A slow introduction to TensorFlow

SlowIntro2TensorFlow.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro to TensorFlow using MNIST\n",
    "\n",
    "Walkthrough using TensorFlow on the MNIST dataset.\n",
    "\n",
    "###  Table of contents\n",
    "\n",
    "1. [Implementing a Perceptron](#Implementing-a-Perceptron)\n",
    "\n",
    "2. [Adding regularization to the loss function](#Adding-regularization-to-the-loss-function)\n",
    "\n",
    "3. [Adding a hidden layer](#Adding-a-hidden-layer)\n",
    "\n",
    "4. [Problem: create a network with 3 hidden layers](#Problem:-create-a-network-with-3-hidden-layers)\n",
    "\n",
    "\n",
    "\n",
    "I will be updating this notebook as I get feedback.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab as pl\n",
    "import matplotlib.cm as cm\n",
    "%matplotlib inline\n",
    "\n",
    "import time\n",
    "from IPython.display import clear_output\n",
    "\n",
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### This just defines a colormap that is more suitable for the\n",
    "### visualization that we will use\n",
    "\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "cdict2 = {'red':  ((0.0, 1.0, 1.0),\n",
    "                   (0.5, 0.0, 0.0),\n",
    "                   (1.0, 0.0, 0.0)),\n",
    "\n",
    "         'green': ((0.0, 0.0, 0.0),\n",
    "                   (1.0, 0.0, 0.0)),\n",
    "\n",
    "         'blue':  ((0.0, 0.0, 0.0),\n",
    "                   (0.5, 0.0, 0.0),\n",
    "                   (1.0, 1.0, 1.0))\n",
    "        }\n",
    "\n",
    "\n",
    "blue_red2 = LinearSegmentedColormap('BlueRed2', cdict2)\n",
    "pl.register_cmap(cmap=blue_red2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importing MNIST data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "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": [
    "import tensorflow.examples.tutorials.mnist as mnist_data\n",
    "mnist = mnist_data.input_data.read_data_sets(\"MNIST_data/\", one_hot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this dataset we have 55 thousand images for training and 10 thousand for validation. To access the input images, you can use ```mnist.train.images``` or ```mnist.test.images```. The labels can be accessed via ```mnist.train.labels```. Here is the shape of the images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55000, 784)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.train.images.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that every image 28 x 28 pixels. For simplicity, these images have been flattened (placed in one single line). Let's visualize one of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5dd02d110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  0.  0.  0.  0.  0.  1.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "pl.imshow( np.reshape( mnist.train.images[0,:], (28,28) ), cmap = pl.get_cmap('RdYlBu'), vmax = 1.0, vmin = -1 )\n",
    "pl.axis('off')\n",
    "pl.show()\n",
    "\n",
    "print mnist.train.labels[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that the first example is a 7. As you can see, this dataset is not the classical MNIST, it is a bit harder."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing a Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simplest neural network consists of 1 single layerwith the inputs, and one layer for the output. Originally proposed as a binary classifier (i.e., classifies patterns into two categories or classes), this connectivity is also known as [Perceptron](https://en.wikipedia.org/wiki/Perceptron).\n",
    "\n",
    "The model can be defined using functions defined in the tensorflow library. We will use $x$ as our input vector, with dimension  $N_{samples} \\times 784$. The weights connecting the input to the decision layer are stored in the matrix $W$, such that \n",
    "\n",
    "$$ y^{in} = W x + b \\, ,  $$\n",
    "\n",
    "where $b$ is a bias applied to each unit. The dimensions of $y^{in}$ is $N_{samples} \\times 10$. It is usual to apply a softmax function on the output of these neural networks, in order to turn these into something with properties of a probability:\n",
    "\n",
    "$$ y = softmax (y^{in})  \\quad \\rightarrow \\quad  y_j = \\dfrac{\\exp\\left( y^{in}_{j} \\right)}{ \\sum_{k=1}^{10} \\exp\\left( y^{in}_{k} \\right) } . $$\n",
    "|\n",
    "Thus, the element with higher probability is considered the prediction of this neural network. During training, both $W$ and $b$ are jointly optimized with respect to a given loss function. In this first example, we will use the cross entropy,\n",
    "\n",
    "$$ H ( y, \\hat{y} ) = - \\sum_{j}^{N_{samples}} \\sum_{k=1}^{10} y \\log \\left( \\hat{y} \\right) . $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = tf.placeholder(tf.float32, [None, 784])\n",
    "\n",
    "W = tf.Variable(tf.zeros([784, 10]))\n",
    "b = tf.Variable(tf.zeros([10]))\n",
    "\n",
    "y = tf.nn.softmax(tf.matmul(x, W) + b)\n",
    "y_ = tf.placeholder(tf.float32, [None, 10])\n",
    "\n",
    "cross_entropy = -tf.reduce_sum( y_*tf.log(y) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we need to define the optimization procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get tensorflow started:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "sess = tf.Session(config=tf.ConfigProto(log_device_placement=True))\n",
    "sess.run(init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We next run the training..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2423\n",
      "0.9183\n",
      "0.9187\n",
      "0.9203\n",
      "0.9166\n",
      "0.923\n",
      "0.9199\n",
      "0.9155\n",
      "0.919\n",
      "0.9225\n",
      "0.9171\n",
      "Elapsed time: 46.061363 s\n"
     ]
    }
   ],
   "source": [
    "# Total number of epochs\n",
    "nepochs  = 50000\n",
    "\n",
    "# Defining the interval at which we evaluate the performance\n",
    "intcheck = int(nepochs*0.1)\n",
    "\n",
    "# This will store the evolution of the performance\n",
    "# during the training \n",
    "perfEvol = []\n",
    "\n",
    "\n",
    "# Evaluating training time\n",
    "tic = time.time()\n",
    "\n",
    "for i in range(nepochs + 1):\n",
    "    batch_xs, batch_ys = mnist.train.next_batch(30)\n",
    "    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})\n",
    "    \n",
    "    if i % intcheck == 0:\n",
    "        correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))\n",
    "        accuracy = tf.reduce_mean(tf.cast(correct_prediction, \"float\"))\n",
    "        \n",
    "        perfEvol.append( sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels}) )\n",
    "        \n",
    "        print perfEvol[-1]\n",
    "\n",
    "\n",
    "\n",
    "# Printing the elapsed time during the training process\n",
    "toc = time.time()\n",
    "print \"Elapsed time: %f s\" % (toc - tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best performance: 0.920\n"
     ]
    },
    {
     "data": {
      "image/png": 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8FLQR3A48DMSB+9x9vZndBTS7+1LgO8APzWwL8ArZxBGmYV+CGoVU58qgOleG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\nk0UDhlsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5b43d9f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print \"Best performance: %4.3f\" % np.mean( perfEvol[-3:] )\n",
    "\n",
    "pl.plot(np.arange(0,nepochs+1,intcheck), perfEvol, 'o--', markersize=12)\n",
    "pl.xlim( -nepochs*.05, nepochs*1.05 )\n",
    "pl.ylim( 0, 1.0 )\n",
    "\n",
    "pl.ylabel('Accuracy')\n",
    "pl.xlabel('Iteration')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l8MpWopYffflrEPPEf/916OsdlU4vWUF0p/n264OifesmPP8XWsZFu6EIK3QM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\nJiIicuA/I5YlMyfAD2UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5b7c45550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f,axs = pl.subplots(3,3, figsize=(8,8))\n",
    "\n",
    "c = 0\n",
    "for ax in axs:\n",
    "    for sax in ax:\n",
    "        w__ = sess.run(W)[:,c]\n",
    "        sax.imshow( np.reshape(w__, (28,28)), cmap = pl.get_cmap('Blues') )\n",
    "        c += 1\n",
    "        sax.axis('off')\n",
    "\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like just a bunch of blobs, right?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding regularization to the loss function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our next goal is to learn how to include a [regularization](https://en.wikipedia.org/wiki/Regularization_(mathematics) term in the loss function. The model remains the same:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = tf.placeholder(tf.float32, [None, 784])\n",
    "\n",
    "W = tf.Variable(tf.zeros([784, 10]))\n",
    "b = tf.Variable(tf.zeros([10]))\n",
    "\n",
    "y = tf.nn.softmax(tf.matmul(x, W) + b)\n",
    "y_ = tf.placeholder(tf.float32, [None, 10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, this time we will add regularization terms to the loss function. To do so, all you need to change is the variable ```loss```. In the example below, we add the L2 regularization on both the weights $W$ and biases $b$. The loss function then becomes\n",
    "\n",
    "$$ L( y, \\hat{y}, W, b ) = H ( y, \\hat{y} ) + \\beta \\left( \\dfrac{|| W ||^2}{2} + \\dfrac{|| b ||^2}{2} \\right) . $$\n",
    "\n",
    "Thus, the higher the $\\beta$, the stronger the effects of the regularization. If $\\beta \\to \\infty$, there is no learning because both $W$ and $b$ tend to zero. In principle, $\\beta$ should be cross-validated and optimized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta = 0.005\n",
    "\n",
    "loss = tf.reduce_mean( tf.nn.softmax_cross_entropy_with_logits(logits=y, labels=y_)\n",
    "                         + beta*( tf.nn.l2_loss(W) + tf.nn.l2_loss(b) ) )\n",
    "\n",
    "train_step = tf.train.GradientDescentOptimizer(0.02).minimize(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest works pretty much the same. This time, however, we will store in a matrix ```TOSAVE``` the weights $W$ as a function of the number of iterations to later generate a video."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 47.527899 s\n",
      "Epoch     0 with curr performance 0.098\n",
      "Epoch 50000 with curr performance 0.896\n",
      "Epoch 100000 with curr performance 0.896\n",
      "Epoch 150000 with curr performance 0.896\n",
      "Epoch 200000 with curr performance 0.896\n",
      "Epoch 250000 with curr performance 0.896\n",
      "Epoch 300000 with curr performance 0.896\n",
      "Epoch 350000 with curr performance 0.897\n",
      "Epoch 400000 with curr performance 0.896\n",
      "Epoch 450000 with curr performance 0.897\n",
      "Epoch 500000 with curr performance 0.896\n",
      "Elapsed time: 565.837649 s\n"
     ]
    }
   ],
   "source": [
    "# Getting TF started\n",
    "init = tf.global_variables_initializer()\n",
    "sess = tf.Session()\n",
    "sess.run(init)\n",
    "\n",
    "# Storing the evolution of the performance.\n",
    "perfEvol = []\n",
    "\n",
    "# Total number of epochs\n",
    "nepochs       = 500000\n",
    "intervalCheck = int( nepochs*0.1 )\n",
    "\n",
    "# Matrix to store the weights as a function of the number of iterations\n",
    "TOSAVE = np.zeros( (28,28,10, nepochs/intervalCheck + 1 ) )\n",
    "\n",
    "# Printing the elapsed time during the training process\n",
    "toc = time.time()\n",
    "print \"Elapsed time: %f s\" % (toc - tic)\n",
    "\n",
    "for i in range(nepochs+1):\n",
    "    \n",
    "    if ( i % intervalCheck == 0 ) :\n",
    "        \n",
    "        for c in range(10):\n",
    "            TOSAVE[:,:,c,i/intervalCheck] = np.reshape(sess.run(W),(28,28,10))[:,:,c]\n",
    "        \n",
    "        correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))\n",
    "        accuracy = tf.reduce_mean(tf.cast(correct_prediction, \"float\"))\n",
    "        \n",
    "        currperf = sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels})\n",
    "        perfEvol.append( currperf )\n",
    "        print \"Epoch %5d with curr performance %4.3f\" % (i, currperf)\n",
    "    \n",
    "    batch_xs, batch_ys = mnist.train.next_batch(30)\n",
    "    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})\n",
    "\n",
    "\n",
    "\n",
    "# Printing the elapsed time during the training process\n",
    "toc = time.time()\n",
    "print \"Elapsed time: %f s\" % (toc - tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best performance: 0.896\n"
     ]
    },
    {
     "data": {
      "image/png": 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BCvw6hYtnn8bFs0+LOgwRkZxRsHsK7s62vUdpbe+MOhQRkZwRalIws4VmtsPM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\nCiIikqKkICIiKUoKIiKSoqQgIiIp/x8UKhGPILtvUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5b330a490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AtoxCU5zx+WhTpG8ai8vyGlVV52Bb3xDIvdExrsN3OSpckDFfKvdyF2w7Hm0q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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5b7d11410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print \"Best performance: %4.3f\" % np.mean( perfEvol[-3:] )\n",
    "\n",
    "pl.plot(np.arange(0,nepochs+1,intervalCheck), perfEvol, 'o--', markersize=12)\n",
    "\n",
    "delta = nepochs*0.05\n",
    "pl.xlim(-delta,nepochs+delta)\n",
    "\n",
    "pl.ylabel('Accuracy')\n",
    "pl.xlabel('Iteration')\n",
    "\n",
    "pl.show()\n",
    "\n",
    "f,axs = pl.subplots(3,3, figsize=(8,8))\n",
    "\n",
    "c = 0\n",
    "for ax in axs:\n",
    "    for sax in ax:\n",
    "        im1 = sax.imshow( TOSAVE[:,:,c,-1], interpolation='nearest', cmap = pl.get_cmap('BlueRed2') )\n",
    "        sax.axis('off')\n",
    "        c += 1\n",
    "\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Making a movie with the weights..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZHCL0yUP8zlkPpHYq+t2jmEGhUJBUyqBQKARGMEzIDkQoudMqCO3t6W9pmppC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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5a675b9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.animation import ArtistAnimation\n",
    "\n",
    "f,axs = pl.subplots(3,3, figsize=(4,4))\n",
    "\n",
    "images = []\n",
    "\n",
    "for i in range(TOSAVE.shape[-1]-1):\n",
    "    c = 0\n",
    "    images_ = []\n",
    "    for ax1 in axs:\n",
    "        for ax2 in ax1:\n",
    "            images_.append( ax2.imshow(TOSAVE[:,:,c,i], interpolation='nearest', cmap = pl.get_cmap('BlueRed2') ) )\n",
    "            ax2.axis('off')\n",
    "            c += 1\n",
    "    if i < 101:\n",
    "        images.append(images_)\n",
    "        images.append(images_)\n",
    "    images.append(images_)\n",
    "    \n",
    "line_anim = ArtistAnimation(f, images, interval=50, blit=True)\n",
    "line_anim.save('my_animation.mp4')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This is to free some memory, in the number of frames captured for the video was too high.\n",
    "TOSAVE = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding a hidden layer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next example, we will add a hidden layer. The size of the hidden layer is defined by the variable ```hl_size```. It is common to set the size of the hidden layers in descending order (784 - 100 - 10), but they can also be cross-validated. Also, it may occur that a larger hidden layer may be desirable, which is the case in shallow networks.\n",
    "\n",
    "In the code below, $W_1$ and $b_1$ are the weights and biases, respectively, that connect the input layer and the hidden layer. The activation of the units in the hidden layer is given by $y_1$. Then, $W_2$ and $b_2$ are the weights and biases that connect the hidden layer to the output layer. The rest follows the same logic as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta = 0.0005\n",
    "hl_size = 100\n",
    "\n",
    "x = tf.placeholder(tf.float32, [None, 784])\n",
    "\n",
    "# Propagation to the first layer\n",
    "W1 = tf.Variable(tf.zeros([784, hl_size]))\n",
    "b1 = tf.Variable(tf.truncated_normal([hl_size]))\n",
    "y1 = tf.nn.relu(tf.matmul(x, W1) + b1)\n",
    "\n",
    "# Propagation to the output layer\n",
    "W2 = tf.Variable(tf.zeros([hl_size, 10]))\n",
    "b2 = tf.Variable(tf.truncated_normal([10]))\n",
    "\n",
    "y = tf.matmul(y1, W2) + b2\n",
    "\n",
    "y_ = tf.placeholder(tf.float32, [None, 10])\n",
    "\n",
    "loss = tf.reduce_mean( tf.nn.softmax_cross_entropy_with_logits( logits=y, labels=y_ )\n",
    "                     + beta*( tf.nn.l2_loss(W1) + tf.nn.l2_loss(b1) + tf.nn.l2_loss(W2) + tf.nn.l2_loss(b2) ) )\n",
    "\n",
    "train_step = tf.train.GradientDescentOptimizer(0.05).minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch     0 with curr performance 0.098\n",
      "Epoch 10000 with curr performance 0.947\n",
      "Epoch 20000 with curr performance 0.965\n",
      "Epoch 30000 with curr performance 0.970\n",
      "Epoch 40000 with curr performance 0.972\n",
      "Epoch 50000 with curr performance 0.973\n",
      "Epoch 60000 with curr performance 0.974\n",
      "Epoch 70000 with curr performance 0.976\n",
      "Epoch 80000 with curr performance 0.975\n",
      "Epoch 90000 with curr performance 0.975\n",
      "Epoch 100000 with curr performance 0.976\n",
      "Elapsed time: 139.746448 s\n"
     ]
    }
   ],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "sess = tf.Session()\n",
    "sess.run(init)\n",
    "\n",
    "perfEvol = []\n",
    "\n",
    "nepochs       = 100000\n",
    "intervalCheck = int( nepochs*0.1 )\n",
    "\n",
    "\n",
    "# Evaluating training time\n",
    "tic = time.time()\n",
    "\n",
    "for i in range(nepochs+1):\n",
    "    batch_xs, batch_ys = mnist.train.next_batch(30)\n",
    "    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})\n",
    "    \n",
    "    if i % intervalCheck == 0:\n",
    "        correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))\n",
    "        accuracy = tf.reduce_mean(tf.cast(correct_prediction, \"float\"))\n",
    "        \n",
    "        currperf = sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels})\n",
    "        perfEvol.append( currperf )\n",
    "        print \"Epoch %5d with curr performance %4.3f\" % (i, currperf)\n",
    "        \n",
    "\n",
    "\n",
    "# Printing the elapsed time during the training process\n",
    "toc = time.time()\n",
    "print \"Elapsed time: %f s\" % (toc - tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal performance: 0.976\n"
     ]
    },
    {
     "data": {
      "image/png": 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QUuiH+mQzleVlTB5dHXcoIiJ5oaTQDzv3tzB17DDKE/o3ikhxUJfUfvjW/Dm0tKfiDkNE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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5a7cfe690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print \"Optimal performance: %4.3f\" % max(perfEvol)\n",
    "\n",
    "pl.plot(np.arange(0,nepochs+1,intervalCheck), perfEvol, 'o--', markersize=12)\n",
    "delta = nepochs*0.05\n",
    "pl.xlim(-delta,nepochs+delta)\n",
    "pl.ylim(0.0,1.0)\n",
    "pl.ylabel('Accuracy')\n",
    "pl.xlabel('Iteration')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IjJK919rfHtdHRH80RPEVRrI0aZ0RpZrMuXqnMvJ5LiKfW3IkeWV8uPg0gjOB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KAAAg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\nI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fjD4ntFxj84MX9zSbvAseyXp+U4uFr+o/BtzjNpR98VAWAaCMUEmWCeiUXmH0aWmitk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\nJCIi9iK10Z/l/euVlTNgvObWc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CE6V08ddP3A\nZxFKcL7LksKX1mFu+/5av+cKE/02j66qx/cEYerdXVX0R2k90fvu+M7cKulEVmYyln9n+2lhCH+m\n1BPHHnuq1HPeN2w/3VH+7PSqmI3imV+ofHY8+BVSTfTn/un2id/7LpXHa82npDL+S5o+6x2dJSKa\n+/yGznNmE9X9osXQFD1/W6ef0tm68ktX1rV9V6f1K6JnXe8z9bdHlyCICBoAAAAAAEBP4AUNAAAA\nAACgJyyKPsTDxxKOeXBRQe1dFlS+LkODL7T9JL7xULFC7Z8zXwmS/7x5FYx3MaREk0Ve8ewMwt5m\ne12a9qvmuzCFOjtMODGWgsHvsrCmUnW4PGBuqJXqPbUdWxSS93UqxuKZueUBfa26UZNwlDCuSu0D\ntteftVsuXxpOW9K7rMyA+p6O3KVZzeOjbWA/4qNpT7O9ptvJ1yti/lgxYCMUij/D1uhY335Skn8o\n+L2/nV4dEfG2iIjYZDXruWk9qUcRnbqcUfJSD79vj4iSuiWiCHa76980uNhFEsj9nd8m2cx8linM\nDT49XO2A36tqdVw8KxnYRa1nT7ZT603cMtZOb/f2oJGHdFMRaazvuebTef25+XSvrLC9zsotTzDS\n1O0tdu/f3LYNLoVSu1JLNAH9RtfMRWGqZy5sb1ooH03WX94ejvokX2NrOO2rzNf0WWO51lZExFOy\nn7/J0n+sybbZpZA7U4q21+SW0W57r66+16XutRW15oJamiy/H745rfcseu5xGdZX0n5369ma97pP\nI/lUrnq4zvq9X0zrEkc9B3zFfEXw6ecscb2nA1NCE59c0vSfB3M6xHxSS+PiLaBE1p78QyXuglMJ\nSX06zFvT7u7Uoc0Dn0ZMZ7KMq9unnoJLTt8ZP5dbE+Z7Y0REPNOe7jTlwQWEek72mqHnhblOvuY1\nckXr87R/6rN+yHx/U/Fpusffm09P+d7XNPfbKksG9BNpv2R76Q44156h74jfyy1f7VNiZ78bvph/\nW9Icnp+S3is7z07N9a2tCXcoiKABAAAAAAD0hEWfYa2xUI+vaLr5sI0IaFreK2w/Tbz0EQGN/b7L\nfNPtW7BPiNUI3ePNp2+6uPVc2ybzL3GI0ZxY7+NgO3JUaYONEb2oPX7h3opvbvCJiypVv7zNuM6T\nLT2ERh/9LX2sjcp4jEWRLh/VbFZa32ijDv8ycPSIEuO5ppPmuBkpPzdubj13tOPxJfK0PkfPPcZ5\nY45K3N35vQsxeq7j+fhYU3I+KqIIlifc0JjsLfF28/5gRETssxHMt2d5eHKccjf4SKxG2XzkuRlV\n/DHz1NLsK/2DX936tFUiZ0sHr/+Tlc9nJ+boRtPEvlnfVmqKT15vog3eZm/Ndm+XjQCXKIK3G9+b\n1lMJfX/aW8zXRP38PlqTd9pk5x4kcrZ0WTlgI0pdKb3Id2TbO2R7qR3b3vk+aVq891dE12MYTdxj\nt0Vsdrc6gtLPK3K2s41ARZRR/mHzNZEkjyjVEjLsb+tqd0GT+cGPoScRT+yunup086l9eEnr2ZW/\nYF28v/U9K39nLVWPpy/Xs9r/Nt/O9l73ZxM9Ofya+Z6S1kuwSRyyt9NDqp7MX6xB0TSPKGnJBz+q\nniQ9rYnO7t/Md22bSO495pXO5q9azzPz2ep7bC99el0nrltTSDTX/xR73nti2tnpcrq/Q1fGny7m\nAj+GlEYTHX3Pma23oGiVKzPemNbrs5KDeNqWJj44Zc+ZUuJdb88327J92RWO3iT+xXxKJ+J9V3P/\n+JJbeiLuJoVr2pfaAliHgggaAAAAAABAT+AFDQAAAAAAoCcsisTRxWkSNPhUQQXnz67s91fm01oo\nvk7JjfH03PJ1EyTy8gC8vsknyd6R9pXmU9i1TEyViMhXPtiWYX9PAyHBwDvMJ8GaywDnhlqigCJC\n2Jjnt9P2UjD4unaSfkSpEiUQvjHXehi19eu/P4/h4qX3Vib772lXAimh7G35fTttQrbkUGtNojWW\nstE9Jh3ZmLXH1/FaGJFTTfLXSAtcCqDS22A+iRFGrOZPZa0Yt0QfU1l+O6sTy7ebT6H2vzHfcOeT\niJL8407zKbnKHVHDx2v0qx6q7Qi9wu8A3ZEHKr7Z8txui9Dct+PxH8ynulgS+kxnC73FpChKdXOG\nyUn2tve3J7jRvexyS8mnvDs6M8/OpTw16TYsLbyuqg66HE/XtqwyqakEd9le6p08rUxpaW81n/p8\n79OVHMQTUDRC+nNtza7SA7ow6f4BW9rc8cpe3s+vyfZ/cs7HxWs94AO2reefXzWf2oQXmU/iPH/y\navrt8fhvredTKfHaFle1Pk0K+WP7y1el9bWuyspgnujjP6Z1ueUXB2xExGVp/8l8+h3z/xTg1/e0\nR9yr26JK8H1b/KR5Rwc+dV9JO7Iy21JflXJXm8TNhYrnt39RaCYA3Rp/0HqG0roQUveP/7ZaDzLX\nqCc6w468t30Wf73tqTP0BDzNc+hTTHZ7UyuBdDFp05astH7q+vZeLs/GP5Orxf3XzvPoO9M+y3x/\nHRERP2yekTx/F+crvY2vXPu5zlvPkUMEDQAAAAAAoCcsylCkR130busjYUpYWXvn9CSaN7ZrrHtS\nfY3+eGoETRD2aIBGdf/UfD+b9hPmU+SnTAPU0X7J9npdnBEREaM2XqRxQY+HaIxvYQq+TFddkyPX\nPoZeRvf8imic0kezGl5mkSxNm/7/O3tozOAF5mtGyra1K65H7GxHLj11ajOqOdFJKfucPM8Ptx5d\nXR8/GmlLej7HfMTsRKln2LbqsSfAf0vaUYurrW3Lcn/MZrPt10x8n+hMPdZE9TKm/Bc54uwjtqqn\nvuyBys0XZZhoo4N+F6osawmHoV/UImiewuMzaT2yoPvbU/BoOQ0fY9X3PdF8wxHhKbNLvHV3J3XS\nUFqvV4rCe9REbeYF5lOC6jL6qXTJU60Owb/bIwawNFC99XZbPWNpVT82MH0/oiQZ6EYymr6jm47/\nW3LLR+VV5/1+mK0I2RePi4iIDaa82Z+j7R5zqCVZ0t3n7Wy9v51rVKaefEHPPz6mr0QHfl+r1/LE\nadIneUrz5np9h0XQhgeOHhHxv9L6809J4OIJ6hUlc0XIUGU/PZd5nzn/kTPVJ29R9RzliVLUa3us\np/TQV5v3+Wn9OUltbolBqq/uql2+OGu/EoH0RGy/EhHdhZZUT/3JWHFqj3Kqds71YhCOys2fptbl\nPfViW1pF5bcm/rD1XZXPUSXGHlEShvjCG80d589nI228u/RJd7bPnM+PQS7JZHgRpYz22OeK+V1m\nPmlDPA7tceCjgQgaAAAAAABAT+AFDQAAAAAAoCcsisSxtuqJC1Q0ja82ZfTGzpokCtb6JHRN6nP5\nggKqf2e+JoD8nSZCuDXeEBERuztSmyaY/WpL9aHwtoe8N2YA1CeIKhTqCSM8JD5/SBxaRBWSjbrk\noojXXPqgAH1JN6HUH0+t7DXeSkgiSmIWF/g1sgSXQ0VcntalHkoO8hLzNSI9F8BILtEVGk7FQrHK\njjWVIgD/bao5fmOVqeil5k+09dhXOWkmpg6ZpEerwdxsk9d3ZmD9d01mozVnfCK9BA++7v1kWxtd\n7KoSPrnim085Dsw9ErLcbT4JEF18ozbTJ0FLxu2i2GaK+nkmtJEAyv/yt9t65TIltYC+/p/ugRdU\n9nO51UfSFgFZufO8TkoIROKQpcfUgI0okjUXJjWCxrUmahqr7FVW0vT+W8kDPEGYnhuKlFeJsHab\nfFby8q6IrumBttg5S25Z64X8yWRPa+daij/7iWql9Q3TrXTZZfISYLn4Svef369KnOAy5eGI6K4s\nd0f2heutZ9ZTwLg9s61NmfJER3ynqQ7bzafS8v3UJvgVObHimx88pYxK3KdaqJ918fZ4u2bbM837\n7rT/0XzN5J1NJu/T8fw5c08rHL3IvGqvSzqRjZm26YW2l2q2Sxe/VjmGngKOds2uY8GPoRr5bPPp\n6n6f+V5bma6zKafI/Lb5tILxSOfKqT6V+vzmdqsceXO8OiK6KydL7OsTqkZyesgDNiFLolyXYGpy\nlZ/zkUAEDQAAAAAAoCcsegRN2z4mur6y31DaGzvpmTWRvKwovq0dCStMxnfnVpne97v5Fu7xi59P\ne8CSZiopiY8L633cE/RfkXa4cs4+iqaxO09rOvco6YNPz12fxy3v9Zem/XBn7E8jjm9pPRoR+qDt\nVUZhfFTeE7qLeyu+5hvXxOtaz2R7zpfbfmfn3iUaoJjgeGcc6NhSmB4L3VHSZtRub3xT67kxJ5Ff\nGLM5q51gHjHSjta8wfZovmfYfttMjkj6RPQfz9rjU7l1tTxJiFKfe+TzunYP31Oxap/Wqljwwixi\nAMeDt5Qao/MImtcUoWvtSgPdyz6NvInJerTsl9Nu73yfpknXNAJPqpzLu8ynFtKjHBqb9pqvkXiP\nQEwPWOg3tTFhv8ZqYT3aszL3Wm++RnOzsxPZUVTWoy6NguOyjNxElJTYuy3+oaONWj2aiG+NiIj1\nbZKdiLHs1XebVuacbKO9T9evcKXHnraPO9px9KOheaTzktrf/jqPk6iMPCGQ7snN5lOf5enZmjbh\njk4CqabcPHr09crWd6T9cEcf1cTiLrQS3NG2J+X5Yk0mJZnsLMok7ZU/F84P/sSh51VPSaE4Zffq\nqpy9ffqRtJ5mv3k29Se2fa12aci8ul4en9E9VZYu+MG03rrrnP0YuvO+UfHNToc29/jdK53H7DQf\nJX1fRMRPpfXltd6Y9iPme03a13Xq/VDaohrb19bjsojXy2I26lH9Sr44nz29tdI5+J2lunO0T6pE\n0AAAAAAAAHoCL2gAAAAAAAA9YdFnVitc6G+KWtvEEx68P4OEF5pU4aLc9pV8NIFvZysniFAY/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JxSpRWAeac8UDc04MFTQAAAAAAICWwA80AAAAAACAloDFEQBgzlFWPXsp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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5a6404b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f,axs = pl.subplots(10,10, figsize=(15,15))\n",
    "\n",
    "c=0\n",
    "for ax in axs:\n",
    "    for sax in ax:\n",
    "        sax.imshow( np.reshape(sess.run(W1),(28,28,hl_size))[:,:,c],\n",
    "                    interpolation='nearest', cmap = pl.get_cmap('BlueRed2') )\n",
    "        sax.axis('off')\n",
    "        c += 1\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdoAAAHVCAYAAABWsjp6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9a6UdQBlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5a0f8d310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f,axs = pl.subplots(3,3, figsize=(8,8))\n",
    "\n",
    "c=0\n",
    "for ax in axs:\n",
    "    for sax in ax:\n",
    "        sax.imshow( np.reshape(sess.run(W2),(10,10,10))[:,:,c], \n",
    "                    interpolation='nearest', cmap = pl.get_cmap('BlueRed2') )\n",
    "        sax.axis('off')\n",
    "        c += 1\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem: create a network with 3 hidden layers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try and create a network with 3 hidden layers. Below we have the starting point, we the first hidden layer is connected to the input layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Size of the first hidden layer\n",
    "hl_size_1 = 100\n",
    "\n",
    "x = tf.placeholder(tf.float32, [None, 784])\n",
    "\n",
    "# Propagation to the first layer\n",
    "W1 = tf.Variable(tf.zeros([784, hl_size_1]))\n",
    "b1 = tf.Variable(tf.truncated_normal([hl_size_1]))\n",
    "y1 = tf.nn.relu(tf.matmul(x, W1) + b1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Complete below the other 2 hidden layers and their connectivities. Use ```y``` as the output layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If everything is defined correctly, you should be able to run the rest of the code without errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_ = tf.placeholder(tf.float32, [None, 10])\n",
    "\n",
    "\n",
    "beta = 0.0005\n",
    "\n",
    "loss = tf.reduce_mean( tf.nn.softmax_cross_entropy_with_logits( logits=y, labels=y_ )\n",
    "                     + beta*( tf.nn.l2_loss(W) + tf.nn.l2_loss(b) + tf.nn.l2_loss(Wo) + tf.nn.l2_loss(bo) ) )\n",
    "\n",
    "train_step = tf.train.GradientDescentOptimizer(0.05).minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "sess = tf.Session()\n",
    "sess.run(init)\n",
    "\n",
    "perfEvol = []\n",
    "\n",
    "nepochs       = 1000\n",
    "intervalCheck = int( nepochs*0.1 )\n",
    "\n",
    "\n",
    "# Evaluating training time\n",
    "tic = time.time()\n",
    "\n",
    "for i in range(nepochs+1):\n",
    "    batch_xs, batch_ys = mnist.train.next_batch(30)\n",
    "    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})\n",
    "    \n",
    "    if i % intervalCheck == 0:\n",
    "        correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))\n",
    "        accuracy = tf.reduce_mean(tf.cast(correct_prediction, \"float\"))\n",
    "        \n",
    "        currperf = sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels})\n",
    "        perfEvol.append( currperf )\n",
    "        print \"Epoch %5d with curr performance %4.3f\" % (i, currperf)\n",
    "        \n",
    "\n",
    "\n",
    "# Printing the elapsed time during the training process\n",
    "toc = time.time()\n",
    "print \"Elapsed time: %f s\" % (toc - tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print \"Optimal performance: %4.3f\" % max(perfEvol)\n",
    "\n",
    "pl.plot(np.arange(0,nepochs+1,intervalCheck), perfEvol, 'o--', markersize=12)\n",
    "delta = nepochs*0.05\n",
    "pl.xlim(-delta,nepochs+delta)\n",
    "pl.ylim(0.0,1.0)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}

SlowIntro2TensorFlow_ConvNet.ipynb