Generative Adversarial Networks Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting Started"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to Yann LeCun, “adversarial training is the coolest thing since sliced bread”. I’m inclined to believe so because I don’t think sliced bread ever created this much buzz and excitement within the deep learning community. Generative Adversarial Networks are a set of models that basically learn to create synthetic data that is similar to input data it's given. In more formal terms, a GAN is a generative model that learns the probability distribution (or data distribution) of the training examples it is given. From this distribution, we can then create sample outputs. GANs have seen their largest progress with image training examples, but this idea of modeling data distributions is one that can be applied with other forms of input.In the case described in today’s post, we’ll be creating a GAN that learns to generate synthetic, yet readable, images of MNIST digits. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we'll be explaining generative adversarial networks, and how you can use them to create a generator network that can create realistic MNIST digits through Tensorflow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GAN Architecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s dig a little bit deeper into the structure of this model. The basic idea of these networks is that you have 2 models, a generative model and a discriminative model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![caption](Images/GAN1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The discriminative model has the task of determining whether a given image looks natural (an image from the dataset) or looks like it has been artificially created. This is basically a binary classifier that will take the form of a normal convolutional neural network (CNN).  The task of the generator is to create natural looking images that are similar to the original data distribution. \n",
    "\n",
    "This can be thought of as a zero-sum or minimax two player game. The analogy used in the paper is that the generative model is like “a team of counterfeiters, trying to produce and use fake currency” while the discriminative model is like “the police, trying to detect the counterfeit currency”. The generator is trying to fool the discriminator while the discriminator is trying to not get fooled by the generator. As the models train through alternating optimization, both methods are improved until a point where the “counterfeits are indistinguishable from the genuine articles”. There are specific game theory concepts that prove there is indeed an equilibrium to this game where the generator gets so good that the discriminator outputs a probability of ½ for every input. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Our Task"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Today, we’re going to create a GAN that will generate MNIST digits that can fool even the best classifiers (and humans too of course). Here’s what we’re going to need:\n",
    "\n",
    "- Real MNIST training images\n",
    "- A generator network that takes in a random noise vector and produces a synthetic image\n",
    "- A discriminator network (a CNN) that learns to distinguish between real and synthetic images. You can think of it as just a binary classifier (1 for real image, 0 for fake)\n",
    "- An optimization procedure that jointly updates both networks through SGD. This is the tricky part as we need to train the generator network to fool the discriminator network, which means that we have unique gradient flows and labels. \n",
    "- Tensorflow - Our choice of Deep Learning framework\n",
    "\n",
    "Let’s get started. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading MNIST Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's start with our imports. We'll mainly just need Tensorflow. I've also imported Numpy to help with some matrices, the random library for generating numbers, and Matplotlib for visualizing our image data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we have to import our MNIST images. To do this, we’ll call a TF function called read_data_sets. This loads in the 55,000 training examples in the MNIST database. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting MNIST_data/train-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/train-labels-idx1-ubyte.gz\n",
      "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"MNIST_data/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mnist variable we created above actually contains both the images and their labels. Let's just isolate the images for now. There will be 55,000 images and each of them will be of sixe 28 x 28."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55000, 784)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train = mnist.train.images[:55000,:]\n",
    "x_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at what a random image might look like. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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erzeJjdaWuF3BQ08OyjVSjJsHRZiUxhNhu0SQPc9zP9hWVYTLtlR2XQhhUuYS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1213ad790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "randomNum = random.randint(0,55000)\n",
    "image = x_train[randomNum].reshape([28,28])\n",
    "plt.imshow(image, cmap=plt.get_cmap('gray_r'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discriminator Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   Now, using our classical CS concept of modularity, let’s define a CNN classifier function that takes in an image (of size 28 x 28 x 1) as input. The output will be a single scalar number activation that describes whether or not the input image is real or not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![caption](Images/GAN2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to do that, let's first define some functions that will help us with creating CNNs in Tensorflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def conv2d(x, W):\n",
    "  return tf.nn.conv2d(input=x, filter=W, strides=[1, 1, 1, 1], padding='SAME')\n",
    "\n",
    "def avg_pool_2x2(x):\n",
    "  return tf.nn.avg_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let’s see how we’re going to compose this network. We’ll start off by passing the image through a convolutional layer. First, we create our weight and bias variables through tf.get_variable. Our first weight matrix (or filter) will be of size 5x5 and will have a output depth of 8. It will be randomly initialized from a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we’ll call the function tf.nn.conv2d() through our a helper function called conv2d. tf.nn.conv2d() is the Tensorflow’s function for a common convolution. It takes in 4 arguments. The first is the input volume (our 28 x 28 x 1 image in this case). The next argument is the filter/weight matrix. Finally, you can also change the stride and padding of the convolution. Those two values affect the dimensions of the output volume. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with any convolutional neural network, this module is repeated, and then followed by a series of fully connected layers. At the end of the network, we do a final matrix multiply and return the activation value. For those of you comfortable with CNNs, this is just a simple binary classifier. Nothing fancy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This architecture for this network is based on Tensorflow's sample CNN classifier model that they have explained in detail here: https://www.tensorflow.org/tutorials/mnist/pros/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def discriminator(x_image, reuse=False):\n",
    "    with tf.variable_scope('discriminator') as scope:\n",
    "        if (reuse):\n",
    "            tf.get_variable_scope().reuse_variables()\n",
    "        #First Conv and Pool Layers\n",
    "        W_conv1 = tf.get_variable('d_wconv1', [5, 5, 1, 8], initializer=tf.truncated_normal_initializer(stddev=0.02))\n",
    "        b_conv1 = tf.get_variable('d_bconv1', [8], initializer=tf.constant_initializer(0))\n",
    "        h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)\n",
    "        h_pool1 = avg_pool_2x2(h_conv1)\n",
    "\n",
    "        #Second Conv and Pool Layers\n",
    "        W_conv2 = tf.get_variable('d_wconv2', [5, 5, 8, 16], initializer=tf.truncated_normal_initializer(stddev=0.02))\n",
    "        b_conv2 = tf.get_variable('d_bconv2', [16], initializer=tf.constant_initializer(0))\n",
    "        h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)\n",
    "        h_pool2 = avg_pool_2x2(h_conv2)\n",
    "\n",
    "        #First Fully Connected Layer\n",
    "        W_fc1 = tf.get_variable('d_wfc1', [7 * 7 * 16, 32], initializer=tf.truncated_normal_initializer(stddev=0.02))\n",
    "        b_fc1 = tf.get_variable('d_bfc1', [32], initializer=tf.constant_initializer(0))\n",
    "        h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*16])\n",
    "        h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)\n",
    "\n",
    "        #Second Fully Connected Layer\n",
    "        W_fc2 = tf.get_variable('d_wfc2', [32, 1], initializer=tf.truncated_normal_initializer(stddev=0.02))\n",
    "        b_fc2 = tf.get_variable('d_bfc2', [1], initializer=tf.constant_initializer(0))\n",
    "\n",
    "        #Final Layer\n",
    "        y_conv=(tf.matmul(h_fc1, W_fc2) + b_fc2)\n",
    "    return y_conv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generator Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have our discriminator defined, let’s take a look at the generator module. For this, we’ll be basing our model off the generator introduced in the DCGAN paper (link: https://arxiv.org/pdf/1511.06434v2.pdf). You can think of the generator as being a kind of reverse ConvNet. With CNNs, the goal is to transform a 2 or 3 dimensional matrix of pixel values into a single probability. A generator, however, seeks to take a d-dimensional noise vector and upsample it to become a 28 x 28 image. This upsampling is done through a convolutional transpose (or deconvolution) layer. ReLUs and Batch Norm are then used to stabilize the outputs of each layer. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The structure of the generator is very similar to that of the discriminator, except we're calling the convolution transpose method, instead of the conv2d one. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The conv transpose + relu + batch norm pipeline is repeated 4 times so that the output volume grows larger and larger until a 28 x 28 x 1 image is formed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generator(z, batch_size, z_dim, reuse=False):\n",
    "    with tf.variable_scope('generator') as scope:\n",
    "        if (reuse):\n",
    "            tf.get_variable_scope().reuse_variables()\n",
    "        g_dim = 64 #Number of filters of first layer of generator \n",
    "        c_dim = 1 #Color dimension of output (MNIST is grayscale, so c_dim = 1 for us)\n",
    "        s = 28 #Output size of the image\n",
    "        s2, s4, s8, s16 = int(s/2), int(s/4), int(s/8), int(s/16) #We want to slowly upscale the image, so these values will help\n",
    "                                                                  #make that change gradual.\n",
    "\n",
    "        h0 = tf.reshape(z, [batch_size, s16+1, s16+1, 25])\n",
    "        h0 = tf.nn.relu(h0)\n",
    "        #Dimensions of h0 = batch_size x 2 x 2 x 25\n",
    "\n",
    "        #First DeConv Layer\n",
    "        output1_shape = [batch_size, s8, s8, g_dim*4]\n",
    "        W_conv1 = tf.get_variable('g_wconv1', [5, 5, output1_shape[-1], int(h0.get_shape()[-1])], \n",
    "                                  initializer=tf.truncated_normal_initializer(stddev=0.1))\n",
    "        b_conv1 = tf.get_variable('g_bconv1', [output1_shape[-1]], initializer=tf.constant_initializer(.1))\n",
    "        H_conv1 = tf.nn.conv2d_transpose(h0, W_conv1, output_shape=output1_shape, strides=[1, 2, 2, 1], padding='SAME')\n",
    "        H_conv1 = tf.contrib.layers.batch_norm(inputs = H_conv1, center=True, scale=True, is_training=True, scope=\"g_bn1\")\n",
    "        H_conv1 = tf.nn.relu(H_conv1)\n",
    "        #Dimensions of H_conv1 = batch_size x 3 x 3 x 256\n",
    "\n",
    "        #Second DeConv Layer\n",
    "        output2_shape = [batch_size, s4 - 1, s4 - 1, g_dim*2]\n",
    "        W_conv2 = tf.get_variable('g_wconv2', [5, 5, output2_shape[-1], int(H_conv1.get_shape()[-1])], \n",
    "                                  initializer=tf.truncated_normal_initializer(stddev=0.1))\n",
    "        b_conv2 = tf.get_variable('g_bconv2', [output2_shape[-1]], initializer=tf.constant_initializer(.1))\n",
    "        H_conv2 = tf.nn.conv2d_transpose(H_conv1, W_conv2, output_shape=output2_shape, strides=[1, 2, 2, 1], padding='SAME')\n",
    "        H_conv2 = tf.contrib.layers.batch_norm(inputs = H_conv2, center=True, scale=True, is_training=True, scope=\"g_bn2\")\n",
    "        H_conv2 = tf.nn.relu(H_conv2)\n",
    "        #Dimensions of H_conv2 = batch_size x 6 x 6 x 128\n",
    "\n",
    "        #Third DeConv Layer\n",
    "        output3_shape = [batch_size, s2 - 2, s2 - 2, g_dim*1]\n",
    "        W_conv3 = tf.get_variable('g_wconv3', [5, 5, output3_shape[-1], int(H_conv2.get_shape()[-1])], \n",
    "                                  initializer=tf.truncated_normal_initializer(stddev=0.1))\n",
    "        b_conv3 = tf.get_variable('g_bconv3', [output3_shape[-1]], initializer=tf.constant_initializer(.1))\n",
    "        H_conv3 = tf.nn.conv2d_transpose(H_conv2, W_conv3, output_shape=output3_shape, strides=[1, 2, 2, 1], padding='SAME')\n",
    "        H_conv3 = tf.contrib.layers.batch_norm(inputs = H_conv3, center=True, scale=True, is_training=True, scope=\"g_bn3\")\n",
    "        H_conv3 = tf.nn.relu(H_conv3)\n",
    "        #Dimensions of H_conv3 = batch_size x 12 x 12 x 64\n",
    "\n",
    "        #Fourth DeConv Layer\n",
    "        output4_shape = [batch_size, s, s, c_dim]\n",
    "        W_conv4 = tf.get_variable('g_wconv4', [5, 5, output4_shape[-1], int(H_conv3.get_shape()[-1])], \n",
    "                                  initializer=tf.truncated_normal_initializer(stddev=0.1))\n",
    "        b_conv4 = tf.get_variable('g_bconv4', [output4_shape[-1]], initializer=tf.constant_initializer(.1))\n",
    "        H_conv4 = tf.nn.conv2d_transpose(H_conv3, W_conv4, output_shape=output4_shape, strides=[1, 2, 2, 1], padding='VALID')\n",
    "        H_conv4 = tf.nn.tanh(H_conv4)\n",
    "        #Dimensions of H_conv4 = batch_size x 28 x 28 x 1\n",
    "\n",
    "    return H_conv4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating a Sample Image "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, so now we’ve defined both the generator and discriminator functions. Let’s see what a sample output from an untrained generator looks like. With Tensorflow, we need to first define a session and then create a placeholder for the input to our generator. The purpose of a placeholder is basically to tell Tensorflow \"We're going to input in our random z vector later, but for now, we're going to define this placeholder variable instead\". It lets Tensorflow know about the size of the inputs beforehand. The shape of the placeholder will be None x z_dimensions. The None keyword means that the value can be determined at session runtime. We normally have None as our first dimension so that we can have variable batch sizes (With a batch size of 16, the input to the generator would be 16 x 100). With the None keywoard, we don't have to specify batch_size until later. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = tf.Session()\n",
    "z_dimensions = 100\n",
    "z_test_placeholder = tf.placeholder(tf.float32, [None, z_dimensions])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we create a variable (sample_image) that holds the output of the generator, and also initialize the random noise vector that we’ll use as input. The np.random.normal function has three arguments. The first and second define the range of the output distribution we want (between -1 and 1 in our case), and the third defines the the shape of the vector (1 x 100)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sample_image = generator(z_test_placeholder, 1, z_dimensions)\n",
    "test_z = np.random.normal(-1, 1, [1,z_dimensions])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we initialize all the variables, feed our test_z into the placeholder, and run the session. The sess.run function has two arguments. The first is called the \"fetches\" argument. It defines the value for you're interested in computing. For example, in our case, we want to see what the output of the generator is. If you look back at the last code snippet, the output of the generator function is stored in sample_image. Therefore, we'll use sample_image for our first argument. The second argument is where we input our feed_dict. This data structure is where we provide inputs to all of our placeholders. In our example, we need to feed our test_z variable into the z placeholder we defined earlier. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess.run(tf.global_variables_initializer())\n",
    "temp = (sess.run(sample_image, feed_dict={z_test_placeholder: test_z}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can view the output through matplotlib. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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mDzqpbTix+aBTu7ruq8J7J8Bp8HM1J5mint8hNt3ShL3emkSz9na7zpjt/v5+OjFNJpNR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\n3qcGcTaAtmHC1ISVW82J1SUl1SfLjmiBD4FXe53XtcWG3WZcg6etZUB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GJsDSZzKvrLO1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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1213ad290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_i = temp.squeeze()\n",
    "plt.imshow(my_i, cmap='gray_r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not a very convincing MNIST digit right? Let’s look at how we can make our generator better. Enter loss functions and optimization!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training a GAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 16\n",
    "tf.reset_default_graph() #Since we changed our batch size (from 1 to 16), we need to reset our Tensorflow graph\n",
    "\n",
    "sess = tf.Session()\n",
    "x_placeholder = tf.placeholder(\"float\", shape = [None,28,28,1]) #Placeholder for input images to the discriminator\n",
    "z_placeholder = tf.placeholder(tf.float32, [None, z_dimensions]) #Placeholder for input noise vectors to the generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the trickiest parts about understanding GANs is that the loss function is a little bit more complex than that of a traditional CNN classifiers (For those, a simple MSE or Hinge Loss would do the trick). If you think back to the introduction, a GAN can be thought of as a zero sum minimax game. The generator is constantly improving to produce more and more realistic images, while the discriminator is trying to get better and better at distinguishing between real and generated images. This means that we need to formulate loss functions that affect both networks. Let’s take a look at the inputs and outputs of our networks. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Dx = discriminator(x_placeholder) #Dx will hold discriminator prediction probabilities for the real MNIST images\n",
    "Gz = generator(z_placeholder, batch_size, z_dimensions) #Gz holds the generated images\n",
    "Dg = discriminator(Gz, reuse=True) #Dg will hold discriminator prediction probabilities for generated images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, let’s first think about what we want out of our networks. We want the generator network to create images that will fool the discriminator. The generator wants the discriminator to output a 1 (positive example). Therefore, we want to compute the loss between the Dg and label of 1. This can be done through the tf.nn.sigmoid_cross_entropy_with_logits function. This means that the cross entropy loss will be taken between the two arguments. The \"with_logits\" component means that the function will operate on unscaled values. Basically, this means that instead of using a softmax function to squish the output activations to probability values from 0 to 1, we simply return the unscaled value of the matrix multiplication. Take a look at the last line of our discriminator. There's no softmax or sigmoid layer at the end. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reduce mean function just takes the mean value of all of the components in the matrixx returned by the cross entropy function. This is just a way of reducing the loss to a single scalar value, instead of a vector or matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "g_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=Dg, labels=tf.ones_like(Dg)))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let’s think about the discriminator’s point of view. Its goal is to just get the correct labels (output 1 for each MNIST digit and 0 for the generated ones). We’d like to compute the loss between Dx and the correct label of 1 as well as the loss between Dg and the correct label of 0. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d_loss_real = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=Dx, labels=tf.ones_like(Dx)))\n",
    "d_loss_fake = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=Dg, labels=tf.zeros_like(Dg)))\n",
    "d_loss = d_loss_real + d_loss_fake"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have our 2 loss functions (d_loss and g_loss), we need to define our optimizers. Keep in mind that the optimizer for the generator network needs to only update the generator’s weights, not those of the discriminator. In order to make this distinction, we need to create 2 lists, one with the discriminator’s weights and one with the generator’s weights. This is where naming all of your Tensorflow variables can come in handy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tvars = tf.trainable_variables()\n",
    "d_vars = [var for var in tvars if 'd_' in var.name]\n",
    "g_vars = [var for var in tvars if 'g_' in var.name]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we specify our two optimizers. In today’s era of deep learning, Adam seems to be the best SGD optimizer as it utilizes adaptive learning rates and momentum. We call Adam's minimize function and also specify the variables that we want it to update. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with tf.variable_scope(tf.get_variable_scope(), reuse=False):\n",
    "    trainerD = tf.train.AdamOptimizer().minimize(d_loss, var_list=d_vars)\n",
    "    trainerG = tf.train.AdamOptimizer().minimize(g_loss, var_list=g_vars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also specify a learning rate by passing it as an argument (I’ve found .0002 to be effective). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ah, now the best part of neural networks, the famous training loop. During every iteration, there will be two updates being made, one to the discriminator and one to the generator. For the generator update, we’ll feed in a random z vector to the generator and pass that output to the discriminator to obtain a probability score (this is the Dg variable we specified earlier). As we remember from our loss function, the cross entropy loss gets minimized, and only the generator’s weights and biases get updated. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll do the same for the discriminator update. We’ll be taking a batch of images from the mnist variable we created way at the beginning of our program. These will serve as the positive examples, while the images in the previous section are the negative ones. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "sess.run(tf.global_variables_initializer())\n",
    "iterations = 3000\n",
    "for i in range(iterations):\n",
    "    z_batch = np.random.normal(-1, 1, size=[batch_size, z_dimensions])\n",
    "    real_image_batch = mnist.train.next_batch(batch_size)\n",
    "    real_image_batch = np.reshape(real_image_batch[0],[batch_size,28,28,1])\n",
    "    _,dLoss = sess.run([trainerD, d_loss],feed_dict={z_placeholder:z_batch,x_placeholder:real_image_batch}) #Update the discriminator\n",
    "    _,gLoss = sess.run([trainerG,g_loss],feed_dict={z_placeholder:z_batch}) #Update the generator "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now see what a sample image looks like after training. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f37153e78d0>"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Kb8OI/L7W8tUxvbZuLd/UsTwit4NdkaHE6vVShr3jLYO6Ps1S90Edv/CsaNGc\n1QotsXDJ7FB8G4QIb8rnK+Ib5fh7cb518Cxf7XaIFspMWb8iwKnzXjSL+MySwbI61HVJ1DnWrJ9N\nZofi20C0r9abUMUbWEslVdQZ6PLm242KXQxTLwuUmqVMztH2b1EivAwxXwTLFEcK7/VD8W0YNjHC\nlnnShktm0rKrTaT2ZdayaDl4EWAtvlEcLSG3DYpvg/AGwqwFbK1hL5bXs3xTE3brIsKqlxuPtnpF\nYrGArfXrRTksU3Ap5uS6oPg2kJS1a0U3SiOWzwHiCAYvg00mQ7dLv+s2vRjm7u7ulOtBZ7xZt4ON\nUfViWOe5boRcFxTfhuElP3j+35TbwRMhO4AWLfKoBTZXrChHfl8RXyu2wiKsYQovuW4ovg2kxNdb\nR4BLM9a63e7EZOjastUWrtTtSsR2RWI94Cb9sAkKFF1yW6H4NhhPgD3LN+V6ADDlcrChY7quLV/x\n6VrfruxL1IMOO9NLwacsX7oYyG2H4tsQclEOkc+3NNIhlTSh43TF8pUBNb0Qpt7u7e25k6nbeN+U\n5Ru1lVwrQlYNxbehpERXJ0+URDsAmBBfL2FCiud2ELE9ODjA/v5+VWxChc1wy/l8Z7F+KbzkpkDx\nbSBWSL1oB/s+/X6LFt5IgMWF4AmviK2sRCx1uwx5VI/ifCm85DZD8W0YngUbuRz0++3f6q11O2if\nr04V1ku/64E1EWAR38PDQxwcHLhLkHtFE01GQ2Eltw2Kb8OwGWiexdrt+l97NJGKzkqTetSmB9V0\nSJmEkcn7Njc3a00TyagG0jQovg3Bim7OQs1Zm/pxX4trVNfi66UL2+iFHDaZQrd77yXktkHxbRBe\nFpoVYG11lhY9GY4WXlu2tramrF47V0NqekgtuN6+bq8DxZncRCi+DSJn+YoIbm1tTaUI2+kb9X5u\ndjIt6jaDLTVRTh0L2A4GWkGNBJbCS24qFN8G4Vm+dgJzEUkvrCsK+fJE1u5LXU+cI0XcDrIsfG5u\n3tT0kTkXRPR3hNw0KL4No9VqhS4HEcitra2p9dRsplpq8vPU1vMFy9/r0LIUkbtBv56qU3TJbYDi\n2xCimcdS4mszzKKtXnHCrkCRarPt3vy8ETrMTe8T0hQovg3CCrC3fI91G1iBjKza0mLXavOWBspZ\nvpoSlwOFmdxGKL4NIhftEEUsRPs6TMyKrLcIprZuve0s4iukkkK89xFy06H4NoiSOF/tetArS9ii\n2/Xf59wUnXGQAAAgAElEQVQUNjU4SheeBwosaQIU3wZRGu0wGo2mVppIFTvzWKrupQaXpA1r6oSN\ncZCN3FYovg0jylbzLFA7cU1KEO0KyPK3o9GoaC6GaD9FFMsbbb2/WTR1bi7z9GXep4ObdhwyDcW3\nYUQzldkZzs7PzzEajTAYDCbEQpaWHw6HGAwG6Pf7YUiadmvIVigR4TriVCe8bFkCbOc09taw020l\nfbFRHfpYqXrdc5xHZCnQy4Hi20BKBFgEVv+YRZBFeM/OziZENirav1xi6ZaGmZW8No/oziJg3k3H\nq3c6nfAY0XG1Ja23UVvpOdk5kHPnGH0mRXixUHwbhBWiyOrVQis/zIuLiynh1UKiF8n06rIF4h/p\nPD/eWdKHFy3G7XY7DLGTkDxvforoGHZaTNmm6qXn5M17LPXU9+P1SX8mBXhxUHwbhvdj9+b0PT8/\nn3A1jEYjdLtdDAYDd4Xi3PwPUiwlQrwIN0FdUZrlPZ1OZ2o6TSnn5+fVJPU6oqPURVJ3oLL0PPRn\n6XkyUm4gewwK7nKg+DYQz+q1Aizv04NnuVK66kTErD/ieSyueeZ/sK91u92J5e53dnYwHA4r4RWf\nsNy4cgOEeit/GwlualA0dw454dXUcVGQ+aD4NpiUAGtLzVpbts1GRnjREt5Ukcv88ZY+Olvqui90\ne7fbxd7eHvr9PnZ3dzEcDjEajar3yI1Ikk2sz11/nm6TfmsBt9EquYiU1Dlrl4W2anNWcaqNzA/F\nt4HYH7vndohet20AQhHw9nOU/nCtmJRET5R+VtSWe+/Gxgb6/T7Ozs4qi1dbrd1uF71eD8PhEBsb\nG6H4enV9Pa0lLK/ra1zaf/15Jdc+8hFTdBcPxbdhpH7kVoCjIlaxlMgP6e0Ly/qh5iIAUj7Redt6\nvR4Gg8GE8AIvLF5J4R6NRhOvl9zg2u02Li4u0G63JwRP9uXJQp5WSvtv/cSp78v+HVkuFN8GET3a\natHVbgcZaNNbqet9y3UJrXeMlPiWPpKXCK63v7m56boaJCpka2sLg8EgK76eCIu46n1dF6S99Hxy\n/mJNiduBLA6Kb0PJWb06ptcW264/z36+99qySPmlPQEuEdTSfRFfz9UgFu/29vaE+Mrf5Ur0vtyk\n8yX7s7iFPLeDfCZFeHFQfBtG5N+1bgVJspC43tS2xHept8siNzBoH7HtdUntl3B+fj4x8dDp6Sn6\n/X7lBz47O6uumVw3/bSh63a/JJJE6t6NL9rqAVE9MOrVcxYyhXexUHwbROTXFTeCtWite8H6fnNi\nu6pztCKgH4+996f2hRJhl0mE9ArMcq3l2p6dneH09BSdTqfYry7iG8VQ2/06FnRJbLYWdm8w9Tqj\nWNYJim/D0BaVtnK1ANsi75ES/aj1dtVYf2RKgOX93r71iaYiOrT4Srt24UhmYL/frwbH7LXVRYtw\nKnvQ7kfWtGdZ51LDxW0ibg45Z+1aAVBtKbyLg+LbIOwPz/7YPd+uHmzzLF/5XO9Y3vY6iQTY9tH+\njUULbVREfEWwdMiX9p+L5dtqtSZubqm6iGRuIVOdvGG/p8jFZKf99Pat6yPyOevXKMLzQ/FtCFoE\nPf+udT1Elq91OXjiumrrd17Xg4f1q3rblNtBz4nR7/cBYOJaR1u5/p41GlmqudBAXXJLRenQNbHA\n5Xz1dUs9VZDZoPg2CM/n6wmvtXo9v2+J8N6EH6Mdma/zN/J31vKN5raQJZXslJHW7SACqQctbV3v\ni/h6K0d7dc9tEbXpeSikLt+5fM9y/toCttfH3ozJ/NQV3/cC+EEALwN4B4C/CuBfqtc/DOBvmr/5\nJID3zNg/UhMrvNb6lR++je0tGXCzx1nFuUVhT6lH4VRftXhb4bWP/XqNOp2NZt0O7XYb5+fnGAwG\nRWU0GrmLjnqugm63m/Qj2yKRGVK0i8met3et6oaqkXLqiu8OgMcAPgTgFwHY/+pLAB8F8N2qbTBz\n70gtIsvXs36tpZQbcNPH8I67CrRw1u2HN+BmLV87R68dcANerPAhlq+4JLQl7BX92nA4zK6Rp/20\nXnKMTZKR7c7OTmVha+HVA2pyvpZWq1XNfqf9vWQx1BXfX7oqES2MxfYLM/eIzEyJ+Irlay1jz19Y\n4mK47h9j5O8VUq+l0EJkFx/1rE8t+NryFVHudDpV/K/EAut93a7FNzVXsBzf+utTkSwi9CmLV87T\nZg9KsU9BZDEs2ud7CeB9AF4D8ATArwL4ewD+aMHHIQGR8FoBzs3vkPPxrfKHaC1e77U62CQEb+Vn\n2abcDtIfmaOh3+/j9PR0IhnDqw8Gg4lBsNS21+tNDdhFdbG+PYu31WpNCK+sPC3XQ66FjqCgAC+W\nRYvvRwE8BPB7AL4UwD8A8HEAXwO6H5aOZ/lGqcReeJJtu+k/tkX1TYuNHmDTVq8MtmnxlT6I20H2\nJbVYhPfk5KSq6yLtIr65IiIcpYFH+9riBSYnAtKTAXniqwX4Jv8v3EYWLb4PVf3TAH4TwO8C+GYA\nH1nwsYiDFVLPrysTw1iLxttvCqmUWe8RXD/yS9nY2JjKBgNQia8Ir8yHIeJ6cnIyIcC6/fT0tHIN\nSPHm2xgOh5VIRq97cdzAi8l/9Lltbm5O+IJHo1F104megJr2P7Fqlh1q9nkAvw/gy6I3PHjwAIeH\nhxNt9+7dw/3795fctWZjIxVS4ur9sG77j8z6L6M2K0heaJYUWZ3ZE3IRKy3I2s+rRdUObAr6hili\naFcIuby8DOOFbcig9eV737/Xhyb9HyyThw8f4tGjRxNtR0dHxX+/bPF9K4B3Avhc9IZXXnkFd+7c\nWXI31hfvh1ZSmoCdo8Gbs0EPqokA68lzpIj4ellkngvn/Px8QnztfBpeFqH+WxFguzSTiG9JunjO\nl58TYa9OXnD//v0pI/Hx48e4e/du0d/XFd9dAF+u9r8UwFcD+CKANwD8KIB/jrHF+yUA/iHGg210\nOVwDpcKaSx2+7dj5GmzR75HHce1mEOHVa7Xt7Oyg2+26EQYidHpfYn4lpMyGe1k/bDRQaoXXJs5E\n4Wa5AVUpFgrw9VFXfL8W4wE0YBzZ8BNX9Q8D+D4AXwXgOwC8hLG1+3EA9wAcz9tRkiYVlZCzdJpq\n+QLpiXO8gScrvjs7O9jd3a3EV0+3CWDi8V6iC/R7rC/XRh54lq98lhVeaxl7iTJR0kydJx6K7vVQ\nV3x/BUAqzeUvzt4Vskhm8fnav7/NRKJr57C1lq91Oezu7lal2+1WbgRgcqBNi691NUTTeNpYam35\naivds4pzacU2VTyKYomE97Z//7cBzu3QQFIWrfwQ7fv0+5uCDZnyZi6LfL7W8t3f35+aSlKHZ1nx\n7ff77oCYDv2KLF8RX2m3YYOeW6HE1WBvvl4fvC1ZDhTfhpH6IZX+2Jrw4/N8vXZlCC+8zIrv7u4u\n9vb2sLe3NzH/gQitiK+eXKff7+Pk5MRNcrGWq3yeFkRJT/YsXknzzQ34lQpwyXfehP+HmwjFt4Hk\nLF9r4TbNx+elyVqLV0Q4CjXT4isCLDGwMmmOntf34uLFLGaSvea5A/TWip8dgLu8vJxY1Vgs7ciF\n5Fm1OddDztfbhP+HmwrFt6GkfL65UW5v/zaSEl4rvim3w97eHvb39ysBHA6H6Pf7U+IrcylIAoUn\nft4WQCig3kBh9N1GboxIdO3fC0347m8DFN8G4flsc1avfW9TiNwOVoBLB9z29vbQbrer0DGZ5yHy\n+Z6eniZFzvsetNhKXZ+L1OXv9Taq1wk1a/oT0U2D4ksATP7AU6R8govoQ53Xo30rrt46aFK8zDYR\nXj3gtru7i3a7XVm13tSSEt8rAjzLeadujrnrUfd1sloovg3CC6nyZujq9XpJq8q25fyL9hG6Tn/1\n8bx9Laj2/LxIBpmtK7dir5StrS0cHh7i4OAA+/v7VUzv9vZ2NZmNCHZ0XO8a2nNM1XPY65pLHNFF\nsvMkXdpOT+mtYGyvpz0OWQwU34bgPV5ra8/OS+v5EqNkBBvK5NUBVLN51cEmPXhbK6gloppbj022\nm5ublfDu7+9jb28POzs7lWDZddvsEuspccrd1PRW8B71rashuvF4dRFfT3j1LG02CoTCu3wovg3D\ns3qtAMvcrdYPGu1HqyRIPKqERc3SV29AzCvRwpJ2tQk95aNX7Gubm5vY29ubCCmzlq98rkQfpEQq\nOseUVR/5caOIA30T8KxW3SZuFBFgLb52mSSK8PVC8W0QWsysn1MLb6/Xc+NdI4HyZtGSdgDu4E2d\nPlvB8Kxb2/9UXVaaiG4sut7r9SZSiGUr1q+2fK34poTU+15SxRuIk7p+HXix0rK3yKdti9wOOcuX\ngrt8KL4Nwj6y20UgrfiWPMbLCL8MJHU6nWpeA2AyJXaW/qYsdb21c+umioivdV149Y2NjYnZy8Tq\n1daiXriyjlUYWbyeWyUVAmYtX+tSShXP7aCFVz8p0Oq9Xii+DaPU56stHq+u22RWLjuJuAy06bkI\nZhl0k8folIjo+FsdleC16TXWchZnt9sN5++1A27a8o38vVakUqKrPyuXEKOLvVmllpsvsXwjV02p\nZU9mg+LbIKzbwVq/2vLNWUz6R2nXLQMmLV7dXre/1vVhbxZS39raqtwBOgzM7m9vb09Nep4a8NIx\nvnatNC1UIr6RP1l/ZvS9RK6PdrvtJkFErhy5Wdk4ZW/lY7Hi7YCb/h+wbgfPZUPLd/FQfBuE/ZF7\nbge7Cq/dem0pi1f/aGftc85KF/G18y3oGcfs7GOeCyA6tj6etRx1m6T5ljyWp6zt6DNsCJ++1hpv\nEFKmxLQ3Emv5aqvXfr9ahCPLniwOim9D0BZdypK0oUYlxQqvXpBTx8DO0mfP52ut9F6vNyG8EhIm\nab92v9v1/609l4i4HlL+5jqDUpHIR1avXDudTixPFWIRy1bwvltvzTm7JJJ1O9gnHM+ip8theVB8\nG0TqMT4SYG9r2zyLV8RXZvaaV3yjG4WIhbgdxOqV2NzDw0Ps7+/j4OCgahO3Qyp0S8fQeqKTK1ZM\nI+swZfVqwdPCK+gUYS3A9snGm5vC85Hn4nxnvbmQ2aD4NojoB56yKO2+LbJumRVcaw3O+qPU/dWW\nmLXkREhEfEV4dTk4OMDh4eGE+KaKvCc3eCZlOBxOPZ6XiLMVWi+iRKxdfTwtxHquB8+lFF2vnPDm\nrHr6fJcHxbdheJOjeAM5eo2wlGW7sbGB4+Pjapnzfr8/teT4LKnFwOTAkfZb6vkVpC4+Xi8BwvM7\np+ZI0Oebslhz/ZW+ysxnehn4SJSjqIJo4htvkvSc79YOAka+ZtsnhppdLxTfBuGJrq7rAZ1oxQTr\nz+12uzg5OcHJyUm1PI4IjM58m1V8tcWrB4lsRIMMpknyg/VdWr+0d01yfckN0un+6r5K/2TpoNFo\nVCvWWMQ3l8Ktxdeev7WkPXeH52PPCbA3kEgWA8W3gUSB+lZ45T36Rz4ajaYei8XitZavXhJnlgw3\n7bu0PksruOJuEMtXZ595g36RAMvgltS9PuX6K+4bEV8rvBcXFxPiqz83asutyaa3Uayu3ISiaIXI\n6k35fOl2WB4U34YRDS5ZEfYs3siPeXZ2Vq1LJpbvotwO2n+ZWsbHpv3aBAjP8k31yYpwZN1ZwfH6\nurOzg8FgMDHJkPidNVF/JILEE19PjK1PPkoT9gQ4JcKR75rCuxwovg0kJ7z6x25/YN6PViYQ11vt\ndphXfG2sqje4pi3eEsu39PjRfmQVe5avtnjFj9zr9ZKDfLZEy797Quz5e63P1xs09AYDbXp5Trgp\nxIuD4ttQUj94bflqvy/gC5Ce20Fvxe0gPt9ZUout5SthZTaud2dnZ2IkX+qez1fOV2/tca0rwqvb\ntsjnK8Ir7+l0xlNVWlePt4yQ1O3imrboG52XBBL5fHW/c64HuhyuF4rvGpCygOV1/T7bpl0Mdnaz\neS1fHT1gH+X1+mnb29tuGrAX7VDX7SD73nssOrZ2c3NzwtUggiUZeaWDaJ7Ipuo2IzFKlIgG3VLh\nb6lBQQrwYqH4NohcXKtdTDFnldkIiEgUrsPtsLW1FWbg5QbcUsf39iORsZavdTXom8j29rZ7vXKW\nbcnWm3fDi7su8fd6g20pNwMFeHFQfBtKZOlqH2NqRN1uvZAnu1+X0gE3EV+dWGCTDKJQs9J+lLzH\n3iy2traq1+w5nJ2dVWKpS0lbat+GlXkl5/NNxft6okvLdzlQfBtCFFqVsoCtVRVZWjkhn8XfC5SF\nmsmcDVtbW248qt7mxCH1urV6PSvYiqxuk/4PBgNsb29XA5LiG/dcNnabEmhdvPhcXffcBV6crxdq\nZs/dq5PFQPFtGKkRdRvTK6vtWn+uraeEdRbRFbQlGVm+4nbY3NzMikrK8q0jvCmkv+Jq0G4IT1T1\n4GRUj657VKyAevspt0PkfrCDll6dArw4KL4NxBNaO7Cjw5g8F0LKos0JbuRLtXXrq4weofVgUK5E\nfSjtq27zXkvdyLTFaqNDdNFtUs/5efXTiRXJKGys0+kk53OwURF1rhGZH4pvg4gG1/Sgmedv1BEL\ni3Al2G1U99Jio0lrFiW8qcG03N8K9rrqlGxt2UrRsdHevohv6iapX5PsOX1d7ARKUo/WbIus3ZJr\nSBYDxbdh5Cwzb/TdCnVKeEujCFICaQUjSm+NAv+9Y+g2rz+pvtZp19dWC6K2eLUA67kwpG73bZp2\nNKGOtInwyndh3Td6QvjcyhXRDYwsH4pvg/AGxDwLLSXA8wqvEPkadT03au8NIMln62N49ZL+pfaj\n1+zNzbobRqPRlFWrRVeKnaSoTvif3JQEfaOK5kMuyYYj1wvFt4FYt0PK8o2sXi/hopTUAI9us5ZY\nZP3qBApPgL2t16dUf0veq6+HdedY14MVXhFbvdUCbK93qnQ6nYn3yzXV4ltHeCm+q4Hi2yBSSRXW\nQvNiea3VLJ9Zh2iEPZXWWur31cfI1b39ktdyQhRdW+t28CxeEVxbzs7Oqs/Wx/HqACa+L8/na8U3\nNwEPWQ0U34YRRTpYAbYWb8rynZWU/1Z8lDriwXtPzkJbto/XtnvZf9rqjaxfEVo7PadMwF5yQ5G6\nrC6i23W8tBbf3Jpt3nWlJXw9UHwbRBTXG03QYv2Ken8eUpavtW5zIWae5WuPVdKfWf42FWoWuXMi\nt4MVYF1EfKMBRHstz88nJzLyfL6R5RtNokPBvX4ovg0jF2pm52PwBnTmEWArHKkYVC/ON7KSU4/H\nUV8XKbr2eJE7x4vr9YRXlmUSC9j6w70ECi2+1u1gox2s+OaiHcj1Q/FtICVJAKkMuHndDjnLNxLe\n3KCbnNusfarT7hH5023sdOT39QRYlmey5xztdzqdqZtjasDNm4SoTpIFhXl5UHwbQmqwzRNg+zfe\n/qxY0dXiMKvwSlxrqzU5FaS0Sd3rS0lbKblQs5S/17ocrPhGTwciuBLloC1fOZ9owE3H/KZWvCDX\nD8W3gVhxisQ1qtvPAMoiDHT4mP6xewKwsbGBw8ND7O/vTyyMaRfFBFCJXN1ziM5lVkaj0YRoWt+t\ntFuXgo7n1UkYOtxPJ01oK9ZmrMlsarpY94J1M+SWiNdQiK8Pim+D8cQ0Ei3vbwRvACjat1lVdl+3\nHxwcVAJsl4QXkQBeiG8q9jUKkUtdg7qMRqMJgdVC67Vp8dVzOXhp3UCcLGGLXlJJC3C0pLz3lOEN\n5lGIrxeKb8MoEZ2cSHl4iRNe0SFOubK/v1+V3d3dSnxFNOTHr8U3Ghz0BgtzFnJdERbxjcTW7ttY\n3pz4Ru4DW0R8rQB7C2taF8+yQvhIfSi+DccTnEh4o60V3dRWBMM+GmuhkLpemVjEV1assJZvq9UK\nY5NzscqpUgdr+XqCq+teGrGeQtJa6zpqwcbq6iJLLOlrqi1fG9cb+dTtU4tAkb0eKL4NJrKCZ3kU\njwbRbNGCIdaZCIUWDb2v2/WS8DK4JgkF0RSYtu5FbXihdXUF2Pp8UwIs4mtnMctZvlHUgr6R6Wso\n10wXb2HNKHPQWr6LiAohZdQR3x8C8NcAvBvAKYBPAHgA4P837/sAgPcDeAuAXwfw/QA+PW9HSTmR\nuEa+3ZzPF5gOH4ticr112GRVCimybx+bxYLzLF8Z5femXfT2I5dElEZdQuR2iAbbvPl89WTpNqkl\nJ776RmbdDpHl6yWs5CYsItdDHfF9L4APAvgNABsAfgzAxwB8BYCTq/c8APADAL4LwH8C8CMAfhlj\nwX6+kB6TInIRD/Y93r6gf5ypbDXrdtCrUXhFi4UnHFp8ASSnxYxSp7XoRi6KUs7Pz5NuBv1av9+f\niGywK1aUWr5WeCN/b+TzjcL2rOXLWN/rp474/iWz/90AvgDgZQCvAmhhLLw/BuBfXL3nOwG8BuDb\nAfzsXD0ltfHE1bP2SsKzoqQJ61OMFsHc29vDwcHBxCCb9U3qMDQZkQcmLV+7zlk0TaZ1R9iY51nE\n17N8o3q/33cnr7cCHImvHmzzLF/viUFHO8g256en6K6OeXy+L11t37javgvA2zC2hoUBgF8F8B5Q\nfJdOJKKlghu95gmvHcQREU4t/35wcFCFlx0cHFTiYB+N7YxbUSaZtypHJMDRdhbxLRHgfr/vWune\ndJ76OkdpwvpGZn3A2t/rPT1Ec0QwxGy1zCq+LQA/CeDX8MKf+/ar7WvmvV8A8KdmPA6pScqPmRpk\nKhlwswNtVnhlIUnrdpDl3w8ODvDSSy/h8PAQL7300oR1G8UQi9vAS5HOrQBc4hvW4pfDS7JIiW9d\n8Y9CzXSUyM7OTiW+dqDNm8M3F5dd4nYgy2FW8f0pAF8J4G7h+xeTYkSKWWSIFTAd7eClC8sPPlqB\nWKzet7zlLXjppZeqrC6v2OgEL43XLtvj+VQjv7DUF+V2sG39ft8d5PPq1qdufb5yPeVGZqeLjIR3\nY2Oj+lz9Pdo6hXc1zCK+HwTwLRgPwP2hav/81fZtqu7tT/DgwQMcHh5OtN27dw/379+foWvrTeSX\n9YTSvt/u6zbtj7XFtts0YbFuRXBkmZ2zs7Ok+Npyfn7uDmBp0dX1lPjqIuJXYh16E96kkk4AVO+P\n4qwvL8fLAtnBNG9QzXMtpCZKL3EpUHhn5+HDh3j06NFE29HRUfHf1xHfFsbC+60A3gfg98zrn8VY\nZL8RwL+/ausB+HoAPxh96CuvvII7d+7U6AZJYd0DVnSlRPG6nnB7ohsVCSHTsboiumdnZzg5OUGn\nM15/THy6Fs8azYmvN2dCSWiaiJ/2MUfxzJ1OZ8rtIUVbm8PhsLI6c+cFjAVaJ5vkkihs+vCs8bsU\n3vm4f//+lJH4+PFj3L1b5hCoI74/DeDbMBbfY7zw8T4B0MfYtfCPAfwwxmFm//mq/hzAz9c4DpkB\nb0Al5R6w7d4gWmqCl6hNBEPmZxDxHQ6HlbULjMXUG/SJrE7rYtBz53qvRX5W2wZMZvLZG5e+LtGg\nn4itLufn57Usagm/09l+2vpNLQmUsngjgaXwrp464vu9GAvsr5j27wLwc1f1fwRgG8DPYJxk8UmM\nLeHjeTpJyomiEiJLtY646teiNm2hiYUroqX9oMPhMHx8txZnq9WayfKNwsvsYJtY6HJj0NdOn6MV\nXxHdXq9X1bU7JhXipc+t0+lgf3+/El/P8tUCnJsistTlQFZLHfEtXWnvR68KuWYi69cbFLOzZnmz\naOmYW09wvWgH/TnW8gVQ1e0E4qlMLHncLxXf1Bp1VoD1tYqSHeScLi8v3QgLa/l2u12cn5+HWYB2\nv9vthm4HnT4cTRU5i+VLVg/ndmggkctBi0k05aM3k1YU0+vtW38x8MLytRZv6jNtm/ytnqw8Zfl6\nmWyeCOu+CFHI1+Xl5UREhRzPm/bx4uJi6nxS10+nX4sAez5fbyHMUss3hQyKkuuD4tsgcj5fa5l6\nIUte3GgkIp6o2NRlG1alX0u5Q2wkRanlOxgMQtH16nJ9dNiXtXzlJgRgSnjtsXV/U+dmvw8JI9NW\nrxZga/lG30EqeaLk/0d/P2S5UHwbRuR2sD9+LbbWr2j3Uz902+aFc4nla9s7nY5rNUrRUQTW8k1Z\nwLm5f3VdHvt1CJhcOy2OIr722FHfLy4ukq4d+5oV3FS0Q3T9reU7z/8QBXj5UHwbRGT1en5fm4km\nWzvKvr29PfUZqbpdw0yLr13VV1uVkQtEC2eJ20FbvqnEDdkXK1Vb5vamJf1qtVoTx5KBNivC8pk2\nFteLzZVztdc+mrms1+tlfcie5VtXTCnAy4fi2zC8hAAv4sHLnrLz7sq+HQxLbWXlBgBVuJUeZNML\nSXa73SkXh02S0GIZia63Nlpp8gbwYu4IfQ0j8ZU+DgYD9Ho9V3jlpqFdO/qm4u3bCef1vh1wK4nR\nzkU6UFhXD8W3QXjRDt5gm2f56nkY7Ly7nnWVqgNj4R0MBm6SxfHxMY6Pj6duAMPhEFtbW+6sY5eX\nl0XCK5ZvlE1m26Sv1ufrPSmIZS/XTte1CIvla/3quRK5f6wf3suqi/b1edr/lZL5PCjSy4Pi2xD0\nj04LhrZsZUWFy8vLyrLVImtXlhDL10ud1T9sHbZl3Q6yhI4sp6Ot39FoNOFnTQ0YSpiXN5NZarKc\nKORKjqtvRCn/sySmaGtVh5vZ+Xm1VZ8r+nuy7V48b/R9RANtFNGbCcW3QWjh1aKrw68AVJlodkmf\naITd+kmBeOKe09NTHB8fV5PMSF0EV1uqAKaSFjqdzkSbWJEi8jaMzJssyBOiSKRksMsb4PKmZxSx\njibnkZuFuCWsm6GkrqM8ovjdOswqvBTs5ULxbQjazaDFV9Jv9SP8xsZGuKilJ0BW9FLzJsgSOnq2\nLyl2IUkAU9ES0Vy92sLWFqYXwqavR65sbGxkU3lFCLX4Rla2nIe4JLy4aWtte6/b4+q46ZylK6TE\nMyesFN7lQ/FtENblsLW1NSW87XZ7wsdoH3dtm/g2AUyIrzfPgh5U00un67q4I0ajEVqtVnaCdCkA\narCkOj4AAA1LSURBVFm+XhicFyrnRXyUWL762J6fWCdfeC6NlJtDHzOK37WiW8cipvDeDCi+DcJa\nvlp4RRy63W418Y2dBzZqAzDhbtBhY3qFXuvf9Xy9nuXb7XZriW9OgL304GjeChHfaIBLi6K4KXQ0\nhVx3HRcsbgmdKGKjIUq2XuZgSnRLBJjCe3Og+DYEb7Dt/Py8ek2P3J+dnU3FmnrxpzbBQSIXxPI9\nOzurXApi4VpB9gRarGSxfMXX64mwiC1Qz/L1wsUiKzM1EKatUDl/7WrQg4LymXLjS2W4lWS+WQH2\n/Nh6q5Ebrm1LQeG9Xii+DUKLgAiEFeXNzc0qLMpaWVF9NBpNzdMgLgY7wCbiqpdN19EPuq3Vak0I\n7nA4DK1gAEXCa6+FDa1LFe8JQF8HiRrwXA1azCW5RAunFlY7v4NNF87N2SDfa2profDePCi+DUGL\nrCe8IigifCkR0Nt2u43BYFDF78rAl1iyIr7Pnz/H8+fPp+bXTdUlbjYSXD1xeavVmhpwK3U72GQH\na+Fa69+ri/gK1tUwGo0qd4NEl9RJy/aSYqLMNTlH/d2noPDeTCi+DULPU2CFV8/GJROZe1lqtk2s\nU/nxa8tXJ008e/YMT58+nYh79URU78tnawH2xFgy5bw5eVMDbp4Ae0uup9wS2lerH/v1XBbiB9b9\ntTOmRanA+jqXRGcsUnRL30OWA8W3QegMMxEdbxUHO4+tzZDSbQAq8QUmLV/tdnj27BmOjo6mEg5S\nS/poyzdlAYtQp+bntVg/t03jlWJdC7pu97UIyrwQ9trqa+yl/KbqXraaF+XgcZ3xv2QxUHwbgv6h\nSkZYNKmM/btcXYuvtXxPT0/x/PlzPH36FE+ePJlKDU7NqSuWeYkAi7/Vm6GsjttBr6osy7BbV0vk\nn9WuBntO+tysX9grVlSl354P16vPC4V39VB8G4T94eofmJeIEGH/TseZSptYedqNIL5OeY8VRGBy\nNV9rZdqBJjvgdHl5WW1TAqznjChJ7Y0GuqIBL3ly0H3xsgCtaHr7OR/urLG8pd8vWR0U3zXDE+bo\nPV67ttwin2Tpj9tOJuMVEUnt9pBtVJesNZ0+rRMnbAJDFEsbPernRFBEednW6yxQeG8OFN8Go4XQ\nimKdGNDUI7P1X0Z/4wmQTXBIbXW0RQ5Jn/amZrQRDJGFm4ouSF0nb7/EnRB9xiKh8N4sKL5rRMoq\njcQ4Eg3P+hWBjAaW7H7pdItbW1uVsKcES7Z2qkqbLm3dHZEFnxrk8tpsYoN37fQ1jD4nwkucqPO3\n5GZB8W0YnoUbWbwlrgfv8blEXEtiV73Y26geuQM8kYzieqUu4WORxWut3pJrnLqG0TZ6f+5z60Lh\nvZlQfNeAyM87j+sh5fstzerKZZnpNp1ea8Oz7FY+OzV7mB7gS1nnVoStK0euW0o4c3W6GtYTim8D\nidwLucEwT4zriK4O78qlLOt0XE8c7X5koXqC6SVNRG1afD2fdiSQci3n8QV7r+XaKabNgeLbUFIC\nrMmJsbbyPHGKLN7UVIlRW6puXQSeW8P2oWQSGzthjSe+WoBFcKNt6lqm9ktfI82B4ttgcpauvEeT\nEuxIpDzLt2QymxLr1PpnS0sUs+tFOHgimxps09e2VChnsZBJs6H4Npw6lq73ft2eE17rdkhN2WhX\nbEjNsqZdBKVbayF7+9rq1efuba31q1+fNQqBYrveUHzXDO8HXyLIdQfbrPB6K/N6GW6LKNaPa7eR\nXze6RpG/N3VNCclB8SUT4hG5HfRglnUr6DkT9H6uRPMpeNZsNIgXTYAT3TBKXQql16zEr67hgBkR\nKL4ki1i0elrG7e3tqcU5W63W1LwKdlke3e6Fn0X+2dTcD96gWU5gU5S6EeoKKYWXaCi+JIkImBVf\nmbfXLs5pLeJobTiJ3c0V7Uf2RDmVmWbPoY4Q5wSYwkvmheJLJvAiJLQAbm5uTkyYbiduzyU46HpJ\nFpwXQlYyIY6ciyfEpUQCTOEli4DiS6aw/kzP7aCFVw+y2SSKVPGiEVIRClacPevXE199Traewwow\nhZcsCoovCdGxrHqQzVq8Irx6YvLU4Ji0p7LUUhl0kUh7lq+3rYtOpKj7d4REUHxJFi2wnqtBhFcG\n0aK5HWxbbo6GUkH2RFxYpAAv471kfaH4kizW52uFVxboHAwGWTeBrntJG1FbJMjR3wol9UVC4SWl\nUHxJEhvtoIV3NBpNDMDJcvCl1mo0OBYNnFmRjfblb+x5EHKToPiSLCK2IsKygKS3am8kolHiA5Cf\n97aOQOfcC7R4yU2B4kuyaGvWWzAyWixT11OP/ClBLPHfrtrapfCSWaD4kix1ExQsi4oSyInrKlwL\nFF4yK+38WwiZj7qiOK/YE3IboPiSa2EWMS3x4WpohZLbBMWXXBuzWrM31Qqm2JN5oPiSa2VRQrpK\nQdaDi4TMCsWXXDvLFM5liyJFlyyKOuL7QwB+A8BTAK8B+AiAP23e82EAF6Z8Yu5eksYxz6Ba7u9y\n4XDzFEIWRR3xfS+ADwL48wC+AeMwtY8B2FHvuQTwUQBvV+WbFtJT0kiipInU+wlpAnXifP+S2f9u\nAF8A8DKAV6/aWgAGV+2EzAQFlqwD8/h8X7ravqHaLgG8D2O3xGcA/CyAPzHHMQghpJHMKr4tAD8J\n4NcAfFq1fxTAtwP4CwD+LoCvBfBxAL05+kgIIY1j1vTinwLwlQDumvaHqv5pAL8J4HcBfDPGA3SE\nEEIwm/h+EMC3YDwA94eZ934ewO8D+LLoDQ8ePMDh4eFE271793D//v0ZukYIIdfDw4cP8ejRo4m2\no6Oj4r+vM7LRwlh4vxVjv+7vFPzNWwH8AYD3A/j/zGsvA/jUq6++ijt37tToBiGE3EweP36Mu3fv\nAsDXAPit1Hvr+Hx/GsDfuCrHeBFKtnX1+i6AHwfwdQC+BGOB/lcA/gh0ORBCyAR13A7fi3E0w6+Y\n9u8C8HMAzgF8FYDvwDgS4nMYD7bdw1isCSGEXFFHfHNWch/AX5yjL4QQsjZwbgdCCFkBFF9CCFkB\nFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9C\nCFkBFF9CCFkBFF9CCFkBFF9CCFkBFF9CCFkBN1J8Hz58mH/TLaXJ5wY0+/x4breXm3h+N1J87Yqg\nTaLJ5wY0+/x4breXm3h+N1J8CSGk6VB8CSFkBVB8CSFkBdRZvXgpfOYzn5lqOzo6wuPHj1fQm+XT\n5HMDmn1+PLfby3Wdn6dnEa0l9iPHOwD8AoCvX2EfCCFk0fwqgG8D8LnUm1YpvsBYgN+x4j4QQsgi\n+RwywksIIYQQQgghhBBCCCGEEEIIaRjfB+CzAE4B/CaAu6vtzsL4AIALU/5wlR2ag/cC+NcA/hvG\n5/Gtzns+cPX6CYB/A+Arrqtzc5I7tw9j+nv8xDX2bx5+CMBvAHgK4DUAHwHwp533fQC387srOb8P\n4wZ9fzcpw+2vA/hJAP8AwFcD+DUAHwXwzlV2aoH8BwBvV+XPrbY7M7MD4DGA77/avzSvPwDwA1ev\nfy2AzwP4ZQB719XBOcid2yXG/5P6e/yma+vdfLwXwAcB/HkA34BxgtXHMD5n4TZ/dyXnd5u/v6Xy\n6wB+2rR9GsA/XEFfFs0HMP5RN40LAH9Z7bcwjm/8QdXWA/AmgL99jf1aBPbcgLHl9JHr78pSeCvG\n5yhPl0367oDp8wNu2Pd3UyzfHoCXMb5TaT4G4D3X352l8OUYP879F4wz+9612u4shXcBeBsmv8cB\nxhk/TfgeLwG8D+PH2s8A+FkAf2KVHZqDl662b1xtm/bd2fMDbtj3d1PE960AOhhfFM0XMH40uO18\nEsB3APhGAO/H+Jw+AeCPrbJTS0C+q6Z+jx8F8O0A/gKAv4vxo/nHMTYebhMtjF18v4bx0yXQrO/O\nOz/ghn1/K59YZ034JVX/jwD+HYDfAfCdGP+TrAPWf3ob0cshfBrjQeHfBfDNuEGPswX8FICvRPmA\n9m377qLzu1Hf302xfF8HcI7xY4/mbWhmjvQJgN8G8GWr7siC+fzV1vseP4/m8XkAv4/b9T1+EMC3\nYGz96Yibpnx30fl5rPT7uyniOwDwKYwfyzXfgNsTylOHTYxDeJp2Y/ksxv/Q+nvsYTxzXRO/x7di\nHI1zG77HFsYW4V8B8D8B+D3z+m3/7nLn53Gbvr+lch/AGYDvBvBnMX4cf4pmhJr9OMahMO/COBTm\nXwN4gtt5brsYhwJ+NcajyT9wVZdz+T8wHiH/KwC+CsDPA/ivV39300md2y7G3+PXAfgSjAduPoGx\n5XQbzu1nMP5e3ovJUKst9Z7b/N3lzu+2f39L5+9gfAfuYxww3ZQki1/AONLhDON/5kcA/sxKezQ7\n78OLAPVzVf+n6j3/J8aPfKe4XYH670N8blsY++5fw/h7/N2r9j+5gn7Ogj0nKX/TvO+2fne587vt\n3x8hhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQcrP57xnaAp3nbrfF\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3715b814d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_image = generator(z_placeholder, 1, z_dimensions)\n",
    "z_batch = np.random.normal(-1, 1, size=[1, z_dimensions])\n",
    "temp = (sess.run(sample_image, feed_dict={z_placeholder: z_batch}))\n",
    "my_i = temp.squeeze()\n",
    "plt.imshow(my_i, cmap='gray_r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training Difficulties"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One note that I’d like to make is that GANs are notoriously difficult to train. Without the right hyperparameters, network architecture, and training procedure, there is a high chance that either the generator or discriminator will overpower the other. A common case of this is the situation where the generator is able to find a flaw in the discriminator by repeatedly outputting an image that fits the data distribution the discriminator is looking for, but is nowhere close to being a readable MNIST digit. The generator has collapsed onto a single point, and therefore we won’t output a variety of digits. There are also cases where the discriminator becomes too powerful and is able to easily make the distinction between real and fake images. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mathematical intuition behind this phenomenon lies in that GANs are typically trained using gradient descent techniques that are designed to find the minimum value of a cost function, rather than to find the Nash equilibrium of a game. When used to seek for a Nash equilibrium, these algorithms may fail to converge. Further research into game theory and stable optimization techniques may result in GANs that are as easy to train as ConvNets!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Closing Thoughts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this post, we showed how two networks were able to play a minimax game in order to capture the data distribution of the MNIST digits and generate similar looking samples. With applications in video frame prediction, text-image mappings, and more, GANs are definitely the hottest topic in deep learning. Hopefully, with this tutorial, you’ve gained a better understanding of how these networks work in practice and how you can build your own with Tensorflow!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some more great GAN implementations\n",
    "\n",
    "DCGAN Tensorflow Implentation: https://github.com/carpedm20/DCGAN-tensorflow\n",
    "\n",
    "Arthur Juliani's GAN Implementation: https://github.com/awjuliani/TF-Tutorials/blob/master/DCGAN.ipynb \n",
    "\n",
    "Brandon Amos's Image Completion Project: https://bamos.github.io/2016/08/09/deep-completion/ "
   ]
  }
 ],
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   "codemirror_mode": {
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