fully_connected.ipynb

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    "Assignment 2\n",
    "=============\n",
    "<span style=\"color: lightsteelblue;\">Udacity university | Deep Learning</span>\n",
    "\n",
    "Previously in `1_notmnist.ipynb`, we created a pickle with formatted datasets for training, development and testing on the [notMNIST dataset](http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html).\n",
    "\n",
    "The goal of this assignment is to progressively train deeper and more accurate models using TensorFlow."
   ]
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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\n",
    "from six.moves import range"
   ]
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   "source": [
    "First reload the data we generated in `1_notmnist.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"
     ]
    }
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   "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 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]\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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    "We're first going to train a multinomial logistic regression using simple gradient descent.\n",
    "\n",
    "TensorFlow works like this:\n",
    "* First you describe the computation that you want to see performed: what the inputs, the variables, and the operations look like. These get created as nodes over a computation graph. This description is all contained within the block below:\n",
    "\n",
    "      with graph.as_default():\n",
    "          ...\n",
    "\n",
    "* Then you can run the operations on this graph as many times as you want by calling `session.run()`, providing it outputs to fetch from the graph that get returned. This runtime operation is all contained in the block below:\n",
    "\n",
    "      with tf.Session(graph=graph) as session:\n",
    "          ...\n",
    "\n",
    "Let's load all the data into TensorFlow and build the computation graph corresponding to our training:"
   ]
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    "# With gradient descent training, even this much data is prohibitive.\n",
    "# Subset the training data for faster turnaround.\n",
    "train_subset = 10000\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data.\n",
    "  # Load the training, validation and test data into constants that are\n",
    "  # attached to the graph.\n",
    "  tf_train_dataset = tf.constant(train_dataset[:train_subset, :])\n",
    "  tf_train_labels = tf.constant(train_labels[:train_subset])\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  # These are the parameters that we are going to be training. The weight\n",
    "  # matrix will be initialized using random values following a (truncated)\n",
    "  # normal distribution. The biases get initialized to zero.\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",
    "  # We multiply the inputs with the weight matrix, and add biases. We compute\n",
    "  # the softmax and cross-entropy (it's one operation in TensorFlow, because\n",
    "  # it's very common, and it can be optimized). We take the average of this\n",
    "  # cross-entropy across all training examples: that's our loss.\n",
    "  logits = tf.matmul(tf_train_dataset, weights) + biases\n",
    "  loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))\n",
    "  \n",
    "  # Optimizer.\n",
    "  # We are going to find the minimum of this loss using gradient descent.\n",
    "  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  # These are not part of training, but merely here so that we can report\n",
    "  # accuracy figures as we train.\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)"
   ]
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   "source": [
    "Let's run this computation and iterate:"
   ]
  },
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     "text": [
      "Initialized\n",
      "Loss at step 0: 19.773006\n",
      "Training accuracy: 10.4%\n",
      "Validation accuracy: 11.7%\n",
      "Loss at step 100: 2.231696\n",
      "Training accuracy: 71.7%\n",
      "Validation accuracy: 70.6%\n",
      "Loss at step 200: 1.816425\n",
      "Training accuracy: 74.9%\n",
      "Validation accuracy: 72.9%\n",
      "Loss at step 300: 1.590114\n",
      "Training accuracy: 76.2%\n",
      "Validation accuracy: 73.7%\n",
      "Loss at step 400: 1.434095\n",
      "Training accuracy: 76.9%\n",
      "Validation accuracy: 74.0%\n",
      "Loss at step 500: 1.316440\n",
      "Training accuracy: 77.7%\n",
      "Validation accuracy: 74.2%\n",
      "Loss at step 600: 1.222754\n",
      "Training accuracy: 78.4%\n",
      "Validation accuracy: 74.3%\n",
      "Loss at step 700: 1.145384\n",
      "Training accuracy: 78.9%\n",
      "Validation accuracy: 74.4%\n",
      "Loss at step 800: 1.079941\n",
      "Training accuracy: 79.3%\n",
      "Validation accuracy: 74.5%\n",
      "Test accuracy: 82.1%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 801\n",
    "\n",
    "def accuracy(predictions, labels):\n",
    "  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))\n",
    "          / predictions.shape[0])\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  # This is a one-time operation which ensures the parameters get initialized as\n",
    "  # we described in the graph: random weights for the matrix, zeros for the\n",
    "  # biases. \n",
    "  tf.global_variables_initializer().run()\n",
    "  print('Initialized')\n",
    "  for step in range(num_steps):\n",
    "    # Run the computations. We tell .run() that we want to run the optimizer,\n",
    "    # and get the loss value and the training predictions returned as numpy\n",
    "    # arrays.\n",
    "    _, l, predictions = session.run([optimizer, loss, train_prediction])\n",
    "    if (step % 100 == 0):\n",
    "      print('Loss at step %d: %f' % (step, l))\n",
    "      print('Training accuracy: %.1f%%' % accuracy(\n",
    "        predictions, train_labels[:train_subset, :]))\n",
    "      # Calling .eval() on valid_prediction is basically like calling run(), but\n",
    "      # just to get that one numpy array. Note that it recomputes all its graph\n",
    "      # dependencies.\n",
    "      print('Validation accuracy: %.1f%%' % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Let's now switch to stochastic gradient descent training instead, which is much faster.\n",
    "\n",
    "The graph will be similar, except that instead of holding all the training data into a constant node, we create a `Placeholder` node which will be fed actual data at every call of `session.run()`."
   ]
  },
  {
   "cell_type": "code",
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    "batch_size = 128\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(labels=tf_train_labels, logits=logits))\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)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Let's run it:"
   ]
  },
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     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 14.635202\n",
      "Minibatch accuracy: 9.4%\n",
      "Validation accuracy: 13.9%\n",
      "Minibatch loss at step 500: 1.331702\n",
      "Minibatch accuracy: 75.8%\n",
      "Validation accuracy: 75.5%\n",
      "Minibatch loss at step 1000: 1.496699\n",
      "Minibatch accuracy: 78.1%\n",
      "Validation accuracy: 76.6%\n",
      "Minibatch loss at step 1500: 0.899035\n",
      "Minibatch accuracy: 79.7%\n",
      "Validation accuracy: 77.1%\n",
      "Minibatch loss at step 2000: 0.642580\n",
      "Minibatch accuracy: 84.4%\n",
      "Validation accuracy: 77.6%\n",
      "Minibatch loss at step 2500: 1.052673\n",
      "Minibatch accuracy: 75.0%\n",
      "Validation accuracy: 78.2%\n",
      "Minibatch loss at step 3000: 0.915904\n",
      "Minibatch accuracy: 76.6%\n",
      "Validation accuracy: 78.9%\n",
      "Test accuracy: 86.9%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.global_variables_initializer().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))"
   ]
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   "source": [
    "---\n",
    "Problem\n",
    "-------\n",
    "\n",
    "Turn the logistic regression example with SGD into a 1-hidden layer neural network with rectified linear units [nn.relu()](https://www.tensorflow.org/versions/r0.7/api_docs/python/nn.html#relu) and 1024 hidden nodes. This model should improve your validation / test accuracy.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution\n",
    "\n",
    "To get more sense on what the RELU's nodes are I will try out two implementations of neural model:\n",
    "- 1-node RELU\n",
    "- 1024-nodes RELU\n",
    "\n",
    "### 1-node RELUs\n",
    "\n",
    "So, first let us tune the graph to use one hidden layer and 1-node RELU."
   ]
  },
  {
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   "source": [
    "batch_size = 128\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",
    "  # Hidden layer\n",
    "  hidden_weights = tf.truncated_normal([image_size * image_size, num_labels])\n",
    "  hidden_biases = tf.zeros([num_labels])\n",
    "\n",
    "  # Variables.\n",
    "  weights = tf.Variable(tf.nn.relu(hidden_weights))\n",
    "  biases = tf.Variable(tf.nn.relu(hidden_biases))\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(labels=tf_train_labels, logits=logits))\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)"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "And then let us decrease the number of steps and run the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
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     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 13.040080\n",
      "Minibatch accuracy: 5.5%\n",
      "Validation accuracy: 9.5%\n",
      "Minibatch loss at step 500: 0.790344\n",
      "Minibatch accuracy: 81.2%\n",
      "Validation accuracy: 78.0%\n",
      "Minibatch loss at step 1000: 0.871097\n",
      "Minibatch accuracy: 80.5%\n",
      "Validation accuracy: 78.8%\n",
      "Minibatch loss at step 1500: 0.600124\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 79.6%\n",
      "Test accuracy: 87.0%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 1501\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.global_variables_initializer().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": [
    "### 1024-nodes RELUs\n",
    "\n",
    "Now let us alter the graph to use 1024-nodes RELU."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 128\n",
    "num_nodes = 1024\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",
    "  # Hidden layer variables\n",
    "  hidden_weights = tf.Variable(tf.truncated_normal([image_size * image_size, num_nodes]))\n",
    "  hidden_biases = tf.Variable(tf.zeros([num_nodes]))\n",
    "\n",
    "  # Variables\n",
    "  weights = tf.Variable(tf.truncated_normal([num_nodes, num_labels]))\n",
    "  biases = tf.Variable(tf.zeros([num_labels]))\n",
    "\n",
    "  # Training computation.\n",
    "  hidden_layer_train = tf.nn.relu(tf.matmul(tf_train_dataset, hidden_weights) + hidden_biases)\n",
    "  logits = tf.matmul(hidden_layer_train, weights) + biases\n",
    "  loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))\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",
    "\n",
    "  hidden_layer_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, hidden_weights) + hidden_biases)\n",
    "  valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(hidden_layer_valid, weights) + biases)\n",
    "\n",
    "  hidden_layer_test= tf.nn.relu(tf.matmul(tf_test_dataset, hidden_weights) + hidden_biases)\n",
    "  test_prediction = tf.nn.softmax(\n",
    "    tf.matmul(hidden_layer_test, weights) + biases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then let us decrease the number of steps and run the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 353.067444\n",
      "Minibatch accuracy: 14.1%\n",
      "Validation accuracy: 31.6%\n",
      "Minibatch loss at step 500: 14.566813\n",
      "Minibatch accuracy: 80.5%\n",
      "Validation accuracy: 80.3%\n",
      "Minibatch loss at step 1000: 13.723660\n",
      "Minibatch accuracy: 79.7%\n",
      "Validation accuracy: 79.7%\n",
      "Minibatch loss at step 1500: 8.505621\n",
      "Minibatch accuracy: 89.1%\n",
      "Validation accuracy: 79.7%\n",
      "Minibatch loss at step 2000: 3.880274\n",
      "Minibatch accuracy: 85.9%\n",
      "Validation accuracy: 81.4%\n",
      "Minibatch loss at step 2500: 3.830812\n",
      "Minibatch accuracy: 82.8%\n",
      "Validation accuracy: 82.0%\n",
      "Minibatch loss at step 3000: 2.502412\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 81.9%\n",
      "Test accuracy: 89.5%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.global_variables_initializer().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": [
    "## Conclusion\n",
    "\n",
    "### 1-node RELUs\n",
    "\n",
    "As a result, we got roughly the same accuracy but much faster - it took twice less steps.\n",
    "\n",
    "So, *much faster* - good job!\n",
    "\n",
    "### 1024-nodes RELUs\n",
    "\n",
    "Training proceeded about **10 times slower**. But we got significant increase in accuracy.\n",
    "\n",
    "So, *much more accurate* - great job!"
   ]
  }
 ],
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