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 [35]:
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 [6]:
batch_size = 128
beta = 0.005
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(labels=tf_train_labels, logits=logits)
+ beta*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 [7]:
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 [36]:
batch_size = 128
beta=0.005
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_layer_1 = tf.Variable(
tf.truncated_normal([image_size * image_size, num_labels]))
biases_layer_1 = tf.Variable(tf.zeros([num_labels]))
# Layer 2 weights have an input dimension = output of first layer
weights_layer_2 = tf.Variable(
tf.truncated_normal([num_labels, num_labels]))
biases_layer_2 = tf.Variable(tf.zeros([num_labels]))
# Training computation.
logits_layer_1 = tf.matmul(tf_train_dataset, weights_layer_1) + biases_layer_1
relu_output = tf.nn.relu(logits_layer_1)
logits_layer_2 = tf.matmul(relu_output, weights_layer_2) + biases_layer_2
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits_layer_2)
+ beta*tf.nn.l2_loss(weights_layer_1)
+ beta*tf.nn.l2_loss(weights_layer_2)
)
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits_layer_2)
logits_l_1_valid = tf.matmul(tf_valid_dataset, weights_layer_1) + biases_layer_1
relu_valid = tf.nn.relu(logits_l_1_valid)
logits_l_2_valid = tf.matmul(relu_valid, weights_layer_2) + biases_layer_2
valid_prediction = tf.nn.softmax(logits_l_2_valid)
logits_l_1_test = tf.matmul(tf_test_dataset, weights_layer_1) + biases_layer_1
relu_test = tf.nn.relu(logits_l_1_test)
logits_l_2_test = tf.matmul(relu_test, weights_layer_2) + biases_layer_2
test_prediction = tf.nn.softmax(logits_l_2_test)
In [37]:
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))
beta = 0.01 - Test accuracy: 88.7% beta = 0.5 - Test accuracy: 45.9% (and slow) beta = 0.005 - Test accuracy: 89.2% beta = 0.001 - Test accuracy: 89.2% beta = 0.0001 - Test accuracy: 85.7%
In [11]:
num_steps = 3001
#Restrict training data
reduced_train_dataset = train_dataset[:640, :]
reduced_train_labels = train_labels[:640, :]
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) % (reduced_train_labels.shape[0] - batch_size)
# Generate a minibatch.
batch_data = reduced_train_dataset[offset:(offset + batch_size), :]
batch_labels = reduced_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))
Restricted to 1000 samples in each batch - we get quick convergence and 100% accuracy on the mini-batch but poor performance on the validation dataset and poorer performance on the unseen test dataset.
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?
In [12]:
batch_size = 128
beta=0.005
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_layer_1 = tf.Variable(
tf.truncated_normal([image_size * image_size, num_labels]))
biases_layer_1 = tf.Variable(tf.zeros([num_labels]))
# Layer 2 weights have an input dimension = output of first layer
weights_layer_2 = tf.Variable(
tf.truncated_normal([num_labels, num_labels]))
biases_layer_2 = tf.Variable(tf.zeros([num_labels]))
# Training computation.
logits_layer_1 = tf.matmul(tf_train_dataset, weights_layer_1) + biases_layer_1
relu_output = tf.nn.relu(logits_layer_1)
# Introduce dropout - probability feature is kept is passed as a variable
keep_probability = tf.placeholder(tf.float32)
dropout_output = tf.nn.dropout(relu_output, keep_probability)
logits_layer_2 = tf.matmul(dropout_output, weights_layer_2) + biases_layer_2
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits_layer_2)
+ beta*tf.nn.l2_loss(weights_layer_1)
+ beta*tf.nn.l2_loss(weights_layer_2)
)
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits_layer_2)
logits_l_1_valid = tf.matmul(tf_valid_dataset, weights_layer_1) + biases_layer_1
relu_valid = tf.nn.relu(logits_l_1_valid)
logits_l_2_valid = tf.matmul(relu_valid, weights_layer_2) + biases_layer_2
valid_prediction = tf.nn.softmax(logits_l_2_valid)
logits_l_1_test = tf.matmul(tf_test_dataset, weights_layer_1) + biases_layer_1
relu_test = tf.nn.relu(logits_l_1_test)
logits_l_2_test = tf.matmul(relu_test, weights_layer_2) + biases_layer_2
test_prediction = tf.nn.softmax(logits_l_2_test)
In [13]:
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, keep_probability: 0.5}
_, 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))
Dropout doesn't improve performance for me - maybe I'm applying it wrong - getting test accuracy of 80%.
Try on reduced batch size data below:
In [14]:
num_steps = 3001
#Restrict training data
reduced_train_dataset = train_dataset[:640, :]
reduced_train_labels = train_labels[:640, :]
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) % (reduced_train_labels.shape[0] - batch_size)
# Generate a minibatch.
batch_data = reduced_train_dataset[offset:(offset + batch_size), :]
batch_labels = reduced_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, keep_probability: 0.5}
_, 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))
Does reduce overfitting but does not increase 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)
Try adding an additional layer:
In [26]:
batch_size = 128
beta=0.005
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=(None, num_labels))
# Variables.
weights_layer_1 = tf.Variable(
tf.truncated_normal([image_size * image_size, num_labels]))
biases_layer_1 = tf.Variable(tf.zeros([num_labels]))
# Layer 2 weights have an input dimension = output of first layer
weights_layer_2 = tf.Variable(
tf.truncated_normal([num_labels, num_labels]))
biases_layer_2 = tf.Variable(tf.zeros([num_labels]))
# Layer 3
weights_layer_3 = tf.Variable(
tf.truncated_normal([num_labels, num_labels]))
biases_layer_3 = tf.Variable(tf.zeros([num_labels]))
# Training computation.
# Compute layer 1
logits_layer_1 = tf.matmul(tf_train_dataset, weights_layer_1) + biases_layer_1
relu_output_1 = tf.nn.relu(logits_layer_1)
# Introduce dropout - probability feature is kept is passed as a variable
keep_probability = tf.placeholder(tf.float32)
dropout_output_1 = tf.nn.dropout(relu_output_1, keep_probability)
# Compute layer 2
logits_layer_2 = tf.matmul(dropout_output_1, weights_layer_2) + biases_layer_2
relu_output_2 = tf.nn.relu(logits_layer_2)
dropout_output_2 = tf.nn.dropout(relu_output_2, keep_probability)
# Computer layer 3
logits_layer_3 = tf.matmul(dropout_output_2, weights_layer_3) + biases_layer_3
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits_layer_3)
+ beta*tf.nn.l2_loss(weights_layer_1)
+ beta*tf.nn.l2_loss(weights_layer_2)
+ beta*tf.nn.l2_loss(weights_layer_3)
)
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the data.
train_prediction = tf.nn.softmax(logits_layer_3)
# Determine accuracy
correct_prediction = tf.equal(tf.argmax(train_prediction,1), tf.argmax(tf_train_labels,1))
accuracy_calc = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))*100
In [32]:
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, keep_probability: 1.0}
_, l, accuracy = session.run(
[optimizer, loss, accuracy_calc], feed_dict=feed_dict
)
if (step % 500 == 0):
print("Minibatch loss at step %d: %f" % (step, l))
print("Minibatch accuracy: %.1f%%" % accuracy)
valid_feed_dict = {tf_train_dataset : valid_dataset, tf_train_labels : valid_labels, keep_probability: 1.0}
print("Validation accuracy: %.1f%%" % accuracy_calc.eval(feed_dict=valid_feed_dict))
test_feed_dict = {tf_train_dataset : test_dataset, tf_train_labels : test_labels, keep_probability: 1.0}
print("Test accuracy: %.1f%%" % accuracy_calc.eval(feed_dict=test_feed_dict))
87.2 with 3 layers and no dropout
Dies at 10% accuracy with 0.5 dropout - is it basically destroying all the information?
Yes even with 0.9 keep probability - only get 25%
My code may be wrong somehow.
In [43]:
batch_size = 128
beta=0.005
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_layer_1 = tf.Variable(
tf.truncated_normal([image_size * image_size, num_labels]))
biases_layer_1 = tf.Variable(tf.zeros([num_labels]))
# Layer 2 weights have an input dimension = output of first layer
weights_layer_2 = tf.Variable(
tf.truncated_normal([num_labels, num_labels]))
biases_layer_2 = tf.Variable(tf.zeros([num_labels]))
# Training computation.
logits_layer_1 = tf.matmul(tf_train_dataset, weights_layer_1) + biases_layer_1
relu_output = tf.nn.relu(logits_layer_1)
logits_layer_2 = tf.matmul(relu_output, weights_layer_2) + biases_layer_2
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits_layer_2)
+ beta*tf.nn.l2_loss(weights_layer_1)
+ beta*tf.nn.l2_loss(weights_layer_2)
)
# Optimizer.
global_step = tf.Variable(0) # count the number of steps taken.
learning_rate = tf.train.exponential_decay(0.5, global_step, 100, 0.96)
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits_layer_2)
logits_l_1_valid = tf.matmul(tf_valid_dataset, weights_layer_1) + biases_layer_1
relu_valid = tf.nn.relu(logits_l_1_valid)
logits_l_2_valid = tf.matmul(relu_valid, weights_layer_2) + biases_layer_2
valid_prediction = tf.nn.softmax(logits_l_2_valid)
logits_l_1_test = tf.matmul(tf_test_dataset, weights_layer_1) + biases_layer_1
relu_test = tf.nn.relu(logits_l_1_test)
logits_l_2_test = tf.matmul(relu_test, weights_layer_2) + biases_layer_2
test_prediction = tf.nn.softmax(logits_l_2_test)
In [44]:
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))
Got 89.9% - with rate decay every 500 steps
In [ ]: