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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Deep Learning
Assignment 3
Previously in 2_fullyconnected.ipynb, you trained a logistic regression and a neural network model.
The goal of this assignment is to explore regularization techniques.
Step1:  First reload the data we generated in 1_notmnist.ipynb.
Step2:  Reformat into a shape that's more adapted to the models we're going to train
Step3:  Problem 1
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.
Step4:  Problem 2
Let's demonstrate an extreme case of overfitting. Restrict your training data to just a few batches. What happens?
Step5:  Problem 3
Introduce Dropout on the hidden layer of the neural network. Remember
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Python Code:
# These are all the modules we'll be using later. Make sure you can import them
# before proceeding further.
from __future__ import print_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle
Explanation: Deep Learning
Assignment 3
Previously in 2_fullyconnected.ipynb, you trained a logistic regression and a neural network model.
The goal of this assignment is to explore regularization techniques.
End of explanation
pickle_file = 'notMNIST.pickle'
with open(pickle_file, 'rb') as f:
  save = pickle.load(f)
  train_dataset = save['train_dataset']
  train_labels = save['train_labels']
  valid_dataset = save['valid_dataset']
  valid_labels = save['valid_labels']
  test_dataset = save['test_dataset']
  test_labels = save['test_labels']
  del save  # hint to help gc free up memory
  print('Training set', train_dataset.shape, train_labels.shape)
  print('Validation set', valid_dataset.shape, valid_labels.shape)
  print('Test set', test_dataset.shape, test_labels.shape)
Explanation: First reload the data we generated in 1_notmnist.ipynb.
End of explanation
image_size = 28
num_labels = 10
def reformat(dataset, labels):
  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
  # Map 1 to [0.0, 1.0, 0.0 ...], 2 to [0.0, 0.0, 1.0 ...]
  labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
  return dataset, labels
train_dataset, train_labels = reformat(train_dataset, train_labels)
valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)
test_dataset, test_labels = reformat(test_dataset, test_labels)
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)
def accuracy(predictions, labels):
  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
          / predictions.shape[0])
Explanation: Reformat into a shape that's more adapted to the models we're going to train:
- data as a flat matrix,
- labels as float 1-hot encodings.
End of explanation
batch_size = 128
hidden_nodes = 1024
learning_rate = 0.5
beta = 0.005
graph = tf.Graph()
with graph.as_default():
  # Input data. For the training data, we use a placeholder that will be fed
  # at run time with a training minibatch.
  tf_train_dataset = tf.placeholder(tf.float32,
                                    shape=(batch_size, image_size * image_size))
  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)
  
  # Variables.
  weights_1 = tf.Variable(
    tf.truncated_normal([image_size * image_size, hidden_nodes]))
  biases_1 = tf.Variable(tf.zeros([hidden_nodes]))
  weights_2 = tf.Variable(
    tf.truncated_normal([hidden_nodes, num_labels]))
  biases_2 = tf.Variable(tf.zeros([num_labels]))
  
  # Training computation.
  def forward_prop(input):
    h1 = tf.nn.relu(tf.matmul(input, weights_1) + biases_1)
    return tf.matmul(h1, weights_2) + biases_2
  
  logits = forward_prop(tf_train_dataset)
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
  # Add the regularization term to the loss.
  loss += beta * (tf.nn.l2_loss(weights_1) + tf.nn.l2_loss(weights_2))
  
  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)
  
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(forward_prop(tf_valid_dataset))
  test_prediction = tf.nn.softmax(forward_prop(tf_test_dataset))
num_steps = 3001
with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print("Initialized")
  for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    # Generate a minibatch.
    batch_data = train_dataset[offset:(offset + batch_size), :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
    _, l, predictions = session.run([optimizer, loss, train_prediction], feed_dict=feed_dict)
    if (step % 500 == 0):
      print("Minibatch loss at step %d: %f" % (step, l))
      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
      print("Validation accuracy: %.1f%%" % accuracy(valid_prediction.eval(), valid_labels))
  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))
Explanation: Problem 1
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.
End of explanation
train_dataset_restricted = train_dataset[:130, :]
train_labels_restricted = train_labels[:130, :]
num_steps = 3001
with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print("Initialized")
  for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
    offset = (step * batch_size) % (train_labels_restricted.shape[0] - batch_size)
    # Generate a minibatch.
    batch_data = train_dataset_restricted[offset:(offset + batch_size), :]
    batch_labels = train_labels_restricted[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
    _, l, predictions = session.run([optimizer, loss, train_prediction], feed_dict=feed_dict)
    if (step % 500 == 0):
      print("Minibatch loss at step %d: %f" % (step, l))
      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
      print("Validation accuracy: %.1f%%" % accuracy(valid_prediction.eval(), valid_labels))
  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))
Explanation: Problem 2
Let's demonstrate an extreme case of overfitting. Restrict your training data to just a few batches. What happens?
End of explanation
batch_size = 128
hidden_nodes_1 = 1024
hidden_nodes_2 = 1024
learning_rate = 0.0001
beta = 0.005
graph = tf.Graph()
with graph.as_default():
  # Input data. For the training data, we use a placeholder that will be fed
  # at run time with a training minibatch.
  tf_train_dataset = tf.placeholder(tf.float32,
                                    shape=(batch_size, image_size * image_size))
  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)
  
  # Placeholder to control dropout probability.
  keep_prob = tf.placeholder(tf.float32)
  # Variables.
  weights_1 = tf.Variable(tf.random_normal([image_size * image_size, hidden_nodes_1]))
  biases_1 = tf.Variable(tf.zeros([hidden_nodes_1]))
  weights_2 = tf.Variable(tf.random_normal([hidden_nodes_1, hidden_nodes_2]))
  biases_2 = tf.Variable(tf.zeros([hidden_nodes_2]))
  weights_out = tf.Variable(tf.random_normal([hidden_nodes_2, num_labels]))
  biases_out = tf.Variable(tf.zeros([num_labels]))
  
  # Training computation.
  def forward_prop(input):
    h1 = tf.nn.dropout(tf.nn.relu(tf.matmul(input, weights_1) + biases_1), keep_prob)
    h2 = tf.nn.dropout(tf.nn.relu(tf.matmul(   h1, weights_2) + biases_2), keep_prob)
    return tf.matmul(h2, weights_out) + biases_out
  
  logits = forward_prop(tf_train_dataset)
  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
  # Add the regularization term to the loss.
  loss += beta * (tf.nn.l2_loss(weights_1) + tf.nn.l2_loss(weights_2) + tf.nn.l2_loss(weights_out))
  
  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)
#  optimizer = tf.train.AdamOptimizer(0.001).minimize(loss)
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(forward_prop(tf_valid_dataset))
  test_prediction = tf.nn.softmax(forward_prop(tf_test_dataset))
num_steps = 5001
with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print("Initialized")
  for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    # Generate a minibatch.
    batch_data = train_dataset[offset:(offset + batch_size), :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels, keep_prob: 1.0}
    feed_dict_w_drop = {tf_train_dataset : batch_data, tf_train_labels : batch_labels, keep_prob: 0.5}
    _, l, predictions = session.run([optimizer, loss, train_prediction], feed_dict=feed_dict_w_drop)
    if (step % 500 == 0):
      print("Minibatch loss at step %d: %f" % (step, l))
      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
      print("Validation accuracy: %.1f%%" % accuracy(valid_prediction.eval(feed_dict=feed_dict), valid_labels))
  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(feed_dict=feed_dict), test_labels))
Explanation: Problem 3
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.
What happens to our extreme overfitting case?
End of explanation
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