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









    



e:\python36\lib\site-packages\h5py\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  from ._conv import register_converters as _register_converters



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): #data of shape [batch_size, image_size, image_size, num_channels]
    conv = tf.nn.conv2d(data, layer1_weights, [1, 2, 2, 1], padding='SAME') # shape of [batch_size, image_size/2, image_size/2, depth]
    hidden = tf.nn.relu(conv + layer1_biases)
    conv = tf.nn.conv2d(hidden, layer2_weights, [1, 2, 2, 1], padding='SAME')# shape of [batch_size, image_size/4, image_size/4, depth]
    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]])# shape of [batch_size, image_size/4 * image_size/4* depth]
    hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases) # shape of [batch_size,num_hidden]
    return tf.matmul(hidden, layer4_weights) + layer4_biases # shape of [batch_size,num_labels]
  
  # 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))









    



WARNING:tensorflow:From <ipython-input-5-3b42a02b2811>:45: softmax_cross_entropy_with_logits (from tensorflow.python.ops.nn_ops) is deprecated and will be removed in a future version.
Instructions for updating:

Future major versions of TensorFlow will allow gradients to flow
into the labels input on backprop by default.

See tf.nn.softmax_cross_entropy_with_logits_v2.



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: 3.709145
Minibatch accuracy: 6.2%
Validation accuracy: 10.0%
Minibatch loss at step 50: 2.161718
Minibatch accuracy: 18.8%
Validation accuracy: 30.7%
Minibatch loss at step 100: 1.252872
Minibatch accuracy: 68.8%
Validation accuracy: 54.6%
Minibatch loss at step 150: 0.562339
Minibatch accuracy: 87.5%
Validation accuracy: 72.9%
Minibatch loss at step 200: 0.551096
Minibatch accuracy: 81.2%
Validation accuracy: 75.1%
Minibatch loss at step 250: 0.741751
Minibatch accuracy: 81.2%
Validation accuracy: 74.1%
Minibatch loss at step 300: 0.855445
Minibatch accuracy: 68.8%
Validation accuracy: 78.1%
Minibatch loss at step 350: 0.653634
Minibatch accuracy: 75.0%
Validation accuracy: 79.4%
Minibatch loss at step 400: 0.857386
Minibatch accuracy: 75.0%
Validation accuracy: 79.8%
Minibatch loss at step 450: 0.531369
Minibatch accuracy: 93.8%
Validation accuracy: 80.3%
Minibatch loss at step 500: 0.498323
Minibatch accuracy: 81.2%
Validation accuracy: 78.8%
Minibatch loss at step 550: 0.764663
Minibatch accuracy: 68.8%
Validation accuracy: 80.6%
Minibatch loss at step 600: 0.949739
Minibatch accuracy: 81.2%
Validation accuracy: 80.7%
Minibatch loss at step 650: 0.728670
Minibatch accuracy: 75.0%
Validation accuracy: 82.0%
Minibatch loss at step 700: 0.591814
Minibatch accuracy: 81.2%
Validation accuracy: 81.1%
Minibatch loss at step 750: 0.259869
Minibatch accuracy: 93.8%
Validation accuracy: 83.0%
Minibatch loss at step 800: 0.581929
Minibatch accuracy: 81.2%
Validation accuracy: 82.8%
Minibatch loss at step 850: 0.733538
Minibatch accuracy: 68.8%
Validation accuracy: 83.1%
Minibatch loss at step 900: 0.883641
Minibatch accuracy: 75.0%
Validation accuracy: 82.9%
Minibatch loss at step 950: 0.959609
Minibatch accuracy: 68.8%
Validation accuracy: 82.7%
Minibatch loss at step 1000: 0.553311
Minibatch accuracy: 81.2%
Validation accuracy: 83.3%
Test accuracy: 88.9%

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.



In [ ]:

    
# Variables.
  layer3_weights = tf.Variable(tf.truncated_normal(
      [image_size // 2 * image_size // 2 * num_channels, 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):
    # Data is shaped of [batch_size, image_size, image_size, num_channels]
    hidden = tf.nn.max_pool(data, [1, 2, 2, 1],[1, 2, 2, 1] , padding='SAME') #same shape of [batch_size, image_size/2, image_size/2, num_channels]
    shape = hidden.get_shape().as_list() 
    reshape = tf.reshape(hidden, [shape[0], shape[1] * shape[2] * shape[3]]) #reshaped into 2D array of [batch_size, image_size/2* image_size/2 * num_channels]
    hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
    return tf.matmul(hidden, layer4_weights) + layer4_biases

Output

Initialized
Minibatch loss at step 0: 2.694045
Minibatch accuracy: 0.0%
Validation accuracy: 7.9%
Minibatch loss at step 50: 1.684043
Minibatch accuracy: 50.0%
Validation accuracy: 65.4%
Minibatch loss at step 100: 0.953076
Minibatch accuracy: 81.2%
Validation accuracy: 70.7%
Minibatch loss at step 150: 0.509777
Minibatch accuracy: 87.5%
Validation accuracy: 76.1%
Minibatch loss at step 200: 0.464738
Minibatch accuracy: 87.5%
Validation accuracy: 78.0%
Minibatch loss at step 250: 0.875403
Minibatch accuracy: 75.0%
Validation accuracy: 78.1%
Minibatch loss at step 300: 0.913955
Minibatch accuracy: 75.0%
Validation accuracy: 80.6%
Minibatch loss at step 350: 0.677745
Minibatch accuracy: 75.0%
Validation accuracy: 80.3%
Minibatch loss at step 400: 0.772082
Minibatch accuracy: 68.8%
Validation accuracy: 80.2%
Minibatch loss at step 450: 0.742608
Minibatch accuracy: 93.8%
Validation accuracy: 81.0%
Minibatch loss at step 500: 0.643120
Minibatch accuracy: 81.2%
Validation accuracy: 80.2%
Minibatch loss at step 550: 0.628266
Minibatch accuracy: 75.0%
Validation accuracy: 80.5%
Minibatch loss at step 600: 0.979889
Minibatch accuracy: 81.2%
Validation accuracy: 80.8%
Minibatch loss at step 650: 0.581403
Minibatch accuracy: 87.5%
Validation accuracy: 81.0%
Minibatch loss at step 700: 0.751648
Minibatch accuracy: 75.0%
Validation accuracy: 80.5%
Minibatch loss at step 750: 0.344367
Minibatch accuracy: 87.5%
Validation accuracy: 81.4%
Minibatch loss at step 800: 0.698404
Minibatch accuracy: 87.5%
Validation accuracy: 81.8%
Minibatch loss at step 850: 0.795159
Minibatch accuracy: 68.8%
Validation accuracy: 81.2%
Minibatch loss at step 900: 0.890547
Minibatch accuracy: 75.0%
Validation accuracy: 80.8%
Minibatch loss at step 950: 1.138554
Minibatch accuracy: 75.0%
Validation accuracy: 81.2%
Minibatch loss at step 1000: 0.733926
Minibatch accuracy: 81.2%
Validation accuracy: 81.4%
Test accuracy: 87.4%

We can see that the max_pool on its own is not too bad at all, without any convolution and it is much faster to compute.

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.

2.1 Simple LeNet Idea

Conv2D + max-pool + Conv2D + max-pool + full-network + output



In [ ]:

    
# 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(
      [math.ceil(image_size / 16)  * math.ceil(image_size /16) * 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') # shape of [batch_size, image_size/2, image_size/2, depth]: [16, 14, 14, 16]
    shape1 = conv.get_shape().as_list()
    hidden = tf.nn.relu(conv + layer1_biases)
    hidden1 = tf.nn.max_pool(hidden, [1, 2, 2, 1], [1, 2, 2, 1] , padding='SAME') #shape of [batch_size, image_size/4, image_size/4, depth]: [16, 7, 7, 16]
    shape2 = hidden1.get_shape().as_list()

    conv = tf.nn.conv2d(hidden1, layer2_weights, [1, 2, 2, 1], padding='SAME') #shape of [batch_size, image_size/8, image_size/8, depth]: [16, 4, 4, 16]
    shape3 = conv.get_shape().as_list()
    hidden = tf.nn.relu(conv + layer2_biases)
    hidden2 = tf.nn.max_pool(hidden, [1, 2, 2, 1],[1, 2, 2, 1] , padding='SAME') #same shape of [batch_size, image_size/16, image_size/16, depth]: [16, 2, 2, 16]

    shape = hidden2.get_shape().as_list()
    reshape = tf.reshape(hidden2, [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

Result is not that much better with the same 1000 steps

Minibatch loss at step 1000: 0.579025
Minibatch accuracy: 81.2%
Validation accuracy: 82.5%
LeNet5 Test accuracy: 88.1%

However, adding the max pooling does reduce the size of layer3_weights significantly, thus reducing computation time.

Run it 10 times longer: improved results

Minibatch loss at step 10000: 0.395700
Minibatch accuracy: 87.5%
Validation accuracy: 88.2%
LeNet5 Test accuracy: 93.5%

2.2 Add Dropout

Only adding dropout at the last layer does not seem to help much

shape = hidden2.get_shape().as_list()
    reshape = tf.reshape(hidden2, [shape[0], shape[1] * shape[2] * shape[3]])
    hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
    dropout = tf.nn.dropout(hidden, keep_rate) #dropout if applied after activation

    return tf.matmul(dropout, layer4_weights) + layer4_biases

  # Training computation.
  logits = model(tf_train_dataset, keep_rate = 0.5)

output:

Minibatch loss at step 10000: 0.389177
Minibatch accuracy: 81.2%
Validation accuracy: 87.2%
LeNet5 Test accuracy: 92.5%

2.3 Add Learning Rate Decay

# Optimizer.
  global_step = tf.Variable(0)  # count the number of steps taken.
  learning_rate = tf.train.exponential_decay(0.1, global_step, 3500, 0.86, staircase=True)
  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)

Not much help:

Minibatch loss at step 10000: 0.640076
Minibatch accuracy: 75.0%
Validation accuracy: 86.9%
LeNet5 Test accuracy: 92.7%



In [ ]: