "        x = self.lin1(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.selu(x, inplace=False)\n",
    "        \n",
    "        x = self.lin2(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.selu(x, inplace=False)\n",
    "        \n",
    "        x = self.lin3(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        # ouput values are in range [0.0, 1.0] to match range of input values\n",
    "        # to the Encoder\n",
    "        x = F.sigmoid(x)\n",
    "        return x\n",
    "\n",
    "class Discriminator(nn.Module):\n",
    "    \"\"\"Discriminator of AAE, it extends base class of neural network modules.\n",
    "    \n",
    "    Output of Discriminator is in range [0.0, 1.0]\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        super(Discriminator, self).__init__()\n",
    "        self.lin1 = nn.Linear(z_dim, 1000)\n",
    "        self.lin2 = nn.Linear(1000, 1000)\n",
    "        self.lin3 = nn.Linear(1000, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.lin1(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.selu(x, inplace=False)\n",
    "        \n",
    "        x = self.lin2(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.selu(x, inplace=False)\n",
    "        \n",
    "        x = self.lin3(x)\n",
    "        x = F.dropout(x, p=0.5, training=self.training, inplace=False)\n",
    "        x = F.sigmoid(x)\n",
    "        return x\n",
    "    \n",
    "class AAE(nn.Module):\n",
    "    \"\"\"Simple Adversial Autoencoder, it extends base class of neural network modules.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        super(AAE, self).__init__()\n",
    "        self.nn_enc = Encoder()\n",
    "        self.nn_dec = Decoder()\n",
    "        self.nn_dis = Discriminator()\n",
    "        self.optim_enc = optim.Adam(self.nn_enc.parameters(), lr=1e-5)\n",
    "        self.optim_dec = optim.Adam(self.nn_dec.parameters(), lr=1e-5)\n",
    "        self.optim_gen = optim.Adam(self.nn_enc.parameters(), lr=1e-5)\n",
    "        self.optim_dis = optim.Adam(self.nn_dis.parameters(), lr=1e-5)\n",
    "        self.model_path = \"./aae_model\"\n",
    "        self.log_filename = None\n",
    "        \n",
    "    def forward(self, x):\n",
    "        z = self.nn_enc(x)\n",
    "        recon_x = self.nn_dec(z)\n",
    "        return recon_x\n",
    "    \n",
    "    def save(self, filename):\n",
    "        if not os.path.exists(self.model_path):\n",
    "            os.makedirs(self.model_path)\n",
    "            print(\"Created folder {}\".format(self.model_path))\n",
    "        fname = os.path.join(self.model_path, filename)\n",
    "        torch.save(self.state_dict(), fname)\n",
    "        print(\"Saved {}\".format(fname))\n",
    "        \n",
    "    def load(self, filename):\n",
    "        if filename is None:\n",
    "            return\n",
    "        try:\n",
    "            fname = os.path.join(self.model_path, filename)\n",
    "            self.load_state_dict(torch.load(fname))\n",
    "            print(\"Loaded {}\".format(fname))\n",
    "        except:\n",
    "            print(\"Error loading\")\n",
    "    \n",
    "    def clear_log(self):\n",
    "        if self.log_filename is None:\n",
    "            return\n",
    "        if not os.path.exists(self.model_path):\n",
    "            os.makedirs(self.model_path)\n",
    "            print(\"Created folder {}\".format(self.model_path))\n",
    "        fname = os.path.join(self.model_path, self.log_filename)\n",
    "        fhnd = open(fname, mode=\"w\", buffering=1)\n",
    "        fhnd.write(\"\")\n",
    "        \n",
    "    def log(self, txt):\n",
    "        if self.log_filename is None:\n",
    "            return\n",
    "        if not os.path.exists(self.model_path):\n",
    "            os.makedirs(self.model_path)\n",
    "            print(\"Created folder {}\".format(self.model_path))\n",
    "        fname = os.path.join(self.model_path, self.log_filename)\n",
    "        fhnd = open(fname, mode=\"a\", buffering=1)\n",
    "        fhnd.write(txt+\"\\n\")\n",
    "        \n",
    "def get_recent_model_file(model_path):\n",
    "    list_files = [os.path.basename(f) for f in glob.glob(os.path.join(model_path, \"*.dat\"))]\n",
    "    list_files = sorted(list_files, reverse=True)\n",
    "    if len(list_files) > 0:\n",
    "        return list_files[0]\n",
    "    else:\n",
    "        return None\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded ./aae_model/20170914105249.dat\n"
     ]
    }
   ],
   "source": [
    "nn_aae = AAE()\n",
    "\n",
    "nn_aae.load(get_recent_model_file(\"./aae_model\"))\n",
    "\n",
    "if args.cuda:\n",
    "    nn_aae.cuda()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Start time: 2017-09-14 11:42:23\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2106ddc0eae747d2bc275d5e810c1d94"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:1 2017-09-14 11:42:29 AAE recon_loss:0.000465 dis_loss:0.004158 gen_loss:0.000646\n",
      "Epoch:2 2017-09-14 11:42:34 AAE recon_loss:0.000464 dis_loss:0.004145 gen_loss:0.000664\n",
      "Epoch:3 2017-09-14 11:42:39 AAE recon_loss:0.000464 dis_loss:0.004147 gen_loss:0.000676\n",
      "Epoch:4 2017-09-14 11:42:45 AAE recon_loss:0.000465 dis_loss:0.004150 gen_loss:0.000673\n",
      "Epoch:5 2017-09-14 11:42:51 AAE recon_loss:0.000464 dis_loss:0.004150 gen_loss:0.000668\n",
      "Epoch:6 2017-09-14 11:42:56 AAE recon_loss:0.000464 dis_loss:0.004145 gen_loss:0.000657\n",
      "Epoch:7 2017-09-14 11:43:01 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000660\n",
      "Epoch:8 2017-09-14 11:43:06 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000655\n",
      "Epoch:9 2017-09-14 11:43:12 AAE recon_loss:0.000464 dis_loss:0.004141 gen_loss:0.000658\n",
      "Epoch:10 2017-09-14 11:43:17 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000658\n",
      "Saved ./aae_model/20170914114317.dat\n",
      "Epoch:11 2017-09-14 11:43:22 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000656\n",
      "Epoch:12 2017-09-14 11:43:28 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000650\n",
      "Epoch:13 2017-09-14 11:43:33 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000655\n",
      "Epoch:14 2017-09-14 11:43:38 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000656\n",
      "Epoch:15 2017-09-14 11:43:44 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000651\n",
      "Epoch:16 2017-09-14 11:43:49 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000654\n",
      "Epoch:17 2017-09-14 11:43:54 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000647\n",
      "Epoch:18 2017-09-14 11:44:00 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000656\n",
      "Epoch:19 2017-09-14 11:44:05 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000651\n",
      "Epoch:20 2017-09-14 11:44:10 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000652\n",
      "Saved ./aae_model/20170914114410.dat\n",
      "Epoch:21 2017-09-14 11:44:16 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000652\n",
      "Epoch:22 2017-09-14 11:44:21 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000651\n",
      "Epoch:23 2017-09-14 11:44:26 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000652\n",
      "Epoch:24 2017-09-14 11:44:31 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000652\n",
      "Epoch:25 2017-09-14 11:44:37 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000645\n",
      "Epoch:26 2017-09-14 11:44:42 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000652\n",
      "Epoch:27 2017-09-14 11:44:47 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000651\n",
      "Epoch:28 2017-09-14 11:44:52 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000652\n",
      "Epoch:29 2017-09-14 11:44:58 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000654\n",
      "Epoch:30 2017-09-14 11:45:03 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000644\n",
      "Saved ./aae_model/20170914114503.dat\n",
      "Epoch:31 2017-09-14 11:45:08 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000650\n",
      "Epoch:32 2017-09-14 11:45:13 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000653\n",
      "Epoch:33 2017-09-14 11:45:19 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000654\n",
      "Epoch:34 2017-09-14 11:45:24 AAE recon_loss:0.000464 dis_loss:0.004141 gen_loss:0.000652\n",
      "Epoch:35 2017-09-14 11:45:29 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000655\n",
      "Epoch:36 2017-09-14 11:45:35 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000655\n",
      "Epoch:37 2017-09-14 11:45:40 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000652\n",
      "Epoch:38 2017-09-14 11:45:45 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000651\n",
      "Epoch:39 2017-09-14 11:45:50 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000648\n",
      "Epoch:40 2017-09-14 11:45:56 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000647\n",
      "Saved ./aae_model/20170914114556.dat\n",
      "Epoch:41 2017-09-14 11:46:01 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000655\n",
      "Epoch:42 2017-09-14 11:46:06 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000653\n",
      "Epoch:43 2017-09-14 11:46:11 AAE recon_loss:0.000464 dis_loss:0.004140 gen_loss:0.000655\n",
      "Epoch:44 2017-09-14 11:46:17 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000651\n",
      "Epoch:45 2017-09-14 11:46:22 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000647\n",
      "Epoch:46 2017-09-14 11:46:27 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000653\n",
      "Epoch:47 2017-09-14 11:46:33 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000651\n",
      "Epoch:48 2017-09-14 11:46:38 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000655\n",
      "Epoch:49 2017-09-14 11:46:43 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000654\n",
      "Epoch:50 2017-09-14 11:46:48 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000652\n",
      "Saved ./aae_model/20170914114648.dat\n",
      "Epoch:51 2017-09-14 11:46:54 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000652\n",
      "Epoch:52 2017-09-14 11:46:59 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000650\n",
      "Epoch:53 2017-09-14 11:47:04 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000650\n",
      "Epoch:54 2017-09-14 11:47:09 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000657\n",
      "Epoch:55 2017-09-14 11:47:15 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000648\n",
      "Epoch:56 2017-09-14 11:47:20 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000648\n",
      "Epoch:57 2017-09-14 11:47:25 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000650\n",
      "Epoch:58 2017-09-14 11:47:31 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000650\n",
      "Epoch:59 2017-09-14 11:47:36 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000649\n",
      "Epoch:60 2017-09-14 11:47:41 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000653\n",
      "Saved ./aae_model/20170914114741.dat\n",
      "Epoch:61 2017-09-14 11:47:46 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000651\n",
      "Epoch:62 2017-09-14 11:47:52 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000651\n",
      "Epoch:63 2017-09-14 11:47:57 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000649\n",
      "Epoch:64 2017-09-14 11:48:02 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000647\n",
      "Epoch:65 2017-09-14 11:48:07 AAE recon_loss:0.000464 dis_loss:0.004133 gen_loss:0.000650\n",
      "Epoch:66 2017-09-14 11:48:13 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000650\n",
      "Epoch:67 2017-09-14 11:48:18 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000647\n",
      "Epoch:68 2017-09-14 11:48:23 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000650\n",
      "Epoch:69 2017-09-14 11:48:29 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000650\n",
      "Epoch:70 2017-09-14 11:48:34 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000649\n",
      "Saved ./aae_model/20170914114834.dat\n",
      "Epoch:71 2017-09-14 11:48:39 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000645\n",
      "Epoch:72 2017-09-14 11:48:44 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000649\n",
      "Epoch:73 2017-09-14 11:48:50 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000644\n",
      "Epoch:74 2017-09-14 11:48:55 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000648\n",
      "Epoch:75 2017-09-14 11:49:00 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000649\n",
      "Epoch:76 2017-09-14 11:49:05 AAE recon_loss:0.000464 dis_loss:0.004138 gen_loss:0.000648\n",
      "Epoch:77 2017-09-14 11:49:11 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000652\n",
      "Epoch:78 2017-09-14 11:49:16 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000651\n",
      "Epoch:79 2017-09-14 11:49:21 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000647\n",
      "Epoch:80 2017-09-14 11:49:27 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000650\n",
      "Saved ./aae_model/20170914114927.dat\n",
      "Epoch:81 2017-09-14 11:49:32 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000651\n",
      "Epoch:82 2017-09-14 11:49:37 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000648\n",
      "Epoch:83 2017-09-14 11:49:42 AAE recon_loss:0.000464 dis_loss:0.004133 gen_loss:0.000653\n",
      "Epoch:84 2017-09-14 11:49:48 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000654\n",
      "Epoch:85 2017-09-14 11:49:53 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000647\n",
      "Epoch:86 2017-09-14 11:49:58 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000650\n",
      "Epoch:87 2017-09-14 11:50:04 AAE recon_loss:0.000464 dis_loss:0.004137 gen_loss:0.000650\n",
      "Epoch:88 2017-09-14 11:50:09 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000649\n",
      "Epoch:89 2017-09-14 11:50:14 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000650\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:90 2017-09-14 11:50:19 AAE recon_loss:0.000464 dis_loss:0.004139 gen_loss:0.000644\n",
      "Saved ./aae_model/20170914115019.dat\n",
      "Epoch:91 2017-09-14 11:50:25 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000648\n",
      "Epoch:92 2017-09-14 11:50:30 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000646\n",
      "Epoch:93 2017-09-14 11:50:35 AAE recon_loss:0.000464 dis_loss:0.004134 gen_loss:0.000648\n",
      "Epoch:94 2017-09-14 11:50:41 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000645\n",
      "Epoch:95 2017-09-14 11:50:46 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000647\n",
      "Epoch:96 2017-09-14 11:50:51 AAE recon_loss:0.000464 dis_loss:0.004136 gen_loss:0.000647\n",
      "Epoch:97 2017-09-14 11:50:56 AAE recon_loss:0.000464 dis_loss:0.004135 gen_loss:0.000649\n",
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      "Epoch:261 2017-09-14 12:05:22 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000639\n",
      "Epoch:262 2017-09-14 12:05:27 AAE recon_loss:0.000464 dis_loss:0.004131 gen_loss:0.000640\n",
      "Epoch:263 2017-09-14 12:05:32 AAE recon_loss:0.000464 dis_loss:0.004131 gen_loss:0.000635\n",
      "Epoch:264 2017-09-14 12:05:38 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000638\n",
      "Epoch:265 2017-09-14 12:05:43 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000639\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:266 2017-09-14 12:05:48 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000634\n",
      "Epoch:267 2017-09-14 12:05:53 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000634\n",
      "Epoch:268 2017-09-14 12:05:59 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000636\n",
      "Epoch:269 2017-09-14 12:06:04 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000637\n",
      "Epoch:270 2017-09-14 12:06:09 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000638\n",
      "Saved ./aae_model/20170914120609.dat\n",
      "Epoch:271 2017-09-14 12:06:15 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000634\n",
      "Epoch:272 2017-09-14 12:06:20 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000632\n",
      "Epoch:273 2017-09-14 12:06:25 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000629\n",
      "Epoch:274 2017-09-14 12:06:30 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000635\n",
      "Epoch:275 2017-09-14 12:06:36 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000633\n",
      "Epoch:276 2017-09-14 12:06:41 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000637\n",
      "Epoch:277 2017-09-14 12:06:46 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000634\n",
      "Epoch:278 2017-09-14 12:06:52 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000640\n",
      "Epoch:279 2017-09-14 12:06:57 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000643\n",
      "Epoch:280 2017-09-14 12:07:02 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000632\n",
      "Saved ./aae_model/20170914120702.dat\n",
      "Epoch:281 2017-09-14 12:07:07 AAE recon_loss:0.000464 dis_loss:0.004127 gen_loss:0.000630\n",
      "Epoch:282 2017-09-14 12:07:13 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000638\n",
      "Epoch:283 2017-09-14 12:07:18 AAE recon_loss:0.000464 dis_loss:0.004132 gen_loss:0.000641\n",
      "Epoch:284 2017-09-14 12:07:23 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000638\n",
      "Epoch:285 2017-09-14 12:07:29 AAE recon_loss:0.000464 dis_loss:0.004131 gen_loss:0.000641\n",
      "Epoch:286 2017-09-14 12:07:34 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000637\n",
      "Epoch:287 2017-09-14 12:07:39 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000643\n",
      "Epoch:288 2017-09-14 12:07:44 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000640\n",
      "Epoch:289 2017-09-14 12:07:50 AAE recon_loss:0.000464 dis_loss:0.004132 gen_loss:0.000637\n",
      "Epoch:290 2017-09-14 12:07:55 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000636\n",
      "Saved ./aae_model/20170914120755.dat\n",
      "Epoch:291 2017-09-14 12:08:00 AAE recon_loss:0.000464 dis_loss:0.004131 gen_loss:0.000638\n",
      "Epoch:292 2017-09-14 12:08:05 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000634\n",
      "Epoch:293 2017-09-14 12:08:11 AAE recon_loss:0.000464 dis_loss:0.004127 gen_loss:0.000639\n",
      "Epoch:294 2017-09-14 12:08:16 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000636\n",
      "Epoch:295 2017-09-14 12:08:21 AAE recon_loss:0.000464 dis_loss:0.004128 gen_loss:0.000634\n",
      "Epoch:296 2017-09-14 12:08:27 AAE recon_loss:0.000464 dis_loss:0.004129 gen_loss:0.000640\n",
      "Epoch:297 2017-09-14 12:08:32 AAE recon_loss:0.000464 dis_loss:0.004132 gen_loss:0.000642\n",
      "Epoch:298 2017-09-14 12:08:37 AAE recon_loss:0.000464 dis_loss:0.004133 gen_loss:0.000637\n",
      "Epoch:299 2017-09-14 12:08:42 AAE recon_loss:0.000464 dis_loss:0.004130 gen_loss:0.000636\n",
      "Epoch:300 2017-09-14 12:08:48 AAE recon_loss:0.000464 dis_loss:0.004131 gen_loss:0.000639\n",
      "Saved ./aae_model/20170914120848.dat\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Get the training start time\n",
    "cur_tm = datetime.datetime.now()\n",
    "str_cur_tm = cur_tm.strftime(\"%Y%m%d%H%M%S\")\n",
    "print(\"Start time: {}\".format(cur_tm.strftime(\"%Y-%m-%d %H:%M:%S\")))\n",
    "# Set AAE log filename to simply the training start time\n",
    "nn_aae.log_filename = str_cur_tm + \".log\"\n",
    "# A constant for ensuring log never goes to -infinity\n",
    "TINY = 1e-15\n",
    "# Set AAE to training mode, train function internally sets children network to training mode\n",
    "# Training mode has any effect only on modules such as Dropout or BatchNorm which we are using for\n",
    "# encoder, decoder, and discriminators \n",
    "nn_aae.train()\n",
    "\n",
    "# Train networks\n",
    "for epoch in tqdm.tqdm_notebook(range(1, args.epochs+1), \"Epoch\"):\n",
    "    # Training history\n",
    "    nn_aae.train_tot_recon_loss = 0\n",
    "    nn_aae.train_tot_gen_loss = 0\n",
    "    nn_aae.train_tot_dis_loss = 0\n",
    "    \n",
    "    for batch_idx, (x, y) in enumerate(train_loader):\n",
    "        x = x.view(-1, 784)\n",
    "        x = Variable(x)\n",
    "        if args.cuda:\n",
    "            x = x.cuda()\n",
    "        \n",
    "        # AAE training \n",
    "        # AAE Reconstruction phase\n",
    "        # Clear the gradients of all optimised variables (of type Variable)\n",
    "        # Train Decoder and Encoder\n",
    "        nn_aae.optim_dec.zero_grad()\n",
    "        nn_aae.optim_enc.zero_grad()\n",
    "        recon_x = nn_aae(x)\n",
    "        nn_aae.train_recon_loss = F.binary_cross_entropy(recon_x, x, size_average=True)\n",
    "        nn_aae.train_tot_recon_loss += nn_aae.train_recon_loss.data[0]\n",
    "        # compute gradient of recon_loss Variable\n",
    "        nn_aae.train_recon_loss.backward()\n",
    "        # perform a single optimisation step (parameter update) to decoder\n",
    "        nn_aae.optim_dec.step()\n",
    "        # perform a single optimisation step (parameter update) to encoder\n",
    "        nn_aae.optim_enc.step()\n",
    "        \n",
    "        # AAE Regularisation phase\n",
    "        # Set Generator/Encoder network to evaluation mode \n",
    "        # To prevent any effect on modules such as Dropout or BatchNorm\n",
    "        nn_aae.nn_enc.eval()\n",
    "        z_fake = nn_aae.nn_enc(x)\n",
    "        # Train Discriminator first\n",
    "        # Minimise -log(D(G(z))) depends on Discriminator\n",
    "        # Discriminator must at least know some idea what is constituted as fake and real\n",
    "        # Unless Discriminator is initialised with such knowledge, it won't be able to\n",
    "        # If Discriminator is unable to, Generator will not have incentive to learn\n",
    "        # In order to incentivise Generator to update its weights, Discriminator is set to learn more on fake and real\n",
    "        # This then will provide ample gradients (so that D(G(z)) < 0) for Generator\n",
    "        nn_aae.nn_dis.train()\n",
    "        for _ in range(0, 3):\n",
    "            # Clear the gradients of all optimised variables (of type Variable)\n",
    "            nn_aae.optim_dis.zero_grad()\n",
    "            # Sample real z\n",
    "            # returns a Tensor filled with random numbers from a normal distribution with\n",
    "            # zero mean and standard dev. of 5\n",
    "            z_real = Variable(torch.randn(len(x), z_dim) * 5.0)\n",
    "            if args.cuda:\n",
    "                z_real = z_real.cuda()\n",
    "            \n",
    "            z = torch.cat((z_real, z_fake), dim=0)\n",
    "            prob_z = nn_aae.nn_dis(z)\n",
    "            prob_z_real = prob_z[0:len(z_real)]\n",
    "            prob_z_fake = prob_z[len(z_real):]\n",
    "            nn_aae.train_dis_loss = -torch.mean(torch.log(prob_z_real+TINY) + \n",
    "                                            torch.log(1 - prob_z_fake+TINY))\n",
    "            nn_aae.train_tot_dis_loss += nn_aae.train_dis_loss.data[0]\n",
    "            nn_aae.train_dis_loss.backward(retain_graph=True)\n",
    "            nn_aae.optim_dis.step()\n",
    "        \n",
    "        # Train generator\n",
    "        nn_aae.optim_gen.zero_grad()\n",
    "        nn_aae.nn_enc.train()\n",
    "        z_fake = nn_aae.nn_enc(x)\n",
    "        nn_aae.nn_dis.eval()\n",
    "        prob_z_fake = nn_aae.nn_dis(z_fake)\n",
    "        nn_aae.train_gen_loss = -torch.mean(torch.log(prob_z_fake+TINY))\n",
    "        nn_aae.train_tot_gen_loss += nn_aae.train_gen_loss.data[0]\n",
    "        nn_aae.train_gen_loss.backward()\n",
    "        nn_aae.optim_gen.step()\n",
    "    \n",
    "    cur_tm = datetime.datetime.now()\n",
    "    str_cur_tm = cur_tm.strftime(\"%Y%m%d%H%M%S\")\n",
    "    filename = str_cur_tm + \".dat\"\n",
    "    \n",
    "    nn_aae.train_avg_recon_loss = nn_aae.train_tot_recon_loss / len(train_loader.dataset)\n",
    "    nn_aae.train_avg_dis_loss = nn_aae.train_tot_dis_loss / len(train_loader.dataset)\n",
    "    nn_aae.train_avg_gen_loss = nn_aae.train_tot_gen_loss / len(train_loader.dataset)\n",
    "    print('Epoch:{} {} AAE recon_loss:{:.6f} dis_loss:{:.6f} gen_loss:{:.6f}'.format(\n",
    "          epoch, \n",
    "          cur_tm.strftime(\"%Y-%m-%d %H:%M:%S\"),\n",
    "          nn_aae.train_avg_recon_loss, \n",
    "          nn_aae.train_avg_dis_loss,\n",
    "          nn_aae.train_avg_gen_loss\n",
    "         ))\n",
    "    nn_aae.log(\"{}, {}, {}, {}, {}\".format(epoch, \n",
    "                                              filename,\n",
    "                                              nn_aae.train_avg_recon_loss,\n",
    "                                              nn_aae.train_avg_dis_loss, \n",
    "                                              nn_aae.train_avg_gen_loss))\n",
    "    if (epoch % args.save_epoch_interval == 0) or epoch >= args.epochs:\n",
    "        nn_aae.save(filename)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot Training History"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Epoch                 file  recon loss  dis loss  gen loss\n",
      "0      1   20170914102625.dat    0.000551  0.002577  0.003398\n",
      "1      2   20170914102630.dat    0.000503  0.003165  0.002053\n",
      "2      3   20170914102636.dat    0.000490  0.003386  0.001759\n",
      "3      4   20170914102641.dat    0.000486  0.003602  0.001425\n",
      "4      5   20170914102647.dat    0.000483  0.003718  0.001271\n",
      "(300, 5)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3cb5c5d7b8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wCgMiIiIRLmzDgDYTiIiIBCZsw4B6BkRERAITtmFAPQMiIiKBCdswoJ4BERGRwIRlGDAY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\nMiAiIlJwSgZEREQK7v8BH+o8M0us3ooAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d15709978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_train_hist = pd.read_csv(\"./aae_model/20170914102619.log\", header=None)\n",
    "df_train_hist.columns = [\"Epoch\", \"file\", \"recon loss\", \"dis loss\", \"gen loss\"]\n",
    "print(df_train_hist.head())\n",
    "print(df_train_hist.shape)\n",
    "\n",
    "df_train_hist[\"recon loss\"] = np.log(df_train_hist[\"recon loss\"])\n",
    "df_train_hist[\"dis loss\"] = np.log(df_train_hist[\"dis loss\"])\n",
    "df_train_hist[\"gen loss\"] = np.log(df_train_hist[\"gen loss\"])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,6))\n",
    "df_train_hist.plot(x=\"Epoch\",y=\"recon loss\",ax=ax)\n",
    "df_train_hist.plot(x=\"Epoch\",y=\"dis loss\", ax=ax)\n",
    "df_train_hist.plot(x=\"Epoch\",y=\"gen loss\", ax=ax)\n",
    "ax.grid(linewidth=0.5)\n",
    "ax.set_ylabel(\"Loss in log scale\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_latent(nn_enc, loader):\n",
    "    '''\n",
    "    Create the latent representation for the samples in loader\n",
    "    Return:\n",
    "        z_values: numpy array with the latent representations\n",
    "        labels: the labels corresponding to the latent representations\n",
    "    '''\n",
    "    nn_enc.eval()\n",
    "    labels = []\n",
    "    for batch_idx, (x, y) in enumerate(loader):\n",
    "        x = x.view(-1, 784)\n",
    "        x, y = Variable(x), Variable(y)\n",
    "        if args.cuda:\n",
    "            x, y = x.cuda(), y.cuda()\n",
    "        \n",
    "        labels.extend(y.data.tolist())\n",
    "        # reconstruction phase\n",
    "        z = nn_enc(x)\n",
    "        if batch_idx > 0:\n",
    "            z_values = np.concatenate((z_values, np.array(z.data.tolist())))\n",
    "        else:\n",
    "            z_values = np.array(z.data.tolist())\n",
    "    labels = np.array(labels)\n",
    "    return z_values, labels\n",
    "\n",
    "\n",
    "def create_sample(nn_dec, z_values):\n",
    "    \"\"\"Evaluate Decoder.\n",
    "    \n",
    "    Return FloatTensor of shape [sample count, 28, 28].\n",
    "    \"\"\"\n",
    "    z = torch.from_numpy(z_values).float()\n",
    "    z = Variable(z)\n",
    "    if args.cuda:\n",
    "        z = z.cuda()\n",
    "    nn_dec.eval()\n",
    "    recon_x = nn_dec(z)\n",
    "    recon_x = recon_x.view(len(recon_x.data), 28, -1)\n",
    "    if args.cuda:\n",
    "        recon_x = recon_x.cpu()\n",
    "    return recon_x.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reconstruction of MNIST Training Samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0951941906095 5.22914749582\n",
      "-0.0689380901609 5.12077678238\n"
     ]
    },
    {
     "data": {
      "image/png": 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Y0wH8EMcYY4wxxhhjjDGmA0yLnErDTDmMjMNMd9ttt2w/llVwG8ilGXwMDbvn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\nOMYYY4wxxhhjjDEd4P8DxTtQ5vRGT2AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d24687d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Latent space approaches Gaussian distribution with 0 mean and 5 standard deviation\n",
    "\n",
    "z_values, _ = create_latent(nn_aae.nn_enc, train_loader)\n",
    "print(z_values[:,0].mean(), z_values[:,0].std())\n",
    "print(z_values[:,1].mean(), z_values[:,1].std())\n",
    "recon_x = create_sample(nn_aae.nn_dec, z_values)\n",
    "plot_mnist_sample(recon_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Latent Code of MNIST Training Samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0951941906095 5.22914749582\n",
      "-0.0689380901609 5.12077678238\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f3cb5c6cd68>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TD8CiShONc/JBpeJ470x9QF4gQOr0feavllBs1GFu1fHs63aW1xaLdMpRhwtLuvv3sb3n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XK6r+l05xB33+OQ4WR1nHYGJz7JOjfLSRzf221zujsxtzuJcR/HEOc4sRliAzaDwIKAjKx5Qmio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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cb5840940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_values, labels = create_latent(nn_aae.nn_enc, train_loader)\n",
    "print(z_values[:,0].mean(), z_values[:,0].std())\n",
    "print(z_values[:,1].mean(), z_values[:,1].std())\n",
    "plt.scatter(z_values[:,0], z_values[:,1], s=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reconstruction of MNIST Testing Samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0662365222786 5.16704415197\n",
      "-0.455494006456 5.05237969422\n"
     ]
    },
    {
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6gLatS6Xmu0TJxux/xx57bNM+/fTTW/uxXdk+moeD75/qR1kLe8QRRzRt1aiz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\njDEdwC9xjDHGGGOMMcYYYzrA/wdAF+xIbnf4yAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cb5bd2978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_values, _ = create_latent(nn_aae.nn_enc, test_loader)\n",
    "print(z_values[:,0].mean(), z_values[:,0].std())\n",
    "print(z_values[:,1].mean(), z_values[:,1].std())\n",
    "recon_x = create_sample(nn_aae.nn_dec, z_values)\n",
    "plot_mnist_sample(recon_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Latent Code of MNIST Testing Samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0662365222786 5.16704415197\n",
      "-0.455494006456 5.05237969422\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f3cb582f978>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yXv9wnEFPiKlwjMnpCC3VpfRMThONy6wVfZEkaJQgcfD0EJ/cUIs3GOHckI/2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\nvFFwvUI6DyeTycn5v3brYTE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5mXKLUcSDJ3vdQqrXH47zwYiPHmdAhDwUVJcUU1shx6EP\npAzf+toyrMV67BYjo94w9zbYOdLpxJuaZBS+u2z4JU72eti2qpI/fHQ1F0Z8eIJRYbgVKNycYMpY\nrqst5+KYX1A9dUUSP3xyI//9zW5O9npEwZIc7oEX3pHDQ0c6nWxbVUWPM8B9K+0MeUIMe8PCgI54\nlVi6XrBzNq6wC4qg0qKx3KJn785m/uSVDjEJmPQSH4xMiTBVjS2d+fStf73AX3xmA//xp2eJJ6Gh\nysKmejtNjhKO97jYtKKcp3Y0iwT8qT43zukZZlLGvsysAyQ6xuSJSknEnh308X9uXsEPXrskrkeR\nJPG9X14U4wV5UlZWbIr3r4RElGLAXLTK+bCQ1XsuGrOCfB6+urewsl2hcgwfJTSDfxNgoSGoTCOv\nflVj/XIb65eXZ73hgykdeIUOp2juKHQy9Q2vMHR+fVEOz5zsdQt5YkXMSmHp9LmCnBv0iqSvOxjl\n394fY3xaZq68c9mVxmrxh+NUl5n4xLoazg15sFuMTE7P8NDqKooNev7twhi+UIxwPE4skeT8kE+c\nixInl/n9s+/bzHoSiaQoqNIXSWxurGJzYyUPrl7CH/3TOTzBqAjhKFC8e+W1WCdPiIpxA1mU7b1B\nL6mIi9C1ubveDiRF2GJz47hISBt0RVSXyWGTeCKJyVAkkrnuwCwtNByJ87s/eZendjSnJtEkJ3vd\n/NmvLooxGHRywvbMgBe7xYAnGGWpzUSjw8pUKMb5YR99riD/cHIAi1GHfyZOKJLg2dcu8cGIfI3q\n7GYRv7eZ9dzTUME9DRWcGfDgC8X47XvqaU+FtCQJwtEEL58bZe/OZl48NUgomqDObpYnLl+Y2nJT\nSt9GhqPUiKNULoxrXlKC3TLL0tmVWg0oY1KLkakTsWpWjDpUuRDxsmzsn3x0UPUYlMlASWAX+sx9\n1NAM/k2KfMvGbKXhoFQhpod0MpPLar4xSAQjMRHTB7lxxt31clcf5YZvXlLCse5J4bUBvNU1IVQW\nlQrUWSTZ99t38YX/cYJwLCGMPcBMNM6S0mIm/DMkErIBNegkPndvHZUlRvFQnerzEo7FBY3SF4ql\nGXuAeCJJabFOGPb1taVMheOCxVNbbmJJaTHhaIJ9h7soM+l58eQAE9MRwaxRI5HxOhNPikpZkBk/\nfa6guFZmg1zkZbcYeKdnknf7PLIscSQuU0vfHaQhFdf/4v31dE8EmArHCEcTLC0rTvPKW5daOdrl\npM8VFAVQ62tltVD1OIv1RUTjccHl//NffSgKy/ZsX0mZWS8mCgV63ayMMMCrF0ZRdukLxfjOLzrw\npZrC3LfSTsfIFHV2M2cG5InNZtbT5CjBE4zQ4wxQZpJXVcokq8haLC0rJhiJixg/yKusrolpmpeU\npphlcrP2fYdnwyuK0c3FilGHKhcqwaxGLu59tu+olTjVhVmKJMmNGM4BTTztqnE92pdlw5W0bjtx\neTJVOl/JN3etFeJRSrPxE5cnWVJmEtzwg+2DvHRqSDTbHveF+WBkipO9bjYst1FmNvDUjmaGvWFa\nquV2hslkEv9MjFHfjBCz2tZcxZGLE6JFX8eonwl/mE0r7FwYlQ1mmUnPTCxBIBIXicRoPIk7EGHQ\nE+bQuWH+4KFVdE3IjcElCbyhGHaLgUfvWII/HKOm3MRMLE4kFS8a98+IvwH0uiJR/OWfiVFuNvDg\n6iWilZ9yfICmKjMGnU5ILmSiSJKDDp9YV0OSJKO+MMlkklAq1KOT5JxAhVX2shWWy7h/htMDHgbd\nQf75zDDekJwTWVJanCapEIklUA2dWEKuHq6xmZicloXcjHodU+GYEKoD+ZhNDiv/60v3sMxm5vm3\n++hzBTEZighFEpzq9/CJdUuJJpKMp4rKHCUGwrGECNnEZhcsgBzYG3CHMOnlFc+FkSnGpsLMxOTi\ntmBEFlhz+mfwz8SYiSVErUFJsY4Kq5HpmTjTM3FxjNZlpUTiCVqqSzjZ6xGtKTcsl+m4JkMRmxsr\ngSTff/VSmpCZ0iz+yTZZ0EwRMMvXG7eQ5zRfj9vM72S25cwm5DZfU3al5++Jy5O0LC27Kvuh9bS9\nTshneAvFlUwahdycmVAUHf/Tb6xJUx187s0eoZo56A7y9ycGGHQHhQf/nz9+B72TAWEYGyotNC0p\n5Z/PDHOy18W/XRjHZNBxstfNb91VS6lJz8fXLhP9YyusRnyhqNxYZGMt0zMxzgx4mQpHKSnWCyNR\nXVpMy9JSHKXFwhgJmeBoggl/mL/5nbu5MDJF18Q05WYDH1tbzb+8N0K5xcDlyaAw8K1LS4jEZ40Y\ngD8VCzcbZXXMqXCMJLIapRInV2Ay6EVMXMpyLZPIWvRf2tLAT08NMj0TQxX9IYkcGvnzT6/nzUtO\nwtEEa2vKGPWFqbOb+eYn12IzG5jwh+lzBRl0B5mJJTBIUGLSE1SFicyGIvwz8dSkGCcYTVAkwe9t\nbRNw5YgAACAASURBVOBUn4dIPCmMfrnZwD98+T6aHCW88E4fh86NUiTJk6dihM1GPUWSJNRCx/0R\nZmIJivVFxFUnYdBJJJLwW3fVMuAOMj0Txx+OpTqDydcrLkJXRXhC6fkOkCeg6Rl5xbHUVkwklmDN\n0lJ8oRgT/giReIKvPNBIZYkptXq00zsZ4Av31bNjzRJxzyrGXumFq3ZozEYd9zdV0bK0NKcSZyHP\naTZHKfPZzNcHFxb2XL7wjtwIXq1We6XQDP51gvIDF9K5Ppdhv5JJY74bL9sxlf2HovG0cSie/9am\nSv7jI6uZ8Id5akczjQ4rTz/aQoXVKLwog07i/PAU21ZVYjHqOJvix1eXGRn1yVTEZ3/7Lravdojj\n2K1GOsemhMf2+ocTojG3f2bWQw1E4ny2bTlLy0yMTYWFgW6pLqFYX4SErCBZWqyT5YBjCcZ9YYLR\nuDDYVmMR0XiSUDSOPxzHZtanGX2YpSKCzLLpHJ/GbjEQThnZGptMD9VJsxPO+tpSpmdiRFVu9/hU\nmF9fnGDMP0M2WIw6eicDXJqYpslh5TufWseJyy4GPCFsZgNdE37OpcJQMzFZWiIObFhuwxWICK9d\neZ2JJcSElgRO9XmIJeRise3NVXiCsuSy3WLk/JCXexoqeO3DMYKRhJi0TIYiLk8GqLDocU1HSCLn\nJO5YVsrY1Ax1djMPt1Qx4Z8hEIlTUqxjxBdi9ZJSBlI9Ah67cymnRcLbhr6oCHdKtTPzWtfZzaxZ\nWsqHY35cgSiR1MSzpamSYW8I/0wci1HH79xXz4Q/TGVJMfsOd4lG6GtrbGmedD4892Y333/1EiZD\nkWisruBKHCSY25hd/exme54zn8t8zpz8TOnY3FiRc2VSKG4YeeRbHerWevsOd4sG1tmQK3u/2Eme\n+Ro4KO8p8dJdG2sJRRJ0jPr4+XvDKaG18rRGDjLtsiVt355ghGhcrtL1BiOcGfDhDUWF1kimiuSe\n7Y28mmqAvmt9bYpxMy1i0NZiuS+somWj4PJkgGhcTgCeH/aLZCnAZIoppKDcYiQQma2IfWJDLXar\ngX85MzynGQjIXqxS9GW3GPjk+mWAxAsn+okn5dBNIglmo4FAJN2YxRKy8VK+k4mxqRl2bazFqC/i\nmcdbeb1jXFBAlQI0JVdg1ElE4kkMRfDh6JSYfLJhXU0p/hk5F6EcWykOe7jFIRqvN1RaUho/RYRj\nMoUynMopvD8yq92TYFaaedATor7SyifXL+Of3xsSoZjRFOMnGInzuXtXcG7Il6qElYQMx1JbMaFI\nDGXoS0qMLLOZaKiyCuVNBSd73aJ3sRKPVwT+9u5sTjkhHt7qcvKXn98EFNKhSsp4ncWV1t4oz6Rr\nOpIm96CMZz42Tr7vKFTm6wnN4C8A+fm1uW82BbkM+0JuxkxGAsx9ENTJLaXgJTsTZ1a7+8KIj+M9\nLvpdSkXm/GqDCoVze7ODc0Oyx/fLD0bxh2UNkt1bVooE29amSl7tkGV7mxxWPnVXLa+8P4IvFBPJ\nzcBMgiOdE3xxcz2d41N0jEzhn4kTjSdZUlqMOzBDLCEnSxUDWWkxEE0kqS410uUMUmk1sNxuob7C\nzIhvht1bGwQtc+rCGLXlJiFBINMDPdTZzZSZdXiC0TliX4ohD0ViVFmNTAYiov1g5ncUFOslZmJJ\nbGY9n7unTgjIPdJaLWixD652MOqb5eAnUjuJJiA6E0/bn04iLZ7f6Cjh3JCP9bVlon4B5CT0XXU2\n/lsqgdnnCmIz69FLEuFYQoRrHr2jmm6nrImjnIui919bbuJY9yTHVE2cpNQ5VlgN/PCzG1M6RLNJ\nXwWXxlM0zdQEMxmIMDEdSUlpyPH86Zk4xTq5KGtrUyV/8qk7OXRW7vq1PhW/f/7tXkG7Pdbtytqh\nKtuzuHtLw6JIE2eTccjWKznX85yta9yNwtjRDP4CkE84adfGmnlvNmVJeTVZ/ExGAsxt1SbztCc5\n0ukkGDnP5saqrPtSj9kVkHuyOkqL+fSmWnZtrBWeunJcuYn1CEr7uCfb6nBNz/DrixNC90SR9z3d\n72XXxgjrl9uoq7Bw9JJTGCCb2cCf/+pDoTDZVm/neLeLBLKH+cr7I7gDUb64uV6oRErIyUTFQK1y\nlFBtMwkDvX55OV3OIOeH/ezZvpLKkmIOnB7m0NkR4S0CGP2RVAVsCSDxr+dHhOdv0heJvxXqpWJs\nzw9PUZxacedjiBdJsvEsNxvwhqL80cFzuKYjwrNXVn8/frOHHmdAGMdYlp0qk1o847NfvD9KLCHT\nSdUY9ob54evp7fayVdr2u2cZU0lklo1JrxMxfmXVoawemqtLiCeS/MVnNrCp3p5qEzkLh9WIM6WF\n1OSw0ryklAOnh8REqKy21tbYAMRkMZS61hajTkgqV1iNaTTXbauqxGpSqe/ocU6z54V2MVkq9/18\njlOhBVHZvPJMFc58x8vc/kbi4msGfwG4GuEkBVdblKEunlLffOq+nhVWI3fXl6eokrIi5Pkhr+DQ\nZxvDVx9sEk0ufmPtUiGpALPyCC++OyAoje/0uNi4wi4EwECOfZebDQx7Q3KjjNRD2eSw0ucKCl74\nmQGZh6/IHL/VPavYaDIU4Q5EKbfoMRl1/Oz/2sqhs8P8tF0upnKUGpnwR9jWXMXn7l1BMHIekPjD\nR1fT7wqketKO8adP3EmTw8qoN5hWpOUMRHD2uglFYsI7VsTGwrGEKvwBJUY9X9uxiuff6ScaTwip\nZItRIhjJbvYTSXlSqiyRDb7CvGlyWOf8XurrmQ0NVRZMel2aFw+zE58S268tNxFPJNOknGttJoZ9\nYTFpKChOFZip4QvFWLOylHH/DMPeMK1LS4Aw9zdWMuGfodvpZyokN1P5ye/ey66NNZzud9M9Mc3Y\n1Aw6fZGY4KbCMb7yUBP97iAne93Ulptoq7dztGsyVd0sG/0yk55+d5A9L7Sz/4ttBCMxXIEI3/1F\nh1gtbm2q5NtPrE3p73g41u1ic+M4Jy676HEGqK+wEIzE09Qs8yGfPLEa2bzyTOOer7tcNsG2GwVa\n0nYBUCdklCRQJkVsPmQmjxRq1pGL47zVNUl7v4eWpaU596UwEu5vqiQUjYub7pVzI2mJ35alZYRS\nD8OqJSW8c3mWCWC3Ghl0B/nS1pWAnJiqKTfjDUYEtW1tjQ2TIZUAjchNRLwhuXGJNyTTDE/3e9LY\nLf6ZGM5pmfFh0ks4pyPUlpuwGnWYDDruWlFOtzOA1VjEZCBKja0Yk0HHMpsJVyBCabGOYESOMXuD\nMU73e6gtNzMVjgmv0qQvoqqkmKd2NPPqhXH++cwww94QNouBYESWLZ4Kx3h/WK7IHfGFs8bD3YEZ\nlpQWUyRJIjZfrJOYiSfl5GlSTpKeH/Yy4Y8ILxWgssTEdA66pgJF2wdkvZ2acjN31tg4dG4Eu9XI\nd17pEAnv+1ba2bqqin5XIM04uwJRgtEYkWzufwqKHlBVSbGoIAZZrG4qHGNtrU0wnkidl7IuqLOb\n+dTGWh5qcfAHDzdz2TnNgDskfsNuZ4BQRK51KDcb+JvfkWPpz/zsfY52TVJUJK9mpmdihGMJKqwG\nRrxhLjsDNC+xYjLo2N5cxYA7xKXxaSqsBkwGHc7pCE0OK9ZiPb2TQY5cnMAXinHo3AinB+T+vttW\nVdLWUEHn2BT7Dncz4A7xcIuDpx9t4d6VFQy6g9y7spIfvdFTMNmh0VHCpZRTs1C2TiayES2U92rL\nzXzlwaaC7MFi0bq1pO0iYj7xsoUIJ2XT61YXvQBpOjT5lqD5qvsqrEYGPXLvWV2RlCbX/HrHuCgZ\nB9JWKupCLEUKWVaCbBZJOjmukiQcTXBxbIo1S8uEQBiQVrQ07A0znBrvVEqkrEgW0xOxdItBEsJp\nAKurS9iwvBwkiWFPkJfPjYhzdgWjuIJR/uifzskyzCm097k4M+Bj04py2urthKMJQpE4I74wS0qM\nTEynJ3ejidmuWErYZub/Z+9Nw+SqznvfX41dQ3d1DT3Po1p0a0ISkgAJhIQwYAzEh8EmeQy5Mdi5\nNwQbx/c+djix4+Q5GWwfh/gmsXXP8QnYcTA4tsHEA/MgCQmphSSklrrV81xd8zxX3Q+79upd1dWt\nFiDwsXm/CLp27dq7aq93rfW+/0GBgJHDH00LX1n53uYDhXoxdpMOb3QpJFEOnUbNkTGvcLySmclt\nDhPXrKnGoJWMycNFtXtYLJEpQ9lDqKuUROTGPVEhw9DmMPHVj/Xxjy+dZ3A+uOT9ORbLV4POEBub\nrHz3lWHG3BEhuiaTqeQdSke1WfQipISpEw3h7hozl7dIuveyDaLcAzgy5uVTO1oZmAvgjaSI5O/R\nG0nSYJUczWQ29OYWK/OBOHWVBnrrLTz64nl2dlVx15ZG3hj10mwzAYtql95IEke5flUraXksKWUc\nSr3+TtVql5NFX+465M95v2UYPkz4q4jVbgXfSUglmoxIpsZVOvvI74Xl2X0P7unm5LSfcU8UUx4P\nr3zfIgIhwcnpAA/sal9Sdjg86uHWTQ3YTHoe/KEkfvXArnaMei0npz28Oe5jbZ2FXC4nkvbdV7RI\njdhklngqw4kpHxPeqJgEyrRqwX4FiKZyRP2Lui9Hxny02s0cGfOK2rcsc1BRpsFcpmXEFeHqzoyY\niH6Z5wiY9BpQSSibRqsBQAh+LReZHGjVSwlHcsjJvqHSwM7uKp48Nl3w+kqrfa1axeaWSqZ8MarK\n9UzloY06jUoqBeZ7G8rorTMz5YsTSmTQqaXJqUwDe9bW8tK5BRKZ3JKEDJK3baPVQK2ljEMj7oLX\n5ElCnvzW1JZzaiYozFCKrzkQSzPsCgmI7PFJf4GapFJM7+3ZEFUVhiUN780tlZj0WlGmk5vzIE22\n8oQr2zGCitlAnNlAnHUNlXkWsluUAh8/PIEtr1NfzCK/UFxoLK1mjC+nya+UGSlmrl/oOt7vpu6H\nCX8VcefW5Z1q3m2sBM260MMgP3SyQiUUIhgktx6pDCPbFMJSVM/AnLQ6dwbjfHa3JPLljSSFM9CG\npllOTfuF0uFT/dMFJYsXzjqFUFelUcuNfXVsbrWJ6xh1RwjEgmLAuyMpyss0GHRqyEkJWSbnyM3f\nHx9fbPpJOuxVPH1ynpvW1fF8XlJ50BliR4eDgbkgU74YndVmHt7Xw8NPngCg1lJGk83E6EKhVPKK\nv4dJizeaprPaRKVRD0iM1Bm/xO59Q+EQJUeyuKuaD7nO7olIBjEvD7r41I4Wruqs4rkB5xKUDUgT\nz7gnSjSVP6dKStWJDAwthMUuJBBLi4ReW1EmGq6yjIFOoykQXqvNr9xvv7wJR7nEG5H9b0Eiqo24\nJfJXOpsno8UyBGPSxNzmMHFFm53HDo0RS2X52VvTNFlNaFUx1GoVFoNWlJfkXdbAXIgDw25SmZzo\n1xh0auJ5rZ0rOxy8Oe7lmu5qHj88wfZ2mzjHoDMkJkJfVDKt/0hfHZBbApxYzapcuThS9rqUr680\nxovF0op36UpdndVch3In/n42dT+s4a8ijHoN16ypviBx493U41ZD4ljuuOK+gFxL3NGxSI7qn/Bx\nZjbARF7rRSaneCNJnj4xw4w/jj+WEiQr+eG+rqcai0HHfxyfYXu7HbVKkixQEpq6a8sFTjuRznJs\nwsvHNjaI1UxVuZ4yrZov7FvD8Ukf8ZREIEqmc9y8oZ63pgLYTDqcoYRgmOaQVprZfC392jU1WIxa\n3OEkw64IlUYtyXSW5wacTHpj7Oxy8L/+cBvPDzh59tQcdrOOv7ilj2dPzTGbl+yViVSlgLPZnJTU\n1GoVoXiaXA7GPFHmAglu6qtj1B3GG5WakkqCkUGnLhBYKw67WcefXNfFP7wo+d4uBBP8uH8adyRJ\nMJ4S75WlGrI5ULYc5FOb9CoiyQyVJVi4d13RQv/EYiNWo4JNzZWsratg0hsjmcnSUWXmE9ta+C9b\nmhh1ReioLieeyqLVSPIQPfUVYkJvthm5dk0Vg84wdRYDvfUVnMnLYTxxdJr+CR8npwM48+SscCLD\noDMsZCju2tqMTqPmqf5pGq0Gzs6H8Mckc5rr19ZQXVHG125bx2NvjDPmjoqm65nZEBuapN3QR9fX\nsbO7mp7aCioMWv7hE5dz26bGAubtxcgYXEj64EJj/PE3xvn+4UnRR1C+LhOoai1ltDrMBQTMi2Xq\nvtP4kGn7HsdqfiiZ6ZfL5RiYC15U4l+Jbat8aEo9sMXXJrNiQcX913Rwbi7IjD/OpDeGUa9m0htj\nR4eDKzsdPP7GOD/KO059fHMTN62v55Gfvi2S/SO39PLYoXHmAnH2rq3hsgYL/RM++hos7LusFoNO\nTaPVSCiepslahlGvZdwTFQNnyBnijVEv/liKRDrDkDOMQasik5WS2bm5INva7QznIXY2o5ZkJkuZ\nVkKXWAxa7t7aRIVRxxNHp2iyGWivkurJZ+dDYuLJ5eDGdXVsabUz5Axxdi7Ea+ddomxQZykrKCPJ\nsgHK8MdSdNeUo9eo+dz13Qw5Q7Q5TJyeCRCIp6mp0LOu0UJ5maSJYzFouf6yGgady+8gYqksQ84Q\nrpC0u6o0asXuSDlRLDdl6DUqGqxGPJEUqUyuINkDXH9ZDZVGHTkgEE2SyubIAYPOMGfmQhj1aqFt\no1WreGXQxQ/fnGTUFeGnJ2a4Y0szn97VwckpiUjlDCXoqimnxWHO9xXS7F1bSziR5k/3dNPqMLGx\n2UpffYVkloLk9dtsN7Hvshp299Rw66YG/i3vgVuu14qSVyKdZdAZpjM/2fzy9LyY6P2xFDu7JFx+\no9XIvVe1s2dtDUPOED98c4qRBckMflOzVTBvL4Y9K4+h63trlwVZrDTG5c+SmefF7zs17ecbzw0J\naRJ5fL4X0iuriQ+btu9DLG305JuRcyEODEu63u9Gm1uO1UivFhOy5IbrqWk/m5ptvDkuab3/5W3r\nCtywipU1v/vqiEj2sv+mXDp45uQs/3D3Jp47My/+pqwTR1Nabt3QiEGnwRNO8J1XRuiurcATTnBq\nJkhDpVE0++RGaSYHuVyOB67pEKbkgDDnCMbTDDrDbGzSCqLU9nYba+ss6DRqGq0GnuyXWLRfefo0\n//jJzWxosjLmjjDuiQqyj92kYz6YEH6uo+4w7vBiWWpzixVPOMnxST87u6r451dGRDNR3F8ygzOY\nEKWGYDzNyanF+y8VjVYDV3c6qDTq0GlU/MH2Vv78Z6dFqUXZgJWx/8qQmu8xavJw1OKYDcT51Rmp\n+V5etpioyrRqKg1a0ayus5SJFfz2druweDw86qZ/wiu09eXfVC7/SZr9YUZcER57Y3zRk/XaTr7w\n5AlOzQQJxlPEUlk+0lfH9b21BXDcLS02nuyfZkNjJVqNSpibN9uMfOmmtXjCCfa/Lo2VLa12OqvL\n6by2HG8kybeeHxTlHNmYRamGeTG4+3fbHF2tgVGx3eGHxKvfoih+iGSm33IWgyvFag1QViJ7KAlZ\nyprkhiZrgZSrElVUShMcFhvB1/fW4okk+dHRSfyxFP/16dMiCc7lG63VZj2hZBp/VLLok7Xu5aiz\nSNrnrw65aLIaSaWzBavteCrDySlfSekDgBNTvoLGoswteGhvd8Fx0aSk+rn/tVFu7KvFGYxj0KoJ\nJzJM++Nc3ekQE4QcVWYdnTUSCWvCG8WokywQ5ZAnDBXkZQailGlAvvxxb+lrliOZyvL44UlRm9Zp\n1CLZ11nKCCfShBOZJWxanUZFKpPjmu5qOmvKhTF9cYy4FiUSwokMVpOWbFaajJTN6lBicXKTOQg2\nk05g8uWJ2GbS0V5l5vikH7tZx8P71lBp0gnjG6XZ+CO39PLW5CEB11Ume7tZx4grIjlebazDE0nT\nW2/h+KR0D6dng3xuXw/feWWE7e02emot+fsJ88KAk2gyU+AJfHWnBNO8mDH1fmrUL4faKzVeP0hH\nrA9LOoq42Bp88ZZS3hIWq/m921hpq6ncqtpMOoGjt5v1rG+qZMob5f5rOtjXW7fi9cjnkcWq5MEy\n6grTYjfRape2+G0OE85Qgm1tNjY2WzkzG6SrppwZfxytWirTFCtPJtJZsjlJtMwZSqBSqQpUGWXC\nD0B1uZ6uahONNhP7LqsVKo1Wk5beeovoFQDs6LBz66ZGXhuSXKzmAnG0akkF0hNJEkpk0KhVqFUQ\nSWaZ8sUELl+umcdTWab9cWb8Enw1mZHQRs1WA8FYqoD1KccyPdqSYS7TEE1mRH1795oavJEkwbiU\n6OWGb5PNIEkda1Skc4u1e71WxYgrwqQ3TK3FQI5cgfibLOZm1qupqSjDFUpiNehQq6RVvlwCUoq+\nqVTS5CA3T7tqyhl1R2lzmJgPJuioMku/SzDB4VEP913dzkf66nj25CwLIQnR1VNXwaQnii+SwBlK\ncOumBtyhBM+cnKPJaqTWUkYgliKcyDDpjTLqjrAQigubxZa8L8CjL55nxh/HbtbzxNEpDg67eebk\nHDs67Og0qnx/popv37OZPWtrLmpMKcfnez0mS0Vx/ngvxRIvFB+WdC4QpWbZi932vd8d9lKhvGZZ\n3Ow7r45wZiZAX2NlHlUwUOBUVco16LFDY0L87d6r2pnxxbCatBwY9uQtD6t4aG8XvkiKUzOL2Hsp\nZFVHsJq07Gh38NK5BZKZHHrNIorFZtTii0lSyMUrWjlc4SSufBniI311fOuuTXz+yRPsu6wGUHF8\n0k9vXQUVRi2xVJZnTswy7okKpmcqk2V7ux2bScsrg+6CnYRBq8KXV3WUJyVlOs8I5qpxidhXs82I\nL5osiZVfKUIx6V7kFb7NrOe6nhohEFeXb/SdzevNyPOLTqNCr1Xx1lRgyTllghggOAKRZJZIMo7d\nrBOGMsL4pamSdoeJn5+aExOJjBCa8sVoyMNX5wNxNjRKzdtmm2QXOeGN8re/PMtzZ5z4Yynx95GF\nsCgRAdhMOrF6VtoZ2s06dnVV8fTJOWHCcn4hLDSefnV6Dnc4ycfzEswS3Fay15TLj9f31grHtXuv\nal/1qvj9Hp/F+eP9Eku8mPidTfilfowL/RC/KebEK4kzPXVsiv2vLW79r+upLoCayff9wyOTTHij\neMISeWVxJaviqWNTIiE1Wg3oNOq8FZ9KkF9+kldSlK5HKhfIeOnnBpwisVhNknsVQCIjfUZ5mYZG\nq5HhhfCSpL+mxszutbUYdWpRe/VFUzzZP0OFQVolBeNpBuZDHBnz0Vtfwc4uh1SDNuoKegrKkCUT\nAMo06pLHaNQq9l1WzUIoKYTSOqvNxJIZbCY9eq2acIFzlxTLqWUCxDPSRHNFm41ai5FYKsM5BRlK\nxqNvaKrk7GyAlCyilsmRyuRoqDSQzcF8MI5ZryGSzIhkD9Luqc1hIp3Jsb7RwtFxX4EFYyKvlf/q\nkFtc43wwQSy1OHH11Fron/ATT2eZ8sXZ2VXFgWG3KM09/da0KGFN+WIFome+SJJBZ4hYMoMvKpGP\nOqrKSaazbGqxcfcVzTx2cEySXV5bw2d3d+GLSpDf6vIyMaF95edn8EYkM5jO6nIeffE8/RM+/vGT\nlxeQE0167btK4lKvaxzIceumxoJFz3LHXyz080L1+w9yoXjJE75KpboReBTQAP8jl8v97aX+zNXE\nO9HLuBSsuIudRErhgZUEkGgyzad2tDLiCvO129cVKDV+99URQaaS3//L04srry/dtDYvkDbDhsZK\nTs0EqLUYRD335UEX29ttwKIgVplWxbQ/JhA9d/zLIYFCqSjTUGdZTPipzKKxtRLZogJMZRoiiQw1\nFiOfvbaTxw6N89ihMW7d1MhL5xY4MuYVrNOruhz85PgM6WyOgbkQO7scIkmBtHpVEr0MOjVfuaWX\nv/3VOQKxNNHUUqKUbB7+xqi3QHAsmc4KMpAylEl+BVQmIDWgnz45J3YhIEFA46kM88EEZVr1EntG\nOeRS3aMvDheUcpQx6Y2SzcFsIFZwLa0OIzazgVQmWyC7ABKOv9lmpMFqwKDTCOz99nY7CyHpXq/r\nqWYq32QFxISTzko7q0VlS4m89eypOfE9PbS3m8/vW8O3nh/k8cOTAEx5JfTWn/77cQ4Me7AYtPnv\nXlo0tNpNjLgi1FmkHceBYbd4dl8/76K3vvJdr4qVk8ep6cAFdbCKx/xK43XcHeHf35xkxhfjc/vW\n/EZUAIrjkiZ8lUqlAf4J2AdMA0dVKtUzuVxu4FJ+7mpiNT/G+8GKKzWJrPRQKUkexSQSuXH7pZvW\n8rXb14lzATxzYlY86N+8a1NekMq/2KDMyx1Ixw2zs0tS2NzaZqfSqFv0r62t4MiYT9RiE2nJUu+R\nW3rprC7nYxvqxQAPJTJsarbhCiWZC8ZJZSTN+2A8jU4DqcyirIFWpaK3roJkerHxCtKKbkeHXTRt\nbSYdBq2UoDQq6Kmr4MCwxP6d8kaZ8EaxGHUEYhJevsIgOVd997VRkciLde1hsZyTSi8mVYtBi1G3\nuBuoMuuIpTNEElnaHSam/fElhh+lotKoxazXimTYUGkQCCKg5DnkstOJSR9ajVowZO0mDd5oYeL/\n1I4WfnBkagkfYGghytWdRo6MSbse+fPCiQxGnZqb1tez/7VRdBqN8ASQET8ANnMZt1/eJDSTPrq+\nHlc4wcuDLo6M+TDpNQU9DuWk+NrQQl5kTfrsZpuRZruJbz0/REdVOQeGPTTlparz6wAqjRoe2NUB\nKkk+YdQdFqVHWYb73e6sZWa7vMIvJbNQfLzy35UWfV/88UnGPVHGPRM02ozviXLnex2XeoW/DRjO\n5XKjACqV6gngNuADT/iriUvJilPW0qPJDJ5wgm89P8S9V7Wt+FCVUuyUjys1IcnHXN3p4KG93QJ9\nc+9V7dx7FYI5eWZG0sOXzZmLkUZKWr1Rp+bwqIcjYz6sRgmN8cKAk85ry7n36nYGnWEmPBHmgwkG\nnSH+6fc384f/+iaBWJpIQhrdtnyp55YNDbyab7omPRFiqSw6jTqPwMkJSeYHdrXzzMk55oNxbfEe\n1AAAIABJREFUTkz5RalqX28dt21qJJrMMOGVtPY/vbODuUCcEVeEDU1WsUuBRfTLchFN5YR6ZjCe\nLmhAuyMpGq0GIok45jIJ/7+SJIMcrXYjm5rtHB51M+GNEc+XU1bqB+TyfZFiJm5xsgf40bHpZclf\nofhizyKcyNBbX8GYW/qef3RUQg8dGHbzwDUdpLM5xt0RnKEE29tt3HtVG59+7Kj4DuqtRj6zu5Nk\n+jR9jdJqW4ICS1DPVCYrvue3pgLc9703RQloa5tdLDhkbabDo1KdX9ZeOjUTYsoXxxdNCWZuKQjx\nOwllglUy2y+kg7Uciq3UtXz9jo08/OQJrum+MOP2/dbQkeNSJ/xGYErx/9PAduUBKpXqAeABgJaW\nlkt8ORcXl3JLpvzBISewyEpN/VIPjXxNUvkmw0N7u7hzazMjrrCAzi1HGddrpdWqPPA+c20nn9/X\nw3dfHeHgiIdtbTb6J/z85W19Ag8th/J7MOm1HBnz0VltZsQVEZRyWY6hEELp5eEnT4jVdXW5nkw2\niytf5nGHE9zQW8uT/dNcu6aaUF7h8do11fzdr84Kp6ov3bQWXd7pasIb4Vuf2FSwOvvOKyO0OUwC\nLz7iigiIpaypA6yY7OWIp3NLBNfKyzRUGnUCTSSXqVaxwOfUTIhTMyFRNlpuV6DE5IfiGeosZfii\nKRLpLCadegnpSo5YHnVUKucvSkBLPQxDXt5C1ssJxNJc11ONUacu+N12dFRhN+tZyBPXKgwaYqkM\nf/Gz0xwc8XDNmmoAfHnpjv/nxrUEYyn+9EfHMWi1LIQSAmbbmJfM2NxiJZ3JcnjUw8amSo6Mebmu\np5oH93Tz358fEvLWgDDKub639j0Zhxe7ky6O4tp/qfdtbrXxyhevW9X1SDuN9EXJO78X8YE3bXO5\n3H5gP8DWrVsvAvD2v3co8e5fefo0sGj2sNpyk9I0Qq7rT3qP8dRnrypQ9fzmXZvE67KFnKSzkxSw\ntWgyzdN5xIs8ccj/dlaXl2wUFyN9ZNLWzq4qUpksR8a8YqUmh6tItTIUT4sm5qERD101Zva/Nsr3\n3xgX5YJKoxZPJMlf3baOh586gTeS4rFD47w25GLGF8OgU4sJU+4lTHoXDTKSikRZ7FalDBVwWb2F\ngbkggfyqVl59ylZ/spqkzOBVKoOWCp1ahV6nIpLIFkBRa8r1+GISe1a+JuV1aVTgzyd7rVq1bLLX\n5BP9Sn0EnUZyvGpzmFjXaOX4ZEDsCDY0WuiuKSeWyvLArg780QRvjvu4vNnKd18d4a9vX8df/ecA\n6xososwmT/DK5r6sXxSMZVAZpV7ApCfKXDDOm2PeJQJxzmCch/Z2ce9V7fii0jNxZYedBm+MnroK\nRl0RDgy7eebEbIFY2juNlXa/wIq9O/nYUrX/i9HzUYbdrBfkSCWZ7FLHpU74M4BymdqU/9vvfCiF\nzw4MewSzdbUPTfEDrExyxeJPctIvZh0qEQ+npgN5SQQdD+7pFsJp8gRSqnwkl6Tk817RZs8LmElk\nnb/42ek8jX6+wJzDalQTTuRIZ3OcmllsVgbjaY5PBoTImowyCcTS7H9tFIdZzwsP7+apY1P8IE/d\nH/dMCKjg9nYbj9zSyzMnZuiuKWfCEyGdlUxPYKlVYHHkAH8++STSWaxGHTf01fLGiEesPD2RRebq\nDb11APzo6GQBckYOjVpFKpsjlchRYdBw07p6xt0R3hz3id3DcteUyUEmD19NZ3OY9epF3X6tis4q\ns1T/VrxXRueY9Wp2dVcLtJS8qxn3RKmdD7K93U6r3cRsIEZvQ6VI5F+6aS0Dc0HGPVG++vMzjHui\nbG+3U2cxMOaWJs8mq1E8p3dubealc06OjPkY90TprSsXSK0jY14euKaD884Q917Zxp//7G1m/HFq\nKvSUaTX5CUBChMly0fI1FAsAXszKvPg15f+vVB5VxnIIPmXtf0PTLNFkWsCZlceuNj4IeOalTvhH\ngW6VStWOlOg/AdxziT8T+M2BUF4oilm07yS8kSQvDDjZ/6mtJRm+xd9FsXJgNJnh5UGXKNG8OrRA\nd420ypInkOWaVzKCxhNOcn4hxIgrwsNPnsBu1nN8UlLYlOGUcnRUW9jaauOZk7MSJLHRQjqTZWA+\nLFbQNpOOZpuBUzMhtrfb2NhswxOW5CPuvaqdkYUwU/3T1FnKRDKe8cX54lMnC6CZeo0Kq0lLNJld\nFYbeH03SW1dBIJ7CYdYJKWQZoignz/lgghfPOUWJR44dbZKMRRYwaNRUVuiYDcQJxTNYjXpUqqi4\nR1h5Amq1m7h2jaQkKSd7uTQz4YthLlOhVWnEbkTeA0SSWXzRJHdsaSqQcm5zmASzVl59b2m18dDe\nLkDF9b21vHhWatpaDFoarQZR5qky6wDYs7amYPf4L3+wlY//80HGPVEG5sM8sKuDgbkAvfWVfPba\nTuxmPf/tF2cVpbAkd21pJHTWyfMD8wzMhfjUjhagit76ClEalGVCbt3UCEgs6hFXmGdOzHJs3Cs4\nAMVJVn4uo8k0Jr1WuLWVOna5nfRyCD5l7d+k1wivCJnFXixvcqHJ6INA8VzShJ/L5dIqlepPgF8j\nwTK/l8vlzlzKz5Tjg2qKXGy80x+9sAew1Nd2uWM/kx+ESlnlh/Z2CV35WzZIj8T+10fZ2eXg9ssb\nCyaK4rLOS+ekBPHL03Nc11MjSjjyFl5Z8rCbdKRzWWoq9KIEA7Cp2YZBr2FgPswNfXVMeaO8POgS\nRtffvmdzwT3EkhmG85IC29vteCJJxtwRpv0xpv1S8pchhMlMjoXQIiRxpZIOQDSVZWBeOveMQjoi\nlkpj0qnR61Sk0jkqDIv1fOUq/bCCsBVJZahER6PVgMOs5+kTM0LGWBlyI1mu8ctRV1nGFW02nj45\nQ5VZRzIjacw/fXJeGIkYtFKa16tBCT6SEruK3jozA/MReuvM7Oyu4YmjUwTjaeaCcdocJm7d1Cig\nuz96c5I3x320OUxLmsVKOezvvjrCFW12vv3SeR65pZf/ed8VfOXp03RUlzMwF+DAsIctrXbxrJxR\n7OIqjRKZzx9N449K37PNXMYPbl9fsKqXk3T/hJctrVLD99S0X5RSlpMilv8WTWYKEvJyssilYjVj\nstRC7buvjhTImyw3GcEHl5MueQ0/l8v9AvjFpf6c4ig1S19sk+ZidwiXYlex3DllPL2E0y40NikO\n5XehbO4WI37knsCdW5vF4FJC4eQHdsYX4+CIm6/fsZHre2v5o389yrgnyuOHJ9jcYkW2upsPJriy\nw8ErQy7iqaxwhXrh7KJdYTyd5eenZtmX9wE1aDV8865NfPqxoxyf9NNoMyqw2NLW/7kBp5hQXhly\nEYil2d5uY8YfF9o3kWSGhkoDV7TZODbhw6zXMBeMl3SQulDIJSEAOe9FkgmhQ5/JLTJejToVsbyW\nvUa1CFUs3gkoI5UnRxUbtUhexAFiqayYNG0mPRUGDaG4pO8TT2eFiXhx4/bImJeKPBTTHUmz//Ux\n1tSaBepm3BMVNfK/+eU5AcXNZHN8akcrkOPwmIfzzoiY0EZcYR4/PCG0d/onDmLSSzaVBp2GA8Me\n2hwm3hhxC7by/bs6OD0bIJOVynOd1eW4IwmSaYlYduumBrHTlF2utuV3SjJj96G9XaKUshLjVglq\nUNb+iz0j3m2UmhTkXlix37TydeW/hTuZhguSwN6L+K3V0imlP3MxGhbvRO/inbznQvo98jkNOomc\nIx/31LEpvn94kkarkV3d1eJeL6SrLzdvp7xRPrmtZYlHr/zAKbXBY6lMgbTsf749x5g7ypExD2a9\nZHzRny+jzAXizAUShBMZyss0THqjRItw79mcpHW/s6uKuUCccCLDlFcy34glUzx/doFJT4RIHq76\nqzNObCY9X7r5MoacIU5MBYQmfSKd5bqeav7ytnWMusJCZhkkj12NWsWoO0qZVoMnsrwN4UqxodGC\nSqUil8uSymvt/N6mRuLpNHOBRIHUgTJn55Dq7ZkS/Va7WVeAYZebqLJWf4VBQ22FQVyzSacmlc3h\nDCWEx61ZL3kOZ3I5Mtmc2Lko9f5lWQuZtBWKp8jkpFp8MJ5Gq1bxR7s6aLQauWNLE8+fnccZTBBO\npPmvH+vjp8dnBGmr2Wbka7etY8YfZdAZxqBTCz38+WACjQrW1FZwYiqQ96WtorpCz1P904x7oiQz\nEmfj2/dspn/cizOUoL3KhFatzvs32DHpNbx23k17VTk39tVh1Ks5MOxhz9oa9vXW0VNXwXlnmL6G\nyhW1pWRNqELJcA2pTJaeOssFPSbeSSj9pkudpzgnPf7GON94bogjY94lssoXGx/q4ZeIi9HPVh4r\nJ7wLPRAXc345LjRJyOdMZXJ847khcdxyn3Wh88mCao/c0osvmuRP//0tzs0F2dpmLxgg8sMZS2X4\nwpMnxOTymWs72dBk5diEl11d1fzTKyPs7JYgejN+yZc0nEiRTOckkxNFkVoWLAMp6Y95ooJAJa9u\nXeEkM/5YAas0mZFYoDevr+cjfXUMOUMMOsNc3engpvX1NNmM1FmMPNU/jT+WoqHSgEolNV6D8TSZ\nbA5zmQatRlXS0LxUyGYpbQ4T//7AlTy4t5tkWkIebWisxG7WC5LSSnX4TFZK3p/Y2oI7nCCUX12n\nM9kVkTXJPA9AnthUJWCXcj/hlvW1eMPJArkEKG30kslBuUFNTYWBeDrDsCvC4HwIi1HHD45MMO6J\nUpY3oJ/yRoXRurlMgzucpNKoo8Vh4siYl976CtzhhPhNHeYyNjZZabIZcYZibGqq5HsHJ4gmJf2k\nSqOWH3x6B53V5fz0Lcl0R69V8/ANPTRajdyzvVX8vq+dd7Ozu4oGq5EdHXbu2d6KUa/hO6+O8I3n\nhjDoNFzZ6Vhyf8s9/0rN+iFniGvWVBck3gst1JabFJR/X22ekEP2rdjR4eD+azqW1elfTXyY8EvE\nah2kio9d7cpd+Z7VrhouNEnI5+ypqyipzFn8HvkhSmVy9NRVLHkI7WY9t1/emKe4v8WBYTf9k37h\ngFUc33l1mCeOTrOzy8GffWQtRr2GequRe69qY2OzFYNOA+RwlJfRP+Hjrq3N2Ew6Bp1hVIBBA+nc\nIoKkzWHK4+1T0upOoxJNx2abkRv76ijTqclmc6IG31ktKXWengngCiW4/5oODFo17nCS6nI9//zK\nKMcmvIy5oxK+PJ6mr6ECrVrNpmYr3kiSRquRCa9kg+hbwXBcjhxQZzFQYyljYDbAY29M8MltLSyE\n4rx23i0UL+ssZahUiFV3qUimc5Rp1ahVUiI16hbllYvDpFfTXVMu4KsyZl85qSgTucWgFUJ2q2H9\nytfjCifFNc/4Y/RP+HDKjeSsxAbWadRUl+twhpJicsmRpaZC8rkddkUK+iHOUIL+SR8LoTj+qERa\nq64oYy6QwG7W4Y+mabQa2dom6d7Lu4kpb1QYiyidp1KZLI++OMyetTXsyi8qDo+6OTLmZUeHveTz\nKo8nGT1W7Aw35AzlTdgXx7LNrGdkIUy5QUdfQ2XJxF2cA+TxfWzcJxZiA7PBFfPEiCvMF548wfqm\nSnGv8o7g3ap5fqiWucoo7uqXqqG9E/jUahs0q23arnRccZ1fxvdCbkXMcG99hYDD9U/4lyGAqIr+\nLbymRbRCFw/s6qB/wkswX2/OIYmHgZTst7fb+Zc/2MJTx6Z4+uQss4E4vXVmZpB8Wf/1/9iGzSRx\nCmQjki2tVq5dU8MXf3yywATj5HSAI2Neosk0X7ppLT21Ffzxv/UTS2UxaFUcn5RWpjKC59RMkEar\nAYtBS2e1iRFXdMn9FIc/mhAG3gBzgRhfv2MjICVayZikjFMzSxuxAOVlasJ5ZrFSfTO2wnwTTWbR\nqkuLu3VWm6gqLxNIG5CgrE/2T5c8/p2ESgW5HEI/qKHSUPD6rD/O/smxJe8zaFX0NlRyfNLPvstq\n6J/0c3Wng8cPT9JsM2Iz6eiuqeD6fK/m6LgXbyQlNJoeOzSGSa8t4SWhKuCM3HtVuxinpaIYkACL\n468YnizHCwNO8Ww58s//hYQV5fEtM9OV51vu2mSoMwzwv/5w2weCJPydWuGXiuVKJsp4Jz6UF1ve\neTd1xOJtrvKenjg6RWe1mYeuX8OzJ2dFP+DwqJd0JseWVitGvZYDw27sZsnPVnkdPXUVYout/G7k\n672iTRLbuv8aSYnzwLCHaCotrWo1KjI5qTmbzubQaVTcfUULfQ2VnJjy5bf0GkLxNJFkhkarkWPj\nPp44OkWbw8RXb+1jwhPhJ8enOTkdKLBh/NeD44QSaeorDXz9zo38+sw8Lw+68s1PBdIlb76SzOQI\nxdPMBxNkcxLbtVTJQxnprLTraHMY0agla8gjYx5OTAWwmvTM+GM02oxCo7/4fHI5S4WkIaRVq1b0\nv5UjlpI0iorDF03x0fUNpDKSZaHVpCGeKvTEvZioqSgTpbPiXUMincVi0KJW5wQk1GrSCpewhkoD\nFqN2sUSVhc5qM793eSN/smcN+3pr+elbs9RZyjg7H8p7HsSwmfT01FVwbNwH5BheiLCzy0GD1bTE\nIrCvoZLvvzHOE0enC1bAqxmLy42/Uu9Xllbu2d5KX0PlkvfKfS5519DXUCmxlvPfzaZmqxg/Tx2b\nwpbXtlKOZ2U51W7Wv6e6+B+WdFYZy5VM3qvzvle1/OJQThAn845QOo2K3T014hw1ljIODrsZcUWw\nmXSkMjl2dNgBlSQ/O+njhr46/uwjPaIMdHLKVzDxLWfuLF/vQijOy4MubCZJU2cuECeZznFdTzV/\nf8dGFkJxHtrbzZExT35rLw3kX5+eZ8oXo91hRK/VcPumRv5oV4e4F38sJUyzJ72SGudXbu1jyhvl\n9SE3B/I47I9taGDXmmqxXZebthuaKjHqNEz74yQzOQmCuLGB8jItlzfbODMXLP3FKsJq1HH7pgZ+\ncdrJxuZKJr0x/DEJKrq+sZL+ST8f29DAkDNY0KsoFalMriDZy6WuUiEn+5qKfLlIce4trVYOjXiI\np7MFk4JBq1qVzIMypEnWIJK27A/c1yAZzcg6+yDtwDyRFJtbKtGq1ey9rJbeeoto1jfbjJyeDbKj\nw0Grw8Sd3znEoDMsmq8LoTjBeJqe2gr+7lfn+PWAk1xOaqzv7qnBqNOwsakSc5kWjVrFpDfCsDPM\n0ydnC8qJq42LGX/Fzdbl3qsco7u6qzk86uGfXxnhyJhX9AXklX+pJqyynArvrOe3XHxY0rnIeDck\niPdia3axMFL5wTo86uGRW3pF6UbJppXIKhF2dlXRPyFB3B7a20UslWF7u52NTZVLykBKIokcy0HQ\nYNHDM5rMiNLH5pZKumsr+OZzg4Ig442kCij5B0c8GHVqTs1IWOzGPFsWVDywqx2jXsutmxrY0DSD\nDFuTt8Qys7bZZuSzuzsFvK27toJALMnxyQAGrZpTnqiQAP5vH9+AzaSXDNn9UcEIXS40ahX+mKTt\n/8CuDu7e1syXf/I2R8a8pLNZblxXz5nZIPFUBqNOU2C0ooxmm5HNLVaOT/q5ssPOG6NepnwxLoQO\n7aw2U19pELDEMo2K2zY1YtRr8cdSYrcg8wpiK/QQlgvpGbCy//VRNCrY2mojnsryhRt6ePjJE1ID\nN2/nqFGrBEHr0RfP8/gbE2xvt4vnCFR5C8YcX3n6NN5ICqNOzcP71tBWZc4ntBz9Ez4mvFI5TYas\nvjDgZDYQF4qdcszmoay99ZUfKHlSKXQIFJSbQOpLKcceLPW2LRW/dcSr36ZYTfKFdybMBKV//Aup\nZsqiaDs6nCWlE+T6okxk6aw244ukhP7Jjg6HuLbVMH5LMXbl//dFkzx9YoZxTxSTXifo+s02Iw/u\n6WZHh0NBikkX+N4224zC1ejRF89z19YmXjy3wLVrqvn8vh6AAp2eYDzFlC9GdUWZ+J5kwsv2dmk1\ntbbOgrlMy8uDLj6+uYlnTsxweNRbIBC2Egkrk9eHH/dE+eXpOQbmArTaTXntdx9/96tzHBnzFiSo\nUnFlp4P6SiNtVWbuvaqdcXeEP/nhceYCcXIseubKsabWTCKVE72Ct2ckldFEJseRMS+3X94gJhCA\njjw7GqRVfiKdW7G0I5HAdGg1GjY2Wbl7WzNP9k/ij6Z58ZzU6+k7M4/drCOTNbK5xSb6LTKDFChg\nu8q7RlkbJ5bMcmDYQyyV5dUhF99+6TwvD7p4aG83vfUWASgYnA9yZMwnEn9fYyVb22z4oilGXeF8\neXHiHa9+36sauXJxpZQ/KeVhrRzHxUqcvwns/9+aks57haVdLlYquRRvzWSTkneDqy11XmUUl1qU\nJRibWZ/3su3MY5ctDDlDHJ/0U16mFYl2Y5OVXXnVw9UgjJTfQUd1ubhHg07iBZyYCrCzq4qOKhNj\n7oiARS6E4tx3dTtPHp3kewfGeKp/RnjjgtR4HM2rW56cDjDtizIXSHBswisSjIykSGeziiZqHENe\n131kIcx1a2vwhCV/3N091dx/TSejrojUB3hrlpk8C9di0GIz6VaUWrCZdESTGWwmHc5QIl/OSYry\nRzCWLKjRF4cu7+8bSaT59RknR8a8/OjoFG/PBBhakMxfjDo1f/fxDZyeCQgylCeSIhBLUVdp4MSk\nXzR7rUYd166p5nsHx8nlIJz3yFXuUlYq6eg1KvoaLFzVWcVzZxeYC8Tpn/RxcNjNtjYHg84QvfUV\n9NRVMOOLcWzCTzCe5sZ1tcJbdmOTlTF3hHu2t3Lz+noMOg07Ouz4Iin2vz5KT20FU74o166pZsYf\n48a+WtKZLP9xfIadXQ5sJh37Xx/jji2NfPnmXvZeVotBp6antoLyMi0P7u3m5vUNbGy2Ek6k+fjm\nJgHXfCdj+r2qkS+H7in2sC5G9xSPo0vhZSvH71xJ51LTlldC6hSvzpUmJe9GGOlCW77lXn9hwCnQ\nAI/c0ssLA04euaWXHR2SP6gscfvrM/Pcva2ZzurClchqvDjle9zZ5chr40vKmB3VZh5/Y0K8p9lm\n5OVBFyenDwkrxOt6qoVImeR5K7kbpTLSIGi1mwjG03xubze///8dpq+xEqNOLVaUGxor8USkxH54\n1AuoODjiQa9VC9lm2b5ORiHJOwpZG95Utvyjb9KrSaYz2E1akgrWlMOsp81h5uCIh1BCYvJWVZRx\nZjpA8dTxe5c34QoneHBPN68OuXjs0Dj+WIrjk37Byr2ht45vPj/ElC9Go9XAjD8udHZeP79QsHL/\n3n1X8M3nBgGpQVscSvJXccj3fGomiFEv3ffmFisjC2FGXBGqyvU8tLeb/gmvZCZzTUfeD0fFtWtq\nANjSagdyBWVEmcn64A+PA/Dy4AJTvhjb22XDmhy9DZWLF6JaRHwtyg1LjmQHRzw8c2KGz+/rKeky\npZRFWEkgTblyVj6vFyO4Vupvxeie1XhiLyIAM2InoLyuDyJ+a1b472UDpFRcTBNIvhYZW7xcXIpd\niTeS5PUhN+5wghPTAQ4Ou3nm5JwgdTx7cpY/2tXBwWE3Y54oU94ot1/eWHAtpVAKALFUhoHZIH0N\nleKY8jIdz5ycBcAfSxXsIK7udPCZazp4fsBJJJmhTKuir95CT63UFJRlCVrtJgKxFHvX1hBOpDk3\nH+aPd3fy/Fknr5130z/hY2OzFU84gT+WIp7OCJz6jD/Gjg47e9bWcN/VkuvV8Uk/U94o913dzqgr\nzKRXWm3G01nsJh2ucBKLQUsosVTW2KCVlDpTmRyxVFaQvrI5uG1TI3/xsT6OjnuZC8Tpri3nxFRg\nSQnFbtbx5Zt7+ePdXdRbjVzZ6WBbu50jYx7KtGrBO5jxR1kISfdhNeoIxtN0VJlxhhLMBRJCGjmZ\nyXFkzMPbM0F2djn4q9vX8/a0j2Asxe411cRSGXHOirLCScqsVxfsZGotZdy1tRm9RsXxPKlq72W1\nOMx6fvimhOj60s2XkcvBE0enODbh5ZennfmyDeg0al477y5oSt7QW8erQy4c5Xpc4SRNNmnymvTG\n2NnlEOzZnV0O9qyt4Z7trTx1bEqwTLUadf53dBSgzOTnr3hlfKH/l2O1XJpSr8l/OzMbYMITYVOz\nrYCYWOo9xde9iJbL8o3nhgRx8VLkp985lM47gU5eqljttSxH5lBOABc7KTz+hlQHD8RSBQYlypVT\no9XIQ9evERAxoKA8c3jUw7Fxr2Ayyp//2CGJCn5mNshN6+vpa6jkfx4YE6WSDY0WNGo1V3fasZnL\n+Nrt6/jzn53Gk9d5SWclcs7J6YAo59RbDPzjJy+nrtLAsQkvA3Mhtrfb+b9vXMu2djuv5d2wDFo1\nX9jXw2vnXfijUnKrs5SxpracmgqJCNZoNXLNmmqx/W60GvmjXR2MusKcmgkw4Y3RbDfRUWWmu6ac\nMXdkCUvWqNPQ5jCSTGdpthnJ5qTEf11PNX/+Uem7en7AyZQvxr7LatHk8ZDZvOyCRiVh6RdCcW6/\nvJERV5gHf3icYDzNlz96Ga+cc4rJSi4JmfVq3JEU29vtzAfiEtzUYqCvwcKUL1bgKXBjXx2+aIqF\nUIIxT5S2KjOBWErIJMiM5fIyDcm8EbpGrSKXv8+5QJwdHXZ++tasYB3v7qnmpvX1AtElLw5OzwQE\nHNao07L/9TF2tNuosRh4cE83HdVm7tzazN//+hxn50O4wkm2t9tFg3xHh517r2rnI3112M167tne\nKpKmzazn1UEXgViKj66v44a+OlG6KR4/yyXS5f6/VJQqu660wLGZ9Rwcdgu+R/FEUeozi697EQFo\nESi4GkvZErjmexG/cyWd4vhNaJBcKJYjczx5bIr9n9pKZx7Tu1qTBvlcnkiSMzMBvnBDD0fHvQVN\nVvkY5TZVlke+rqcayImG633fe5MWu0nRmJSyxoFhN1948gQbmqwFTVC5bHBqWlolvzDg5Ot3bOSL\nPz7JugYLT5+cAwoVNOeCcX51Zp4XzzpFCeOtSS/j7giVJh1NNiO1ljIOjniYD8bxRlIroPU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j5HfpgBATE8vxDmwLCbFwac2LZKK61YMsP+10c5Nu4T2O2fn5oTOi8NlQb0WjXb2uw82T9N/4Rf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3d15b7b208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_values, labels = create_latent(nn_aae.nn_enc, test_loader)\n",
    "print(z_values[:,0].mean(), z_values[:,0].std())\n",
    "print(z_values[:,1].mean(), z_values[:,1].std())\n",
    "plt.scatter(z_values[:,0], z_values[:,1], s=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reconstruction of images at specific latent code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3cb5901a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = Variable(torch.FloatTensor([[-5,-5], [-5,5], [5,5], [5,-5], [0,0], [-5,0], [5,0], [0,-5], [0,5], [12,12]]))\n",
    "if args.cuda:\n",
    "    z = z.cuda()\n",
    "nn_aae.nn_dec.eval()\n",
    "recon_x = nn_aae.nn_dec(z)\n",
    "if args.cuda:\n",
    "    recon_x = recon_x.cpu()\n",
    "plot_mnist_sample(recon_x.view(-1, 28,28).data, sample_idx=[0,1,2,3,4,5,6,7,8,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Variational Autoencoder in AAE (Not Completed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_dim = 784\n",
    "z_dim = 2\n",
    "\"\"\"\n",
    "class VAE(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(VAE, self).__init__()\n",
    "\n",
    "        self.fc1 = nn.Linear(x_dim, 500)\n",
    "        self.fc21 = nn.Linear(500, z_dim)\n",
    "        self.fc22 = nn.Linear(500, z_dim)\n",
    "        self.fc3 = nn.Linear(z_dim, 500)\n",
    "        self.fc4 = nn.Linear(500, x_dim)\n",
    "\n",
    "        self.relu = nn.ReLU()\n",
    "        self.sigmoid = nn.Sigmoid()\n",
    "\n",
    "    def encode(self, x):\n",
    "        h1 = self.relu(self.fc1(x))\n",
    "        return self.fc21(h1), self.fc22(h1)\n",
    "\n",
    "    def reparametrize(self, mu, logvar):\n",
    "        # perform element-wise exp(logvar/2)\n",
    "        std = logvar.mul(0.5).exp_()\n",
    "        # sample from normal distribution of mean=0 and std=1\n",
    "        # fills this tensor (eps) with elements samples from the \n",
    "        # normal distribution parameterized by mean=0 and std=1.\n",
    "        if args.cuda:\n",
    "            eps = torch.cuda.FloatTensor(std.size()).normal_()\n",
    "        else:\n",
    "            eps = torch.FloatTensor(std.size()).normal_()\n",
    "        eps = Variable(eps)\n",
    "        return eps.mul(std).add_(mu)\n",
    "\n",
    "    def latent(self, x):\n",
    "        mu, logvar = self.encode(x)\n",
    "        z = self.reparametrize(mu, logvar)\n",
    "        return z\n",
    "    \n",
    "    def decode(self, z):\n",
    "        h3 = self.relu(self.fc3(z))\n",
    "        return self.sigmoid(self.fc4(h3))\n",
    "\n",
    "    def forward(self, x):\n",
    "        mu, logvar = self.encode(x)\n",
    "        z = self.reparametrize(mu, logvar)\n",
    "        return self.decode(z), mu, logvar\n",
    "\"\"\"\n",
    "class VAE_Encoder(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(VAE_Encoder, self).__init__()\n",
    "        self.fc1 = nn.Linear(x_dim, 500)\n",
    "        self.fc21 = nn.Linear(500, z_dim)\n",
    "        self.fc22 = nn.Linear(500, z_dim)\n",
    "        self.relu = nn.ReLU()\n",
    "\n",
    "    def encode(self, x):\n",
    "        h1 = self.relu(self.fc1(x))\n",
    "        return self.fc21(h1), self.fc22(h1)\n",
    "\n",
    "    def reparametrize(self, mu, logvar):\n",
    "        # perform element-wise exp(logvar/2)\n",
    "        std = logvar.mul(0.5).exp_()\n",
    "        # sample from normal distribution of mean=0 and std=1\n",
    "        # fills this tensor (eps) with elements samples from the \n",
    "        # normal distribution parameterized by mean=0 and std=1.\n",
    "        if args.cuda:\n",
    "            eps = torch.cuda.FloatTensor(std.size()).normal_()\n",
    "        else:\n",
    "            eps = torch.FloatTensor(std.size()).normal_()\n",
    "         # wrap tensor into torch.autograd.Variable (automatic differentiation)\n",
    "        eps = Variable(eps)\n",
    "        return eps.mul(std).add_(mu)\n",
    "\n",
    "    def forward(self, x):\n",
    "        mu, logvar = self.encode(x)\n",
    "        z = self.reparametrize(mu, logvar)\n",
    "        return z\n",
    "        \n",
    "class VAE_Decoder(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(VAE_Decoder, self).__init__()\n",
    "        self.fc3 = nn.Linear(z_dim, 500)\n",
    "        self.fc4 = nn.Linear(500, x_dim)\n",
    "        self.relu = nn.ReLU()\n",
    "        self.sigmoid = nn.Sigmoid()\n",
    "        \n",
    "    def forward(self, z):\n",
    "        h3 = self.relu(self.fc3(z))\n",
    "        return self.sigmoid(self.fc4(h3))\n",
    "\n",
    "    \n",
    "class VAE(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(VAE, self).__init__()\n",
    "        self.nn_enc = VAE_Encoder()\n",
    "        self.nn_dec = VAE_Decoder()\n",
    "\n",
    "    def latent(self, x):\n",
    "        z = self.nn_enc.forward(x)\n",
    "        return z\n",
    "    \n",
    "    def decode(self, z):\n",
    "        return self.nn_dec.forward(z)\n",
    "\n",
    "    def forward(self, x):\n",
    "        mu, logvar = self.nn_enc.encode(x)\n",
    "        z = self.nn_enc.reparametrize(mu, logvar)\n",
    "        return self.nn_dec(z), mu, logvar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nn_vae = VAE()\n",
    "nn_vae_dis = Discriminator()\n",
    "if args.cuda:\n",
    "    nn_vae.cuda()\n",
    "    nn_vae_dis.cuda()\n",
    "\n",
    "print(\"VAE Modules\")\n",
    "for idx, m in enumerate(nn_vae.modules()):\n",
    "    print(idx, '->', m)\n",
    "print(\"VAE Parameters\")\n",
    "for param in nn_vae.parameters():\n",
    "    print(type(param.data), param.size())\n",
    "    \n",
    "print(\"Discriminator\")\n",
    "for param in nn_vae_dis.parameters():\n",
    "    print(type(param.data), param.size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "TINY = 1e-15\n",
    "def loss_function(recon_x, x, mu, logvar):\n",
    "    BCE = F.binary_cross_entropy(recon_x, x, \n",
    "                                 weight=None,\n",
    "                                 size_average=False)\n",
    "    # see Appendix B from VAE paper:\n",
    "    # Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014\n",
    "    # https://arxiv.org/abs/1312.6114\n",
    "    # 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2)\n",
    "    KLD_element = mu.pow(2).add_(logvar.exp()).mul_(-1).add_(1).add_(logvar)\n",
    "    KLD = torch.sum(KLD_element).mul_(-0.5)\n",
    "    return BCE + KLD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "optim_vae = optim.Adam(nn_vae.parameters(), lr=0.001)\n",
    "optim_vae_gen = optim.Adam(nn_vae.nn_enc.parameters(), lr=0.001)\n",
    "optim_vae_dis = optim.Adam(nn_vae_dis.parameters(), lr=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nn_vae.train()\n",
    "nn_vae.nn_enc.train()\n",
    "nn_vae.nn_dec.train()\n",
    "nn_vae_dis.train()\n",
    "for epoch in tqdm.tqdm_notebook(range(1, args.epochs+1), \"Epoch\"):\n",
    "    train_loss = 0\n",
    "    total_dis_loss = 0\n",
    "    total_gen_loss = 0\n",
    "    for batch_idx, (x, y) in enumerate(mnist_train_loader):\n",
    "        x = x.view(-1, 784)\n",
    "        x = Variable(x)\n",
    "        if args.cuda:\n",
    "            x, y = x.cuda(), y.cuda()\n",
    "        \n",
    "        # reconstruction phase\n",
    "        optim_vae.zero_grad()\n",
    "        nn_vae.nn_dec.zero_grad()\n",
    "        nn_vae.nn_enc.zero_grad()\n",
    "        recon_batch, mu, logvar = nn_vae(x)\n",
    "        loss = loss_function(recon_batch, x, mu, logvar)\n",
    "        loss.backward()\n",
    "        train_loss += loss.data[0]\n",
    "        optim_vae.step()\n",
    "        \n",
    "        # regularisation phase\n",
    "        # clear the gradients of all optimised variables (of type Variable)\n",
    "        optim_vae_dis.zero_grad()\n",
    "        optim_vae_gen.zero_grad()\n",
    "        # sample real z\n",
    "        # returns a Tensor filled with random numbers from a normal distribution\n",
    "        # with zero mean and standard deviation of 1\n",
    "        z_real = Variable(torch.randn(len(x), z_dim) * 1.0)\n",
    "        if args.cuda:\n",
    "            z_real = z_real.cuda()\n",
    "        # set generator network to evaluation mode \n",
    "        # this has any effect only on modules such as Dropout or BatchNorm\n",
    "        nn_vae.nn_enc.eval()\n",
    "        z_fake = nn_vae.nn_enc(x)\n",
    "        prob_z_real = nn_vae_dis(z_real)\n",
    "        prob_z_fake = nn_vae_dis(z_fake)\n",
    "        dis_loss = -torch.mean(torch.log(prob_z_real+TINY) + \n",
    "                               torch.log(1 - prob_z_fake+TINY))\n",
    "        total_dis_loss += dis_loss.data[0]\n",
    "        dis_loss.backward()\n",
    "        optim_vae_dis.step()\n",
    "\n",
    "        # set generator to training mode\n",
    "        nn_vae.nn_enc.train()\n",
    "        optim_vae_gen.zero_grad()\n",
    "        z_fake = nn_vae.nn_enc(x)\n",
    "        prob_z_fake = nn_vae_dis(z_fake)\n",
    "        gen_loss = -torch.mean(torch.log(prob_z_fake+TINY))\n",
    "        total_gen_loss += gen_loss.data[0]\n",
    "        gen_loss.backward()\n",
    "        optim_vae_gen.step()\n",
    "        \n",
    "        if (not args.log_interval is None) and (batch_idx % args.log_interval == 0):\n",
    "            print('Epoch:{} [{}/{} ({:.0f}%)] recon_loss:{:.6f} dis_loss:{:.6f} gen_loss:{:.6f}'.format(\n",
    "                epoch, batch_idx * len(x), len(mnist_train_loader.dataset),\n",
    "                100. * batch_idx / len(mnist_train_loader),\n",
    "                loss.data[0] / len(x),\n",
    "                dis_loss.data[0] / len(x),\n",
    "                gen_loss.data[0] / len(x)\n",
    "                ))\n",
    "\n",
    "    print('Epoch:{} avg recon_loss:{:.6f} avg dis_loss:{:.6f} avg gen_loss:{:.6f}'.format(\n",
    "          epoch, train_loss / len(mnist_train_loader.dataset),\n",
    "          total_dis_loss / len(mnist_train_loader.dataset),\n",
    "          total_gen_loss / len(mnist_train_loader.dataset)))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def vae_latent(nn_vae, loader):\n",
    "    '''\n",
    "    Create the latent representation for the samples in loader\n",
    "    Return:\n",
    "        z_values: numpy array with the latent representations\n",
    "        labels: the labels corresponding to the latent representations\n",
    "    '''\n",
    "    nn_vae.eval()\n",
    "    labels = []\n",
    "    for batch_idx, (x, y) in enumerate(loader):\n",
    "        x = x.view(-1, 784)\n",
    "        x, y = Variable(x), Variable(y)\n",
    "        if args.cuda:\n",
    "            x, y = x.cuda(), y.cuda()\n",
    "        \n",
    "        labels.extend(y.data.tolist())\n",
    "        # reconstruction phase\n",
    "        z = nn_vae.latent(x)\n",
    "        if batch_idx > 0:\n",
    "            z_values = np.concatenate((z_values, np.array(z.data.tolist())))\n",
    "        else:\n",
    "            z_values = np.array(z.data.tolist())\n",
    "    labels = np.array(labels)\n",
    "    return z_values, labels\n",
    "\n",
    "\n",
    "def vae_recon(nn_vae, z_values):\n",
    "    \"\"\"Evaluate Decoder.\n",
    "    \n",
    "    Return FloatTensor of shape [sample count, 28, 28].\n",
    "    \"\"\"\n",
    "    z = torch.from_numpy(z_values).float()\n",
    "    z = Variable(z)\n",
    "    if args.cuda:\n",
    "        z = z.cuda()\n",
    "    nn_vae.eval()\n",
    "    recon_x = nn_vae.decode(z)\n",
    "    recon_x = recon_x.view(len(recon_x.data), 28, -1)\n",
    "    if args.cuda:\n",
    "        recon_x = recon_x.cpu()\n",
    "    return recon_x.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Reconstruction of MNIST Training Samples\n",
    "z_values, _ = vae_latent(nn_vae, mnist_train_loader)\n",
    "print(z_values[:,0].mean(), z_values[:,0].std())\n",
    "print(z_values[:,1].mean(), z_values[:,1].std())\n",
    "recon_x = vae_recon(nn_vae, z_values)\n",
    "plot_mnist_sample(recon_x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z_values, labels = vae_latent(nn_vae, mnist_train_loader)\n",
    "plt.plot(z_values[:,0], z_values[:,1], \".\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Reconstruction of MNIST Testing Samples\n",
    "z_values, _ = vae_latent(nn_vae, mnist_test_loader)\n",
    "print(z_values[:,0].mean(), z_values[:,0].std())\n",
    "print(z_values[:,1].mean(), z_values[:,1].std())\n",
    "recon_x = vae_recon(nn_vae, z_values)\n",
    "plot_mnist_sample(recon_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z_values, labels = vae_latent(nn_vae, mnist_test_loader)\n",
    "plt.plot(z_values[:,0], z_values[:,1], \".\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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