Deep Learning

Assignment 4

Previously in 2_fullyconnected.ipynb and 3_regularization.ipynb, we trained fully connected networks to classify notMNIST characters.

The goal of this assignment is make the neural network convolutional.



In [1]:

    
# 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



In [2]:

    
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)









    



Training set (200000, 28, 28) (200000,)
Validation set (10000, 28, 28) (10000,)
Test set (10000, 28, 28) (10000,)

Reformat into a TensorFlow-friendly shape:

convolutions need the image data formatted as a cube (width by height by #channels)
labels as float 1-hot encodings.



In [3]:

    
image_size = 28
num_labels = 10
num_channels = 1 # grayscale

import numpy as np

def reformat(dataset, labels):
  dataset = dataset.reshape(
    (-1, image_size, image_size, num_channels)).astype(np.float32)
  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)









    



Training set (200000, 28, 28, 1) (200000, 10)
Validation set (10000, 28, 28, 1) (10000, 10)
Test set (10000, 28, 28, 1) (10000, 10)



In [4]:

    
def accuracy(predictions, labels):
  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
          / predictions.shape[0])

Let's build a small network with two convolutional layers, followed by one fully connected layer. Convolutional networks are more expensive computationally, so we'll limit its depth and number of fully connected nodes.



In [5]:

    
batch_size = 16
patch_size = 5
depth = 16
num_hidden = 64

graph = tf.Graph()

with graph.as_default():

  # Input data.
  tf_train_dataset = tf.placeholder(
    tf.float32, shape=(batch_size, image_size, image_size, num_channels))
  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.
  layer1_weights = tf.Variable(tf.truncated_normal(
      [patch_size, patch_size, num_channels, depth], stddev=0.1))
  layer1_biases = tf.Variable(tf.zeros([depth]))
  layer2_weights = tf.Variable(tf.truncated_normal(
      [patch_size, patch_size, depth, depth], stddev=0.1))
  layer2_biases = tf.Variable(tf.constant(1.0, shape=[depth]))
  layer3_weights = tf.Variable(tf.truncated_normal(
      [image_size // 4 * image_size // 4 * depth, num_hidden], stddev=0.1))
  layer3_biases = tf.Variable(tf.constant(1.0, shape=[num_hidden]))
  layer4_weights = tf.Variable(tf.truncated_normal(
      [num_hidden, num_labels], stddev=0.1))
  layer4_biases = tf.Variable(tf.constant(1.0, shape=[num_labels]))
  
  # Model.
  def model(data):
    conv = tf.nn.conv2d(data, layer1_weights, [1, 2, 2, 1], padding='SAME')
    hidden = tf.nn.relu(conv + layer1_biases)
    conv = tf.nn.conv2d(hidden, layer2_weights, [1, 2, 2, 1], padding='SAME')
    hidden = tf.nn.relu(conv + layer2_biases)
    shape = hidden.get_shape().as_list()
    reshape = tf.reshape(hidden, [shape[0], shape[1] * shape[2] * shape[3]])
    hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
    return tf.matmul(hidden, layer4_weights) + layer4_biases
  
  # Training computation.
  logits = model(tf_train_dataset)
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))
    
  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(0.05).minimize(loss)
  
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(model(tf_valid_dataset))
  test_prediction = tf.nn.softmax(model(tf_test_dataset))



In [6]:

    
num_steps = 1001

with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print('Initialized')
  for step in range(num_steps):
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    batch_data = train_dataset[offset:(offset + batch_size), :, :, :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    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 % 50 == 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))









    



Initialized
Minibatch loss at step 0: 4.088092
Minibatch accuracy: 6.2%
Validation accuracy: 10.0%
Minibatch loss at step 50: 1.463636
Minibatch accuracy: 56.2%
Validation accuracy: 52.4%
Minibatch loss at step 100: 1.038435
Minibatch accuracy: 62.5%
Validation accuracy: 66.8%
Minibatch loss at step 150: 0.348989
Minibatch accuracy: 87.5%
Validation accuracy: 73.9%
Minibatch loss at step 200: 0.789049
Minibatch accuracy: 75.0%
Validation accuracy: 78.4%
Minibatch loss at step 250: 1.234629
Minibatch accuracy: 62.5%
Validation accuracy: 78.9%
Minibatch loss at step 300: 0.370029
Minibatch accuracy: 87.5%
Validation accuracy: 79.1%
Minibatch loss at step 350: 0.409205
Minibatch accuracy: 93.8%
Validation accuracy: 77.3%
Minibatch loss at step 400: 0.265402
Minibatch accuracy: 100.0%
Validation accuracy: 80.5%
Minibatch loss at step 450: 0.884739
Minibatch accuracy: 87.5%
Validation accuracy: 79.4%
Minibatch loss at step 500: 0.721552
Minibatch accuracy: 87.5%
Validation accuracy: 80.2%
Minibatch loss at step 550: 0.868262
Minibatch accuracy: 75.0%
Validation accuracy: 80.6%
Minibatch loss at step 600: 0.229684
Minibatch accuracy: 93.8%
Validation accuracy: 81.5%
Minibatch loss at step 650: 0.859158
Minibatch accuracy: 75.0%
Validation accuracy: 81.9%
Minibatch loss at step 700: 1.008474
Minibatch accuracy: 62.5%
Validation accuracy: 81.8%
Minibatch loss at step 750: 0.069665
Minibatch accuracy: 100.0%
Validation accuracy: 82.8%
Minibatch loss at step 800: 0.703431
Minibatch accuracy: 75.0%
Validation accuracy: 82.6%
Minibatch loss at step 850: 0.840352
Minibatch accuracy: 81.2%
Validation accuracy: 81.7%
Minibatch loss at step 900: 0.546095
Minibatch accuracy: 81.2%
Validation accuracy: 83.1%
Minibatch loss at step 950: 0.506319
Minibatch accuracy: 87.5%
Validation accuracy: 83.4%
Minibatch loss at step 1000: 0.392565
Minibatch accuracy: 87.5%
Validation accuracy: 82.8%
Test accuracy: 89.8%

Problem 1

The convolutional model above uses convolutions with stride 2 to reduce the dimensionality. Replace the strides by a max pooling operation (nn.max_pool()) of stride 2 and kernel size 2.

With adding the max_pool of stride 2 and kernel size 2 and increasing num_of_steps, the performance has improved from 89.8 to 93.3%



In [7]:

    
batch_size = 16
patch_size = 5
depth = 16
num_hidden = 64

graph = tf.Graph()

with graph.as_default():

  # Input data.
  tf_train_dataset = tf.placeholder(
    tf.float32, shape=(batch_size, image_size, image_size, num_channels))
  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.
  layer1_weights = tf.Variable(tf.truncated_normal(
      [patch_size, patch_size, num_channels, depth], stddev=0.1))
  layer1_biases = tf.Variable(tf.zeros([depth]))
  layer2_weights = tf.Variable(tf.truncated_normal(
      [patch_size, patch_size, depth, depth], stddev=0.1))
  layer2_biases = tf.Variable(tf.constant(1.0, shape=[depth]))
  layer3_weights = tf.Variable(tf.truncated_normal(
      [image_size // 4 * image_size // 4 * depth, num_hidden], stddev=0.1))
  layer3_biases = tf.Variable(tf.constant(1.0, shape=[num_hidden]))
  layer4_weights = tf.Variable(tf.truncated_normal(
      [num_hidden, num_labels], stddev=0.1))
  layer4_biases = tf.Variable(tf.constant(1.0, shape=[num_labels]))
  
  # Model.
  def model(data):
    conv = tf.nn.conv2d(data, layer1_weights, [1, 2, 2, 1], padding='SAME')
    hidden = tf.nn.relu(conv + layer1_biases)
    # Adding the max pool
    max_pool = tf.nn.max_pool(hidden, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')
    conv = tf.nn.conv2d(hidden, layer2_weights, [1, 2, 2, 1], padding='SAME')
    hidden = tf.nn.relu(conv + layer2_biases)
    max_pool = tf.nn.max_pool(hidden, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')
    shape = hidden.get_shape().as_list()
    reshape = tf.reshape(hidden, [shape[0], shape[1] * shape[2] * shape[3]])
    hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
    return tf.matmul(hidden, layer4_weights) + layer4_biases
  
  # Training computation.
  logits = model(tf_train_dataset)
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))
    
  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(0.05).minimize(loss)
  
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(model(tf_valid_dataset))
  test_prediction = tf.nn.softmax(model(tf_test_dataset))



In [8]:

    
num_steps = 5001

with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print('Initialized')
  for step in range(num_steps):
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    batch_data = train_dataset[offset:(offset + batch_size), :, :, :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    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 % 250 == 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))









    



Initialized
Minibatch loss at step 0: 3.246793
Minibatch accuracy: 6.2%
Validation accuracy: 11.4%
Minibatch loss at step 250: 1.070142
Minibatch accuracy: 62.5%
Validation accuracy: 77.4%
Minibatch loss at step 500: 0.644496
Minibatch accuracy: 87.5%
Validation accuracy: 80.8%
Minibatch loss at step 750: 0.087890
Minibatch accuracy: 100.0%
Validation accuracy: 82.2%
Minibatch loss at step 1000: 0.346607
Minibatch accuracy: 87.5%
Validation accuracy: 82.8%
Minibatch loss at step 1250: 0.542959
Minibatch accuracy: 81.2%
Validation accuracy: 83.4%
Minibatch loss at step 1500: 0.662297
Minibatch accuracy: 81.2%
Validation accuracy: 84.2%
Minibatch loss at step 1750: 0.478397
Minibatch accuracy: 81.2%
Validation accuracy: 84.9%
Minibatch loss at step 2000: 0.047928
Minibatch accuracy: 100.0%
Validation accuracy: 85.0%
Minibatch loss at step 2250: 0.578277
Minibatch accuracy: 81.2%
Validation accuracy: 85.4%
Minibatch loss at step 2500: 0.821100
Minibatch accuracy: 75.0%
Validation accuracy: 85.7%
Minibatch loss at step 2750: 1.148358
Minibatch accuracy: 75.0%
Validation accuracy: 85.8%
Minibatch loss at step 3000: 0.716762
Minibatch accuracy: 87.5%
Validation accuracy: 85.8%
Minibatch loss at step 3250: 0.309506
Minibatch accuracy: 87.5%
Validation accuracy: 86.4%
Minibatch loss at step 3500: 0.330827
Minibatch accuracy: 87.5%
Validation accuracy: 86.1%
Minibatch loss at step 3750: 0.674126
Minibatch accuracy: 87.5%
Validation accuracy: 86.5%
Minibatch loss at step 4000: 0.426180
Minibatch accuracy: 81.2%
Validation accuracy: 86.7%
Minibatch loss at step 4250: 0.516610
Minibatch accuracy: 81.2%
Validation accuracy: 86.8%
Minibatch loss at step 4500: 0.667352
Minibatch accuracy: 81.2%
Validation accuracy: 86.9%
Minibatch loss at step 4750: 0.861585
Minibatch accuracy: 62.5%
Validation accuracy: 86.6%
Minibatch loss at step 5000: 1.121639
Minibatch accuracy: 75.0%
Validation accuracy: 86.8%
Test accuracy: 93.3%

Problem 2

Try to get the best performance you can using a convolutional net. Look for example at the classic LeNet5 architecture, adding Dropout, and/or adding learning rate decay.