Deep Learning with TensorFlow¶
Credits: Forked from TensorFlow by Google
Setup¶
Refer to the setup instructions.
Exercise 6¶
After training a skip-gram model in 5_word2vec.ipynb, the goal of this exercise is to train a LSTM character model over Text8 data.
# These are all the modules we'll be using later. Make sure you can import them
# before proceeding further.
import os
import numpy as np
import random
import string
import tensorflow as tf
import urllib
import zipfile
url = 'http://mattmahoney.net/dc/'
def maybe_download(filename, expected_bytes):
"""Download a file if not present, and make sure it's the right size."""
if not os.path.exists(filename):
filename, _ = urllib.urlretrieve(url + filename, filename)
statinfo = os.stat(filename)
if statinfo.st_size == expected_bytes:
print 'Found and verified', filename
else:
print statinfo.st_size
raise Exception(
'Failed to verify ' + filename + '. Can you get to it with a browser?')
return filename
filename = maybe_download('text8.zip', 31344016)
def read_data(filename):
f = zipfile.ZipFile(filename)
for name in f.namelist():
return f.read(name)
f.close()
text = read_data(filename)
print "Data size", len(text)
Create a small validation set.
valid_size = 1000
valid_text = text[:valid_size]
train_text = text[valid_size:]
train_size = len(train_text)
print train_size, train_text[:64]
print valid_size, valid_text[:64]
Utility functions to map characters to vocabulary IDs and back.
vocabulary_size = len(string.ascii_lowercase) + 1 # [a-z] + ' '
first_letter = ord(string.ascii_lowercase[0])
def char2id(char):
if char in string.ascii_lowercase:
return ord(char) - first_letter + 1
elif char == ' ':
return 0
else:
print 'Unexpected character:', char
return 0
def id2char(dictid):
if dictid > 0:
return chr(dictid + first_letter - 1)
else:
return ' '
print char2id('a'), char2id('z'), char2id(' '), char2id('ï')
print id2char(1), id2char(26), id2char(0)
Function to generate a training batch for the LSTM model.
batch_size=64
num_unrollings=10
class BatchGenerator(object):
def __init__(self, text, batch_size, num_unrollings):
self._text = text
self._text_size = len(text)
self._batch_size = batch_size
self._num_unrollings = num_unrollings
segment = self._text_size / batch_size
self._cursor = [ offset * segment for offset in xrange(batch_size)]
self._last_batch = self._next_batch()
def _next_batch(self):
"""Generate a single batch from the current cursor position in the data."""
batch = np.zeros(shape=(self._batch_size, vocabulary_size), dtype=np.float)
for b in xrange(self._batch_size):
batch[b, char2id(self._text[self._cursor[b]])] = 1.0
self._cursor[b] = (self._cursor[b] + 1) % self._text_size
return batch
def next(self):
"""Generate the next array of batches from the data. The array consists of
the last batch of the previous array, followed by num_unrollings new ones.
"""
batches = [self._last_batch]
for step in xrange(self._num_unrollings):
batches.append(self._next_batch())
self._last_batch = batches[-1]
return batches
def characters(probabilities):
"""Turn a 1-hot encoding or a probability distribution over the possible
characters back into its (mostl likely) character representation."""
return [id2char(c) for c in np.argmax(probabilities, 1)]
def batches2string(batches):
"""Convert a sequence of batches back into their (most likely) string
representation."""
s = [''] * batches[0].shape[0]
for b in batches:
s = [''.join(x) for x in zip(s, characters(b))]
return s
train_batches = BatchGenerator(train_text, batch_size, num_unrollings)
valid_batches = BatchGenerator(valid_text, 1, 1)
print batches2string(train_batches.next())
print batches2string(train_batches.next())
print batches2string(valid_batches.next())
print batches2string(valid_batches.next())
def logprob(predictions, labels):
"""Log-probability of the true labels in a predicted batch."""
predictions[predictions < 1e-10] = 1e-10
return np.sum(np.multiply(labels, -np.log(predictions))) / labels.shape[0]
def sample_distribution(distribution):
"""Sample one element from a distribution assumed to be an array of normalized
probabilities.
"""
r = random.uniform(0, 1)
s = 0
for i in xrange(len(distribution)):
s += distribution[i]
if s >= r:
return i
return len(distribution) - 1
def sample(prediction):
"""Turn a (column) prediction into 1-hot encoded samples."""
p = np.zeros(shape=[1, vocabulary_size], dtype=np.float)
p[0, sample_distribution(prediction[0])] = 1.0
return p
def random_distribution():
"""Generate a random column of probabilities."""
b = np.random.uniform(0.0, 1.0, size=[1, vocabulary_size])
return b/np.sum(b, 1)[:,None]
Simple LSTM Model.
num_nodes = 64
graph = tf.Graph()
with graph.as_default():
# Parameters:
# Input gate: input, previous output, and bias.
ix = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))
im = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))
ib = tf.Variable(tf.zeros([1, num_nodes]))
# Forget gate: input, previous output, and bias.
fx = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))
fm = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))
fb = tf.Variable(tf.zeros([1, num_nodes]))
# Memory cell: input, state and bias.
cx = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))
cm = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))
cb = tf.Variable(tf.zeros([1, num_nodes]))
# Output gate: input, previous output, and bias.
ox = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))
om = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))
ob = tf.Variable(tf.zeros([1, num_nodes]))
# Variables saving state across unrollings.
saved_output = tf.Variable(tf.zeros([batch_size, num_nodes]), trainable=False)
saved_state = tf.Variable(tf.zeros([batch_size, num_nodes]), trainable=False)
# Classifier weights and biases.
w = tf.Variable(tf.truncated_normal([num_nodes, vocabulary_size], -0.1, 0.1))
b = tf.Variable(tf.zeros([vocabulary_size]))
# Definition of the cell computation.
def lstm_cell(i, o, state):
"""Create a LSTM cell. See e.g.: http://arxiv.org/pdf/1402.1128v1.pdf
Note that in this formulation, we omit the various connections between the
previous state and the gates."""
input_gate = tf.sigmoid(tf.matmul(i, ix) + tf.matmul(o, im) + ib)
forget_gate = tf.sigmoid(tf.matmul(i, fx) + tf.matmul(o, fm) + fb)
update = tf.matmul(i, cx) + tf.matmul(o, cm) + cb
state = forget_gate * state + input_gate * tf.tanh(update)
output_gate = tf.sigmoid(tf.matmul(i, ox) + tf.matmul(o, om) + ob)
return output_gate * tf.tanh(state), state
# Input data.
train_data = list()
for _ in xrange(num_unrollings + 1):
train_data.append(
tf.placeholder(tf.float32, shape=[batch_size,vocabulary_size]))
train_inputs = train_data[:num_unrollings]
train_labels = train_data[1:] # labels are inputs shifted by one time step.
# Unrolled LSTM loop.
outputs = list()
output = saved_output
state = saved_state
for i in train_inputs:
output, state = lstm_cell(i, output, state)
outputs.append(output)
# State saving across unrollings.
with tf.control_dependencies([saved_output.assign(output),
saved_state.assign(state)]):
# Classifier.
logits = tf.nn.xw_plus_b(tf.concat(0, outputs), w, b)
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(
logits, tf.concat(0, train_labels)))
# Optimizer.
global_step = tf.Variable(0)
learning_rate = tf.train.exponential_decay(
10.0, global_step, 5000, 0.1, staircase=True)
optimizer = tf.train.GradientDescentOptimizer(learning_rate)
gradients, v = zip(*optimizer.compute_gradients(loss))
gradients, _ = tf.clip_by_global_norm(gradients, 1.25)
optimizer = optimizer.apply_gradients(
zip(gradients, v), global_step=global_step)
# Predictions.
train_prediction = tf.nn.softmax(logits)
# Sampling and validation eval: batch 1, no unrolling.
sample_input = tf.placeholder(tf.float32, shape=[1, vocabulary_size])
saved_sample_output = tf.Variable(tf.zeros([1, num_nodes]))
saved_sample_state = tf.Variable(tf.zeros([1, num_nodes]))
reset_sample_state = tf.group(
saved_sample_output.assign(tf.zeros([1, num_nodes])),
saved_sample_state.assign(tf.zeros([1, num_nodes])))
sample_output, sample_state = lstm_cell(
sample_input, saved_sample_output, saved_sample_state)
with tf.control_dependencies([saved_sample_output.assign(sample_output),
saved_sample_state.assign(sample_state)]):
sample_prediction = tf.nn.softmax(tf.nn.xw_plus_b(sample_output, w, b))
num_steps = 7001
summary_frequency = 100
with tf.Session(graph=graph) as session:
tf.global_variables_initializer().run()
print 'Initialized'
mean_loss = 0
for step in xrange(num_steps):
batches = train_batches.next()
feed_dict = dict()
for i in xrange(num_unrollings + 1):
feed_dict[train_data[i]] = batches[i]
_, l, predictions, lr = session.run(
[optimizer, loss, train_prediction, learning_rate], feed_dict=feed_dict)
mean_loss += l
if step % summary_frequency == 0:
if step > 0:
mean_loss = mean_loss / summary_frequency
# The mean loss is an estimate of the loss over the last few batches.
print 'Average loss at step', step, ':', mean_loss, 'learning rate:', lr
mean_loss = 0
labels = np.concatenate(list(batches)[1:])
print 'Minibatch perplexity: %.2f' % float(
np.exp(logprob(predictions, labels)))
if step % (summary_frequency * 10) == 0:
# Generate some samples.
print '=' * 80
for _ in xrange(5):
feed = sample(random_distribution())
sentence = characters(feed)[0]
reset_sample_state.run()
for _ in xrange(79):
prediction = sample_prediction.eval({sample_input: feed})
feed = sample(prediction)
sentence += characters(feed)[0]
print sentence
print '=' * 80
# Measure validation set perplexity.
reset_sample_state.run()
valid_logprob = 0
for _ in xrange(valid_size):
b = valid_batches.next()
predictions = sample_prediction.eval({sample_input: b[0]})
valid_logprob = valid_logprob + logprob(predictions, b[1])
print 'Validation set perplexity: %.2f' % float(np.exp(
valid_logprob / valid_size))
Problem 1¶
You might have noticed that the definition of the LSTM cell involves 4 matrix multiplications with the input, and 4 matrix multiplications with the output. Simplify the expression by using a single matrix multiply for each, and variables that are 4 times larger.
Problem 2¶
We want to train a LSTM over bigrams, that is pairs of consecutive characters like ‘ab’ instead of single characters like ‘a’. Since the number of possible bigrams is large, feeding them directly to the LSTM using 1-hot encodings will lead to a very sparse representation that is very wasteful computationally.
a- Introduce an embedding lookup on the inputs, and feed the embeddings to the LSTM cell instead of the inputs themselves.
b- Write a bigram-based LSTM, modeled on the character LSTM above.
c- Introduce Dropout. For best practices on how to use Dropout in LSTMs, refer to this article.
Problem 3¶
(difficult!)
Write a sequence-to-sequence LSTM which mirrors all the words in a sentence. For example, if your input is:
the quick brown fox
the model should attempt to output:
eht kciuq nworb xof
Reference: http://arxiv.org/abs/1409.3215