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
First reload the data we generated in 1_notmnist.ipynb.
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)
Reformat into a shape that's more adapted to the models we're going to train:
In [3]:
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)
In [4]:
def accuracy(predictions, labels):
return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
/ predictions.shape[0])
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.
In [5]:
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)
# Setting the beta value as 0.001
beta_l2_reg = tf.constant(1e-3)
# 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
# new loss for L2 Regularization is L' = L + beta * l2_loss(weights)
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits)) \
+ beta_l2_reg * tf.nn.l2_loss(weights)
# 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)
In [6]:
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))
In [7]:
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)
# Setting the beta value as 0.001
beta_l2_reg = tf.constant(1e-3)
# Variables.
weights = {
'hidden': tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes])),
'output': tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
}
biases = {
'hidden': tf.Variable(tf.zeros([num_hidden_nodes])),
'output': tf.Variable(tf.zeros([num_labels]))
}
# Training computation.
hidden_train = tf.nn.relu(tf.matmul(tf_train_dataset, weights['hidden']) + biases['hidden'])
logits = tf.matmul(hidden_train, weights['output']) + biases['output']
# Adding l2_loss of weights for hidden and output summed up multiplied by beta_l2_reg to the loss
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=tf_train_labels)) + \
beta_l2_reg * (tf.nn.l2_loss(weights['hidden']) + tf.nn.l2_loss(weights['output']))
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits)
hidden_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights['hidden']) + biases['hidden'])
valid_prediction = tf.nn.softmax(tf.matmul(hidden_valid, weights['output']) + biases['output'])
hidden_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights['hidden']) + biases['hidden'])
test_prediction = tf.nn.softmax(tf.matmul(hidden_test, weights['output']) + biases['output'])
In [8]:
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))
Try the neural network model with less number of batches, no L2 Regularization and observe the pattern of Mini batch accuracy reaches 100 % - i.e. overfitting, loss becomes 0 and there is no change in accuracy of validation batch.
In [9]:
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.
weights = {
'hidden': tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes])),
'output': tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
}
biases = {
'hidden': tf.Variable(tf.zeros([num_hidden_nodes])),
'output': tf.Variable(tf.zeros([num_labels]))
}
# Training computation.
hidden_train = tf.nn.relu(tf.matmul(tf_train_dataset, weights['hidden']) + biases['hidden'])
logits = tf.matmul(hidden_train, weights['output']) + biases['output']
# Adding l2_loss of weights for hidden and output summed up multiplied by beta_l2_reg to the loss
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=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)
hidden_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights['hidden']) + biases['hidden'])
valid_prediction = tf.nn.softmax(tf.matmul(hidden_valid, weights['output']) + biases['output'])
hidden_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights['hidden']) + biases['hidden'])
test_prediction = tf.nn.softmax(tf.matmul(hidden_test, weights['output']) + biases['output'])
In [12]:
num_steps = 201
num_batches = 4
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)
# Changing the offset value to run for less number of batches
# Dividing the step by num_branches
offset = ((step % num_batches) * 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 % 10 == 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))
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?
Now let's try to introduce dropout at the hidden layer, i.e after building hidden layer, construct new hidden layer with the drop out.
In [13]:
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.
weights = {
'hidden': tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes])),
'output': tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
}
biases = {
'hidden': tf.Variable(tf.zeros([num_hidden_nodes])),
'output': tf.Variable(tf.zeros([num_labels]))
}
# Training computation.
hidden_train = tf.nn.relu(tf.matmul(tf_train_dataset, weights['hidden']) + biases['hidden'])
# Seeting half of them to zero
hidden_train_with_dropout = tf.nn.dropout(hidden_train, 0.5)
logits = tf.matmul(hidden_train, weights['output']) + biases['output']
# Adding l2_loss of weights for hidden and output summed up multiplied by beta_l2_reg to the loss
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=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)
hidden_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights['hidden']) + biases['hidden'])
valid_prediction = tf.nn.softmax(tf.matmul(hidden_valid, weights['output']) + biases['output'])
hidden_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights['hidden']) + biases['hidden'])
test_prediction = tf.nn.softmax(tf.matmul(hidden_test, weights['output']) + biases['output'])
In [14]:
num_steps = 201
num_batches = 4
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)
# Changing the offset value to run for less number of batches
# Dividing the step by num_branches
offset = ((step % num_batches) * 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 % 10 == 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))
You can notice after introducing Dropout even if we achieve 100% accuracy at one stage, the next stage is not overfit, and there is change and improvement in both validation and test accuracy.
Try to get the best performance you can using a multi-layer model! The best reported test accuracy using a deep network is 97.1%.
One avenue you can explore is to add multiple layers.
Another one is to use learning rate decay:
global_step = tf.Variable(0) # count the number of steps taken.
learning_rate = tf.train.exponential_decay(0.5, global_step, ...)
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
Lets build multi-layer neural network model i.e. with more hidden layers including L2 Regularization and dropout.
In [33]:
batch_size = 128
num_hidden_nodes_1 = 1024
num_hidden_nodes_2 = 256
num_hidden_nodes_3 = 128
dropout_prob = 0.5
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)
beta_l2_reg = tf.constant(1e-3)
global_step = tf.Variable(0)
# Variables.
weights = {
'hidden_1': tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes_1],
stddev=np.sqrt(2.0 / (image_size * image_size)))),
'hidden_2': tf.Variable(tf.truncated_normal([num_hidden_nodes_1, num_hidden_nodes_2],
stddev=np.sqrt(2.0 / (num_hidden_nodes_1)))),
'hidden_3': tf.Variable(tf.truncated_normal([num_hidden_nodes_2, num_hidden_nodes_3],
stddev=np.sqrt(2.0 / (num_hidden_nodes_2)))),
'output': tf.Variable(tf.truncated_normal([num_hidden_nodes_3, num_labels],
stddev=np.sqrt(2.0 / (num_hidden_nodes_3))))
}
biases = {
'hidden_1': tf.Variable(tf.zeros([num_hidden_nodes_1])),
'hidden_2': tf.Variable(tf.zeros([num_hidden_nodes_2])),
'hidden_3': tf.Variable(tf.zeros([num_hidden_nodes_3])),
'output': tf.Variable(tf.zeros([num_labels]))
}
# Training computation. 1st hidden layer
hidden_train_1 = tf.nn.relu(tf.matmul(tf_train_dataset, weights['hidden_1']) + biases['hidden_1'])
# Dropout - Seeting half of them to zero
hidden_train_1_with_dropout = tf.nn.dropout(hidden_train_1, dropout_prob)
# 2nd Hidden Layer
hidden_train_2 = tf.nn.relu(tf.matmul(hidden_train_1_with_dropout, weights['hidden_2']) + biases['hidden_2'])
hidden_train_2_with_dropout = tf.nn.dropout(hidden_train_2, dropout_prob)
# 3rd hidden layer
hidden_train_3 = tf.nn.relu(tf.matmul(hidden_train_2_with_dropout, weights['hidden_3']) + biases['hidden_3'])
hidden_train_3_with_dropout = tf.nn.dropout(hidden_train_3, dropout_prob)
logits = tf.matmul(hidden_train_3_with_dropout, weights['output']) + biases['output']
# Adding l2_loss of weights for hidden and output summed up multiplied by beta_l2_reg to the loss
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=tf_train_labels)) + \
beta_l2_reg * (tf.nn.l2_loss(weights['hidden_1']) + tf.nn.l2_loss(weights['hidden_2']) + \
tf.nn.l2_loss(weights['hidden_3']) + tf.nn.l2_loss(weights['output']))
# Optimizer.
learning_rate = tf.train.exponential_decay(0.5, global_step, 4000, 0.65, staircase=True)
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
#optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits)
hidden_1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights['hidden_1']) + biases['hidden_1'])
hidden_2_valid = tf.nn.relu(tf.matmul(hidden_1_valid, weights['hidden_2']) + biases['hidden_2'])
hidden_3_valid = tf.nn.relu(tf.matmul(hidden_2_valid, weights['hidden_3']) + biases['hidden_3'])
valid_prediction = tf.nn.softmax(tf.matmul(hidden_3_valid, weights['output']) + biases['output'])
# Testing
hidden_1_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights['hidden_1']) + biases['hidden_1'])
hidden_2_test = tf.nn.relu(tf.matmul(hidden_1_test, weights['hidden_2']) + biases['hidden_2'])
hidden_3_test = tf.nn.relu(tf.matmul(hidden_2_test, weights['hidden_3']) + biases['hidden_3'])
test_prediction = tf.nn.softmax(tf.matmul(hidden_3_test, weights['output']) + biases['output'])
In [34]:
num_steps = 18001
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))
Improved Performance and reached 95% using multi-layer neural net, by fine tuning the parameters