Credits: Forked from TensorFlow by Google
Refer to the setup instructions.
Previously in 2_fullyconnected.ipynb, you trained a logistic regression and a neural network model.
The goal of this exercise is to explore regularization techniques.
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# These are all the modules we'll be using later. Make sure you can import them
# before proceeding further.
import cPickle as pickle
import numpy as np
import tensorflow as tf
First reload the data we generated in notmist.ipynb.
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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:
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image_size = 28
num_labels = 10
def reformat(dataset, labels):
dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
# Map 2 to [0.0, 1.0, 0.0 ...], 3 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
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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 compue the L2 loss for a tensor t using nn.l2_loss(t). The right amount of regularization should improve your validation / test accuracy.
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import numpy as np
import tensorflow as tf
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batch_size = 128
image_size = 28
num_labels = 10
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=(None, 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.
l1_size = 1000
l2_size = 30
weights_l1 = tf.Variable(
tf.truncated_normal([image_size * image_size, l1_size],seed=1))
biases_l1 = tf.Variable(tf.zeros([l1_size]))
weights_output = tf.Variable(
tf.truncated_normal([l1_size ,num_labels],seed=1))
biases_output = tf.Variable(tf.zeros([num_labels]))
# Training computation.
l1_output = tf.nn.relu(tf.matmul(tf_train_dataset,weights_l1) + biases_l1)
logits = tf.matmul(l1_output, weights_output) + biases_output
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels)) + tf.nn.l2_loss(weights_l1)*.01
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
train_prediction = tf.nn.softmax(logits)
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num_steps = 3001
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print "Initialized"
for step in xrange(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 = session.run(
[optimizer, loss], feed_dict=feed_dict)
if (step % 500 == 0):
print "Minibatch loss at step", step, ":", l
print "Valid_dataset Set Validation",accuracy(
session.run(train_prediction,feed_dict={tf_train_dataset:valid_dataset,}),valid_labels)
print "Testing Set Validation",accuracy(
session.run(train_prediction,feed_dict={tf_train_dataset:test_dataset,}),test_labels)
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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?
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batch_size = 128
image_size = 28
num_labels = 10
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=(None, 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.
l1_size = 1000
l2_size = 30
weights_l1 = tf.Variable(
tf.truncated_normal([image_size * image_size, l1_size],seed=1))
biases_l1 = tf.Variable(tf.zeros([l1_size]))
weights_output = tf.Variable(
tf.truncated_normal([l1_size ,num_labels],seed=1))
biases_output = tf.Variable(tf.zeros([num_labels]))
# Training computation.
drop_weights_l1 = tf.nn.dropout(weights_l1,keep_prob=0.5)
drop_l1_output = tf.nn.relu(tf.matmul(tf_train_dataset,drop_weights_l1) + biases_l1)
drop_logits = tf.matmul(drop_l1_output, weights_output) + biases_output
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(drop_logits, tf_train_labels)) + tf.nn.l2_loss(drop_weights_l1)*.01
# prediction graph
l1_output = tf.nn.relu(tf.matmul(tf_train_dataset,weights_l1) + biases_l1)
logits = tf.matmul(l1_output, weights_output) + biases_output
train_prediction = tf.nn.softmax(logits)
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
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num_steps = 3001
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print "Initialized"
for step in xrange(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 = session.run(
[optimizer, loss], feed_dict=feed_dict)
if (step % 500 == 0):
print "Minibatch loss at step", step, ":", l
print "Valid_dataset Set Validation",accuracy(
session.run(train_prediction,feed_dict={tf_train_dataset:valid_dataset,}),valid_labels)
print "Testing Set Validation",accuracy(
session.run(train_prediction,feed_dict={tf_train_dataset:test_dataset,}),test_labels)
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, step, ...)
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
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