3_regularization.ipynb

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    "Deep Learning\n",
    "=============\n",
    "\n",
    "Assignment 3\n",
    "------------\n",
    "\n",
    "Previously in `2_fullyconnected.ipynb`, you trained a logistic regression and a neural network model.\n",
    "\n",
    "The goal of this assignment is to explore regularization techniques."
   ]
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   "source": [
    "# These are all the modules we'll be using later. Make sure you can import them\n",
    "# before proceeding further.\n",
    "from __future__ import print_function\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from six.moves import cPickle as pickle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1HrCK6e17WzV"
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   "source": [
    "First reload the data we generated in _notmist.ipynb_."
   ]
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     "text": [
      "Training set (200000, 28, 28) (200000,)\n",
      "Validation set (10000, 28, 28) (10000,)\n",
      "Test set (10000, 28, 28) (10000,)\n"
     ]
    }
   ],
   "source": [
    "pickle_file = 'notMNIST.pickle'\n",
    "\n",
    "with open(pickle_file, 'rb') as f:\n",
    "  save = pickle.load(f)\n",
    "  train_dataset = save['train_dataset']\n",
    "  train_labels = save['train_labels']\n",
    "  valid_dataset = save['valid_dataset']\n",
    "  valid_labels = save['valid_labels']\n",
    "  test_dataset = save['test_dataset']\n",
    "  test_labels = save['test_labels']\n",
    "  del save  # hint to help gc free up memory\n",
    "  print('Training set', train_dataset.shape, train_labels.shape)\n",
    "  print('Validation set', valid_dataset.shape, valid_labels.shape)\n",
    "  print('Test set', test_dataset.shape, test_labels.shape)"
   ]
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   "source": [
    "Reformat into a shape that's more adapted to the models we're going to train:\n",
    "- data as a flat matrix,\n",
    "- labels as float 1-hot encodings."
   ]
  },
  {
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     "text": [
      "Training set (200000, 784) (200000, 10)\n",
      "Validation set (10000, 784) (10000, 10)\n",
      "Test set (10000, 784) (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "image_size = 28\n",
    "num_labels = 10\n",
    "\n",
    "def reformat(dataset, labels):\n",
    "  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)\n",
    "  # Map 2 to [0.0, 1.0, 0.0 ...], 3 to [0.0, 0.0, 1.0 ...]\n",
    "  labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)\n",
    "  return dataset, labels\n",
    "train_dataset, train_labels = reformat(train_dataset, train_labels)\n",
    "valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)\n",
    "test_dataset, test_labels = reformat(test_dataset, test_labels)\n",
    "print('Training set', train_dataset.shape, train_labels.shape)\n",
    "print('Validation set', valid_dataset.shape, valid_labels.shape)\n",
    "print('Test set', test_dataset.shape, test_labels.shape)"
   ]
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      "startup": false,
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   "source": [
    "def accuracy(predictions, labels):\n",
    "  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))\n",
    "          / predictions.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "---\n",
    "Problem 1\n",
    "---------\n",
    "\n",
    "Introduce and tune L2 regularization for both logistic and neural network models. Remember that L2 amounts to adding a penalty on the norm of the weights to the loss. In TensorFlow, you can compute the L2 loss for a tensor `t` using `nn.l2_loss(t)`. The right amount of regularization should improve your validation / test accuracy.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "batch_size = 128\n",
    "beta = 0.01\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  weights = tf.Variable(\n",
    "    tf.truncated_normal([image_size * image_size, num_labels]))\n",
    "  biases = tf.Variable(tf.zeros([num_labels]))\n",
    "  \n",
    "  # Training computation.\n",
    "  logits = tf.matmul(tf_train_dataset, weights) + biases\n",
    "  loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  regularizers = tf.nn.l2_loss(weights)\n",
    "  loss +=  beta*regularizers\n",
    "  \n",
    "  # Optimizer.\n",
    "  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits)\n",
    "  valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(tf_valid_dataset, weights) + biases)\n",
    "  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 46.332329\n",
      "Minibatch accuracy: 15.6%\n",
      "Validation accuracy: 15.7%\n",
      "Minibatch loss at step 500: 0.741115\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 81.1%\n",
      "Minibatch loss at step 1000: 0.729404\n",
      "Minibatch accuracy: 82.8%\n",
      "Validation accuracy: 81.4%\n",
      "Minibatch loss at step 1500: 0.584653\n",
      "Minibatch accuracy: 83.6%\n",
      "Validation accuracy: 81.2%\n",
      "Minibatch loss at step 2000: 0.675657\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 80.9%\n",
      "Minibatch loss at step 2500: 0.702339\n",
      "Minibatch accuracy: 80.5%\n",
      "Validation accuracy: 80.6%\n",
      "Minibatch loss at step 3000: 0.796859\n",
      "Minibatch accuracy: 78.1%\n",
      "Validation accuracy: 81.6%\n",
      "Test accuracy: 88.4%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 393.349396\n",
      "Minibatch accuracy: 11.7%\n",
      "Validation accuracy: 30.5%\n",
      "Minibatch loss at step 500: 51.456112\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 79.8%\n",
      "Minibatch loss at step 1000: 36.810547\n",
      "Minibatch accuracy: 79.7%\n",
      "Validation accuracy: 80.2%\n",
      "Minibatch loss at step 1500: 29.921005\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 80.3%\n",
      "Minibatch loss at step 2000: 26.010359\n",
      "Minibatch accuracy: 87.5%\n",
      "Validation accuracy: 82.0%\n",
      "Minibatch loss at step 2500: 27.791925\n",
      "Minibatch accuracy: 81.2%\n",
      "Validation accuracy: 82.5%\n",
      "Minibatch loss at step 3000: 23.349836\n",
      "Minibatch accuracy: 84.4%\n",
      "Validation accuracy: 82.9%\n",
      "Test accuracy: 89.9%\n"
     ]
    }
   ],
   "source": [
    "def prediction(tf_dataset, W1, b1, W2, b2):\n",
    "    Y1 = tf.matmul(tf_dataset, W1) + b1\n",
    "    X2 = tf.nn.relu(Y1)\n",
    "    Y2 = tf.matmul(X2, W2) + b2\n",
    "    return tf.nn.softmax(Y2)\n",
    "\n",
    "batch_size = 128\n",
    "num_nodes = 1024\n",
    "beta = 1e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  W1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_nodes]))\n",
    "  b1 = tf.Variable(tf.zeros([num_nodes]))\n",
    "    \n",
    "  W2 = tf.Variable(tf.truncated_normal([num_nodes, num_labels]))\n",
    "  b2 = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "  # Training computation.\n",
    "  Y1 = tf.matmul(tf_train_dataset, W1) + b1\n",
    "  X2 = tf.nn.relu(Y1)\n",
    "  logits = tf.matmul(X2, W2) + b2\n",
    "  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  regularizers = tf.nn.l2_loss(W1) + tf.nn.l2_loss(W2)\n",
    "  loss +=  beta*regularizers\n",
    "  \n",
    "  # Optimizer.\n",
    "  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits)\n",
    "  valid_prediction = prediction(tf_valid_dataset, W1, b1, W2, b2)\n",
    "  test_prediction = prediction(tf_test_dataset, W1, b1, W2, b2)\n",
    "\n",
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "na8xX2yHZzNF"
   },
   "source": [
    "---\n",
    "Problem 2\n",
    "---------\n",
    "Let's demonstrate an extreme case of overfitting. Restrict your training data to just a few batches. What happens?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 283.608490\n",
      "Minibatch accuracy: 12.5%\n",
      "Validation accuracy: 20.1%\n",
      "Minibatch loss at step 100: 32.222389\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 200: 31.901567\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 300: 31.584476\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 400: 31.270300\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 500: 30.959166\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 600: 30.650906\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 700: 30.345928\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 800: 30.044022\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Minibatch loss at step 900: 29.745174\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 56.3%\n",
      "Test accuracy: 61.6%\n"
     ]
    }
   ],
   "source": [
    "batch_size = 16\n",
    "num_nodes = 1024\n",
    "\n",
    "num_train = 100\n",
    "mini_train_dataset = train_dataset[:num_train]\n",
    "mini_train_labels = train_labels[:num_train]\n",
    "\n",
    "num_steps = 1000\n",
    "\n",
    "def prediction(tf_dataset, W1, b1, W2, b2):\n",
    "    Y1 = tf.matmul(tf_dataset, W1) + b1\n",
    "    X2 = tf.nn.relu(Y1)\n",
    "    Y2 = tf.matmul(X2, W2) + b2\n",
    "    return tf.nn.softmax(Y2)\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  W1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_nodes]))\n",
    "  b1 = tf.Variable(tf.zeros([num_nodes]))\n",
    "    \n",
    "  W2 = tf.Variable(tf.truncated_normal([num_nodes, num_labels]))\n",
    "  b2 = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "  # Training computation.\n",
    "  Y1 = tf.matmul(tf_train_dataset, W1) + b1\n",
    "  X2 = tf.nn.relu(Y1)\n",
    "  logits = tf.matmul(X2, W2) + b2\n",
    "  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  regularizers = tf.nn.l2_loss(W1)+ tf.nn.l2_loss(W2)\n",
    "  loss +=  beta*regularizers\n",
    "  \n",
    "  # Optimizer.\n",
    "  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits)\n",
    "  valid_prediction = prediction(tf_valid_dataset, W1, b1, W2, b2)\n",
    "  test_prediction = prediction(tf_test_dataset, W1, b1, W2, b2)\n",
    "\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (mini_train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = mini_train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = mini_train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 100 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ww3SCBUdlkRc"
   },
   "source": [
    "---\n",
    "Problem 3\n",
    "---------\n",
    "Introduce Dropout on the hidden layer of the neural network. Remember: Dropout should only be introduced during training, not evaluation, otherwise your evaluation results would be stochastic as well. TensorFlow provides `nn.dropout()` for that, but you have to make sure it's only inserted during training.\n",
    "\n",
    "What happens to our extreme overfitting case?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 5.226927\n",
      "Minibatch accuracy: 14.8%\n",
      "Validation accuracy: 26.1%\n",
      "Minibatch loss at step 500: 0.832427\n",
      "Minibatch accuracy: 85.9%\n",
      "Validation accuracy: 84.8%\n",
      "Minibatch loss at step 1000: 0.939864\n",
      "Minibatch accuracy: 80.5%\n",
      "Validation accuracy: 85.2%\n",
      "Minibatch loss at step 1500: 0.688759\n",
      "Minibatch accuracy: 88.3%\n",
      "Validation accuracy: 86.2%\n",
      "Minibatch loss at step 2000: 0.751130\n",
      "Minibatch accuracy: 87.5%\n",
      "Validation accuracy: 86.5%\n",
      "Minibatch loss at step 2500: 0.685890\n",
      "Minibatch accuracy: 87.5%\n",
      "Validation accuracy: 86.8%\n",
      "Minibatch loss at step 3000: 0.718394\n",
      "Minibatch accuracy: 84.4%\n",
      "Validation accuracy: 86.7%\n",
      "Minibatch loss at step 3500: 0.710362\n",
      "Minibatch accuracy: 84.4%\n",
      "Validation accuracy: 87.2%\n",
      "Minibatch loss at step 4000: 0.680502\n",
      "Minibatch accuracy: 89.1%\n",
      "Validation accuracy: 87.6%\n",
      "Minibatch loss at step 4500: 0.643781\n",
      "Minibatch accuracy: 88.3%\n",
      "Validation accuracy: 88.0%\n",
      "Minibatch loss at step 5000: 0.634077\n",
      "Minibatch accuracy: 89.8%\n",
      "Validation accuracy: 87.7%\n",
      "Minibatch loss at step 5500: 0.739334\n",
      "Minibatch accuracy: 83.6%\n",
      "Validation accuracy: 87.9%\n",
      "Minibatch loss at step 6000: 0.641728\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 88.2%\n",
      "Minibatch loss at step 6500: 0.512300\n",
      "Minibatch accuracy: 92.2%\n",
      "Validation accuracy: 88.2%\n",
      "Minibatch loss at step 7000: 0.703740\n",
      "Minibatch accuracy: 85.2%\n",
      "Validation accuracy: 88.6%\n",
      "Minibatch loss at step 7500: 0.646085\n",
      "Minibatch accuracy: 85.2%\n",
      "Validation accuracy: 88.5%\n",
      "Minibatch loss at step 8000: 0.812132\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 88.4%\n",
      "Minibatch loss at step 8500: 0.490160\n",
      "Minibatch accuracy: 91.4%\n",
      "Validation accuracy: 88.5%\n",
      "Minibatch loss at step 9000: 0.712511\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 87.5%\n",
      "Minibatch loss at step 9500: 0.490762\n",
      "Minibatch accuracy: 89.8%\n",
      "Validation accuracy: 88.7%\n",
      "Minibatch loss at step 10000: 0.540083\n",
      "Minibatch accuracy: 85.9%\n",
      "Validation accuracy: 88.3%\n",
      "Test accuracy: 94.5%\n"
     ]
    }
   ],
   "source": [
    "def prediction(tf_dataset, W1, b1, W2, b2):\n",
    "    Y1 = tf.matmul(tf_dataset, W1) + b1\n",
    "    X2 = tf.nn.relu(Y1)\n",
    "    Y2 = tf.matmul(X2, W2) + b2\n",
    "    return tf.nn.softmax(Y2)\n",
    "\n",
    "batch_size = 128\n",
    "num_nodes = 1024\n",
    "beta = 1e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  W1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_nodes], stddev=0.1))\n",
    "  b1 = tf.Variable(tf.zeros([num_nodes]))\n",
    "    \n",
    "  W2 = tf.Variable(tf.truncated_normal([num_nodes, num_labels], stddev=0.1))\n",
    "  b2 = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "  keep_prob = tf.placeholder(tf.float32)\n",
    "    \n",
    "  # Training computation.\n",
    "  Y1 = tf.matmul(tf_train_dataset, W1) + b1\n",
    "  X2 = tf.nn.relu(Y1)\n",
    "  X2_drop = tf.nn.dropout(X2, keep_prob)\n",
    "\n",
    "  logits = tf.matmul(X2_drop, W2) + b2\n",
    "  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  regularizers = tf.nn.l2_loss(W1) + tf.nn.l2_loss(W2)\n",
    "  loss += beta*regularizers\n",
    "  \n",
    "  # Optimizer.\n",
    "  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits)\n",
    "  valid_prediction = prediction(tf_valid_dataset, W1, b1, W2, b2)\n",
    "  test_prediction = prediction(tf_test_dataset, W1, b1, W2, b2)\n",
    "\n",
    "num_steps = 10001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels, keep_prob: 0.5}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-b1hTz3VWZjw"
   },
   "source": [
    "---\n",
    "Problem 4\n",
    "---------\n",
    "\n",
    "Try to get the best performance you can using a multi-layer model! The best reported test accuracy using a deep network is [97.1%](http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html?showComment=1391023266211#c8758720086795711595).\n",
    "\n",
    "One avenue you can explore is to add multiple layers.\n",
    "\n",
    "Another one is to use learning rate decay:\n",
    "\n",
    "    global_step = tf.Variable(0)  # count the number of steps taken.\n",
    "    learning_rate = tf.train.exponential_decay(0.5, global_step, ...)\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)\n",
    " \n",
    " ---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2 hidden layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 5.844415\n",
      "Minibatch accuracy: 8.6%\n",
      "Validation accuracy: 23.4%\n",
      "Minibatch loss at step 500: 0.895038\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 85.1%\n",
      "Minibatch loss at step 1000: 0.999021\n",
      "Minibatch accuracy: 83.6%\n",
      "Validation accuracy: 86.1%\n",
      "Minibatch loss at step 1500: 0.751644\n",
      "Minibatch accuracy: 91.4%\n",
      "Validation accuracy: 86.9%\n",
      "Minibatch loss at step 2000: 0.734268\n",
      "Minibatch accuracy: 93.0%\n",
      "Validation accuracy: 87.9%\n",
      "Minibatch loss at step 2500: 0.745342\n",
      "Minibatch accuracy: 89.8%\n",
      "Validation accuracy: 88.4%\n",
      "Minibatch loss at step 3000: 0.842993\n",
      "Minibatch accuracy: 84.4%\n",
      "Validation accuracy: 88.2%\n",
      "Test accuracy: 94.3%\n"
     ]
    }
   ],
   "source": [
    "def prediction(tf_dataset, W1, b1, W2, b2, W3, b3):\n",
    "    Y1 = tf.matmul(tf_dataset, W1) + b1\n",
    "    \n",
    "    X2 = tf.nn.relu(Y1)\n",
    "    Y2 = tf.matmul(X2, W2) + b2\n",
    "    \n",
    "    X3 = tf.nn.relu(Y2)\n",
    "    Y3 = tf.matmul(X3, W3) + b3\n",
    "    \n",
    "    return tf.nn.softmax(Y3)\n",
    "\n",
    "batch_size = 128\n",
    "num_nodes1 = 1024\n",
    "num_nodes2 = 512\n",
    "\n",
    "beta = 1e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  W1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_nodes1],stddev=0.1))\n",
    "  b1 = tf.Variable(tf.zeros([num_nodes1]))\n",
    "  \n",
    "  W2 = tf.Variable(tf.truncated_normal([num_nodes1, num_nodes2],stddev=0.1))\n",
    "  b2 = tf.Variable(tf.zeros([num_nodes2]))\n",
    "\n",
    "  W3 = tf.Variable(tf.truncated_normal([num_nodes2, num_labels],stddev=0.1))\n",
    "  b3 = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "  keep_prob = tf.placeholder(tf.float32)\n",
    "    \n",
    "  # Training computation.\n",
    "  Y1 = tf.matmul(tf_train_dataset, W1) + b1\n",
    "  \n",
    "  X2 = tf.nn.relu(Y1)\n",
    "  X2_drop = tf.nn.dropout(X2, keep_prob)\n",
    "  Y2 = tf.matmul(X2_drop, W2) + b2\n",
    "\n",
    "  X3 = tf.nn.relu(Y2)\n",
    "  X3_drop = tf.nn.dropout(X3, keep_prob)\n",
    "\n",
    "  logits = tf.matmul(X3_drop, W3) + b3\n",
    "  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  regularizers = tf.nn.l2_loss(W1) + tf.nn.l2_loss(W2) + tf.nn.l2_loss(W3)\n",
    "  loss += beta*regularizers\n",
    "  \n",
    "  # Optimizer.\n",
    "  # optimizer = tf.train.GradientDescentOptimizer(0.01).minimize(loss)\n",
    "  global_step = tf.Variable(0)  # count the number of steps taken.\n",
    "  learning_rate = tf.train.exponential_decay(0.5, global_step, 500, 0.96)\n",
    "  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits)\n",
    "  valid_prediction = prediction(tf_valid_dataset, W1, b1, W2, b2, W3, b3)\n",
    "  test_prediction = prediction(tf_test_dataset, W1, b1, W2, b2, W3, b3)\n",
    "\n",
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels, keep_prob: 0.8}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3 hidden layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 9.664207\n",
      "Minibatch accuracy: 10.2%\n",
      "Validation accuracy: 12.2%\n",
      "Minibatch loss at step 5000: 0.945761\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 87.2%\n",
      "Minibatch loss at step 10000: 0.702300\n",
      "Minibatch accuracy: 85.9%\n",
      "Validation accuracy: 88.5%\n",
      "Minibatch loss at step 15000: 0.532235\n",
      "Minibatch accuracy: 88.3%\n",
      "Validation accuracy: 89.4%\n",
      "Minibatch loss at step 20000: 0.614385\n",
      "Minibatch accuracy: 85.9%\n",
      "Validation accuracy: 89.9%\n",
      "Minibatch loss at step 25000: 0.515885\n",
      "Minibatch accuracy: 88.3%\n",
      "Validation accuracy: 90.3%\n",
      "Minibatch loss at step 30000: 0.387454\n",
      "Minibatch accuracy: 92.2%\n",
      "Validation accuracy: 90.8%\n",
      "Test accuracy: 96.0%\n"
     ]
    }
   ],
   "source": [
    "def prediction(tf_dataset, W1, b1, W2, b2, W3, b3, W4, b4):\n",
    "    Y1 = tf.matmul(tf_dataset, W1) + b1\n",
    "    \n",
    "    X2 = tf.nn.relu(Y1)\n",
    "    Y2 = tf.matmul(X2, W2) + b2\n",
    "    \n",
    "    X3 = tf.nn.relu(Y2)\n",
    "    Y3 = tf.matmul(X3, W3) + b3\n",
    "    \n",
    "    X4 = tf.nn.relu(Y3)\n",
    "    Y4 = tf.matmul(X4, W4) + b4\n",
    "    \n",
    "    return tf.nn.softmax(Y4)\n",
    "\n",
    "batch_size = 128\n",
    "num_nodes1 = 1024\n",
    "num_nodes2 = 512\n",
    "num_nodes3 = 64\n",
    "\n",
    "beta = 5e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  W1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_nodes1],stddev=0.1))\n",
    "  b1 = tf.Variable(tf.zeros([num_nodes1]))\n",
    "  \n",
    "  W2 = tf.Variable(tf.truncated_normal([num_nodes1, num_nodes2],stddev=0.1))\n",
    "  b2 = tf.Variable(tf.zeros([num_nodes2]))\n",
    "\n",
    "  W3 = tf.Variable(tf.truncated_normal([num_nodes2, num_nodes3],stddev=0.1))\n",
    "  b3 = tf.Variable(tf.zeros([num_nodes3]))\n",
    "\n",
    "  W4 = tf.Variable(tf.truncated_normal([num_nodes3, num_labels],stddev=0.1))\n",
    "  b4 = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "  keep_prob = tf.placeholder(tf.float32)\n",
    "    \n",
    "  # Training computation.\n",
    "  Y1 = tf.matmul(tf_train_dataset, W1) + b1\n",
    "  \n",
    "  X2 = tf.nn.relu(Y1)\n",
    "  X2_drop = tf.nn.dropout(X2, keep_prob)\n",
    "  Y2 = tf.matmul(X2_drop, W2) + b2\n",
    "  \n",
    "  X3 = tf.nn.relu(Y2)\n",
    "  X3_drop = tf.nn.dropout(X3, keep_prob)\n",
    "  Y3 = tf.matmul(X3_drop, W3) + b3\n",
    "\n",
    "  X4 = tf.nn.relu(Y3)\n",
    "  X4_drop = tf.nn.dropout(X4, keep_prob)\n",
    "\n",
    "  logits = tf.matmul(X4_drop, W4) + b4\n",
    "  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  regularizers = tf.nn.l2_loss(W1) + tf.nn.l2_loss(W2) + tf.nn.l2_loss(W3) + tf.nn.l2_loss(W4)\n",
    "\n",
    "  loss +=  beta*regularizers\n",
    "  \n",
    "  # Optimizer.\n",
    "  global_step = tf.Variable(0)  # count the number of steps taken.\n",
    "  learning_rate = tf.train.exponential_decay(0.5, global_step, 500, 0.96)\n",
    "  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)\n",
    "\n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits)\n",
    "  valid_prediction = prediction(tf_valid_dataset, W1, b1, W2, b2, W3, b3, W4, b4)\n",
    "  test_prediction = prediction(tf_test_dataset, W1, b1, W2, b2, W3, b3, W4, b4)\n",
    "\n",
    "num_steps = 30001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels, keep_prob: 0.5}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 5000 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "default_view": {},
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