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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 2
Previously in 1_notmnist.ipynb, we created a pickle with formatted datasets for training, development and testing on the notMNIST dataset.
The goal of this assignment is to progressively train deeper and more accurate models using TensorFlow.
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:  We're first going to train a multinomial logistic regression using simple gradient descent.
TensorFlow works like this
Step4:  Let's run this computation and iterate
Step5:  Let's now switch to stochastic gradient descent training instead, which is much faster.
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().
Step6:  Let's run it
Step7:  Problem
Turn the logistic regression example with SGD into a 1-hidden layer neural network with rectified linear units nn.relu() and 1024 hidden nodes. This model should improve your validation / test accuracy.
Step8:  Now we actually run the training
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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
from six.moves import range
Explanation: Deep Learning
Assignment 2
Previously in 1_notmnist.ipynb, we created a pickle with formatted datasets for training, development and testing on the notMNIST dataset.
The goal of this assignment is to progressively train deeper and more accurate models using TensorFlow.
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 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]
  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)
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
# With gradient descent training, even this much data is prohibitive.
# Subset the training data for faster turnaround.
train_subset = 10000
graph = tf.Graph()
with graph.as_default():
  # Input data.
  # Load the training, validation and test data into constants that are
  # attached to the graph.
  tf_train_dataset = tf.constant(train_dataset[:train_subset, :])
  tf_train_labels = tf.constant(train_labels[:train_subset])
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)
  
  # Variables.
  # These are the parameters that we are going to be training. The weight
  # matrix will be initialized using random valued following a (truncated)
  # normal distribution. The biases get initialized to zero.
  weights = tf.Variable(
    tf.truncated_normal([image_size * image_size, num_labels]))
  biases = tf.Variable(tf.zeros([num_labels]))
  
  # Training computation.
  # We multiply the inputs with the weight matrix, and add biases. We compute
  # the softmax and cross-entropy (it's one operation in TensorFlow, because
  # it's very common, and it can be optimized). We take the average of this
  # cross-entropy across all training examples: that's our loss.
  logits = tf.matmul(tf_train_dataset, weights) + biases
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
  
  # Optimizer.
  # We are going to find the minimum of this loss using gradient descent.
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
  
  # Predictions for the training, validation, and test data.
  # These are not part of training, but merely here so that we can report
  # accuracy figures as we train.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(
    tf.matmul(tf_valid_dataset, weights) + biases)
  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)
Explanation: We're first going to train a multinomial logistic regression using simple gradient descent.
TensorFlow works like this:
* 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:
  with graph.as_default():
      ...
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:
with tf.Session(graph=graph) as session:
      ...
Let's load all the data into TensorFlow and build the computation graph corresponding to our training:
End of explanation
num_steps = 801
def accuracy(predictions, labels):
  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
          / predictions.shape[0])
with tf.Session(graph=graph) as session:
  # This is a one-time operation which ensures the parameters get initialized as
  # we described in the graph: random weights for the matrix, zeros for the
  # biases. 
  tf.initialize_all_variables().run()
  print('Initialized')
  for step in range(num_steps):
    # Run the computations. We tell .run() that we want to run the optimizer,
    # and get the loss value and the training predictions returned as numpy
    # arrays.
    _, l, predictions = session.run([optimizer, loss, train_prediction])
    if (step % 100 == 0):
      print('Loss at step %d: %f' % (step, l))
      print('Training accuracy: %.1f%%' % accuracy(
        predictions, train_labels[:train_subset, :]))
      # Calling .eval() on valid_prediction is basically like calling run(), but
      # just to get that one numpy array. Note that it recomputes all its graph
      # dependencies.
      print('Validation accuracy: %.1f%%' % accuracy(
        valid_prediction.eval(), valid_labels))
  print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))
Explanation: Let's run this computation and iterate:
End of explanation
batch_size = 128
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 = tf.Variable(
    tf.truncated_normal([image_size * image_size, num_labels]))
  biases = tf.Variable(tf.zeros([num_labels]))
  
  # Training computation.
  logits = tf.matmul(tf_train_dataset, weights) + biases
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
  
  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
  
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(
    tf.matmul(tf_valid_dataset, weights) + biases)
  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)
Explanation: Let's now switch to stochastic gradient descent training instead, which is much faster.
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().
End of explanation
num_steps = 3001
with tf.Session(graph=graph) as session:
  tf.initialize_all_variables().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: Let's run it:
End of explanation
batch_size = 128
num_hidden_nodes = 1024
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, input layer
    w1 = tf.Variable(
    tf.truncated_normal([image_size * image_size, num_hidden_nodes]))
    b1 = tf.Variable(tf.zeros([num_hidden_nodes]))
    # Variables, output layer
    w2 = tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
    b2 = tf.Variable(tf.zeros([num_labels]))
    # Forward propagation
    # To get the prediction, apply softmax to the output of this
    def forward_prop(dataset, w1, b1, w2, b2):
        o1 = tf.nn.softmax(tf.matmul(dataset, w1) + b1)
        output_hidden = tf.nn.relu(o1)
        return tf.matmul(output_hidden, w2) + b2
    train_output = forward_prop(tf_train_dataset, w1, b1, w2, b2)
    
    loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(train_output, tf_train_labels))
    tf.scalar_summary('loss', loss)
    
    # Optimizer.
    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
    # Predictions for the training, validation, and test data.
    train_prediction = tf.nn.softmax(train_output)
    valid_prediction = tf.nn.softmax(forward_prop(tf_valid_dataset, w1, b1, w2, b2))
    test_prediction = tf.nn.softmax(forward_prop(tf_test_dataset, w1, b1, w2, b2))
Explanation: Problem
Turn the logistic regression example with SGD into a 1-hidden layer neural network with rectified linear units nn.relu() and 1024 hidden nodes. This model should improve your validation / test accuracy.
End of explanation
num_steps = 3001
with tf.Session(graph=graph) as session:
    merged = tf.merge_all_summaries()
    train_writer = tf.train.SummaryWriter('logs', graph)
    tf.initialize_all_variables().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}
        summary, _, l, predictions = session.run(
          [merged, optimizer, loss, train_prediction], feed_dict=feed_dict)
        
        if (step % 10 == 0):
            train_writer.add_summary(summary, step)
            
        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: Now we actually run the training
End of explanation
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