Chapter 14 – Recurrent Neural Networks
This notebook contains all the sample code and solutions to the exercises in chapter 14.
First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:
In [1]:
# To support both python 2 and python 3
from __future__ import division, print_function, unicode_literals
# Common imports
import numpy as np
import os
# to make this notebook's output stable across runs
def reset_graph(seed=42):
tf.reset_default_graph()
tf.set_random_seed(seed)
np.random.seed(seed)
# To plot pretty figures
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
# Where to save the figures
PROJECT_ROOT_DIR = "."
CHAPTER_ID = "rnn"
def save_fig(fig_id, tight_layout=True):
path = os.path.join(PROJECT_ROOT_DIR, "images", CHAPTER_ID, fig_id + ".png")
print("Saving figure", fig_id)
if tight_layout:
plt.tight_layout()
plt.savefig(path, format='png', dpi=300)
Then of course we will need TensorFlow:
In [2]:
import tensorflow as tf
In [3]:
reset_graph()
n_inputs = 3
n_neurons = 5
X0 = tf.placeholder(tf.float32, [None, n_inputs])
X1 = tf.placeholder(tf.float32, [None, n_inputs])
Wx = tf.Variable(tf.random_normal(shape=[n_inputs, n_neurons],dtype=tf.float32))
Wy = tf.Variable(tf.random_normal(shape=[n_neurons,n_neurons],dtype=tf.float32))
b = tf.Variable(tf.zeros([1, n_neurons], dtype=tf.float32))
Y0 = tf.tanh(tf.matmul(X0, Wx) + b)
Y1 = tf.tanh(tf.matmul(Y0, Wy) + tf.matmul(X1, Wx) + b)
init = tf.global_variables_initializer()
In [4]:
import numpy as np
X0_batch = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8], [9, 0, 1]]) # t = 0
X1_batch = np.array([[9, 8, 7], [0, 0, 0], [6, 5, 4], [3, 2, 1]]) # t = 1
with tf.Session() as sess:
init.run()
Y0_val, Y1_val = sess.run([Y0, Y1], feed_dict={X0: X0_batch, X1: X1_batch})
In [5]:
print(Y0_val)
In [6]:
print(Y1_val)
Note: tf.contrib.rnn was partially moved to the core API in TensorFlow 1.2. Most of the *Cell and *Wrapper classes are now available in tf.nn.rnn_cell, and the tf.contrib.rnn.static_rnn() function is available as tf.nn.static_rnn().
In [7]:
n_inputs = 3
n_neurons = 5
In [8]:
reset_graph()
X0 = tf.placeholder(tf.float32, [None, n_inputs])
X1 = tf.placeholder(tf.float32, [None, n_inputs])
basic_cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
output_seqs, states = tf.nn.static_rnn(basic_cell, [X0, X1],
dtype=tf.float32)
Y0, Y1 = output_seqs
In [9]:
init = tf.global_variables_initializer()
In [10]:
X0_batch = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8], [9, 0, 1]])
X1_batch = np.array([[9, 8, 7], [0, 0, 0], [6, 5, 4], [3, 2, 1]])
with tf.Session() as sess:
init.run()
Y0_val, Y1_val = sess.run([Y0, Y1], feed_dict={X0: X0_batch, X1: X1_batch})
In [11]:
Y0_val
Out[11]:
In [12]:
Y1_val
Out[12]:
In [13]:
from tensorflow_graph_in_jupyter import show_graph
In [14]:
show_graph(tf.get_default_graph())
In [15]:
n_steps = 2
n_inputs = 3
n_neurons = 5
In [16]:
reset_graph()
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
X_seqs = tf.unstack(tf.transpose(X, perm=[1, 0, 2]))
basic_cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
output_seqs, states = tf.nn.static_rnn(basic_cell, X_seqs,
dtype=tf.float32)
outputs = tf.transpose(tf.stack(output_seqs), perm=[1, 0, 2])
In [17]:
init = tf.global_variables_initializer()
In [18]:
X_batch = np.array([
# t = 0 t = 1
[[0, 1, 2], [9, 8, 7]], # instance 1
[[3, 4, 5], [0, 0, 0]], # instance 2
[[6, 7, 8], [6, 5, 4]], # instance 3
[[9, 0, 1], [3, 2, 1]], # instance 4
])
with tf.Session() as sess:
init.run()
outputs_val = outputs.eval(feed_dict={X: X_batch})
In [19]:
print(outputs_val)
In [20]:
print(np.transpose(outputs_val, axes=[1, 0, 2])[1])
In [21]:
n_steps = 2
n_inputs = 3
n_neurons = 5
In [22]:
reset_graph()
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
basic_cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
outputs, states = tf.nn.dynamic_rnn(basic_cell, X, dtype=tf.float32)
In [23]:
init = tf.global_variables_initializer()
In [24]:
X_batch = np.array([
[[0, 1, 2], [9, 8, 7]], # instance 1
[[3, 4, 5], [0, 0, 0]], # instance 2
[[6, 7, 8], [6, 5, 4]], # instance 3
[[9, 0, 1], [3, 2, 1]], # instance 4
])
with tf.Session() as sess:
init.run()
outputs_val = outputs.eval(feed_dict={X: X_batch})
In [25]:
print(outputs_val)
In [26]:
show_graph(tf.get_default_graph())
In [27]:
n_steps = 2
n_inputs = 3
n_neurons = 5
reset_graph()
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
basic_cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
In [28]:
seq_length = tf.placeholder(tf.int32, [None])
outputs, states = tf.nn.dynamic_rnn(basic_cell, X, dtype=tf.float32,
sequence_length=seq_length)
In [29]:
init = tf.global_variables_initializer()
In [30]:
X_batch = np.array([
# step 0 step 1
[[0, 1, 2], [9, 8, 7]], # instance 1
[[3, 4, 5], [0, 0, 0]], # instance 2 (padded with zero vectors)
[[6, 7, 8], [6, 5, 4]], # instance 3
[[9, 0, 1], [3, 2, 1]], # instance 4
])
seq_length_batch = np.array([2, 1, 2, 2])
In [31]:
with tf.Session() as sess:
init.run()
outputs_val, states_val = sess.run(
[outputs, states], feed_dict={X: X_batch, seq_length: seq_length_batch})
In [32]:
print(outputs_val)
In [33]:
print(states_val)
Note: the book uses tensorflow.contrib.layers.fully_connected() rather than tf.layers.dense() (which did not exist when this chapter was written). It is now preferable to use tf.layers.dense(), because anything in the contrib module may change or be deleted without notice. The dense() function is almost identical to the fully_connected() function. The main differences relevant to this chapter are:
scope becomes name, activation_fn becomes activation (and similarly the _fn suffix is removed from other parameters such as normalizer_fn), weights_initializer becomes kernel_initializer, etc.activation is now None rather than tf.nn.relu.
In [34]:
reset_graph()
n_steps = 28
n_inputs = 28
n_neurons = 150
n_outputs = 10
learning_rate = 0.001
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.int32, [None])
basic_cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
outputs, states = tf.nn.dynamic_rnn(basic_cell, X, dtype=tf.float32)
logits = tf.layers.dense(states, n_outputs)
xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y,
logits=logits)
loss = tf.reduce_mean(xentropy)
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
correct = tf.nn.in_top_k(logits, y, 1)
accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))
init = tf.global_variables_initializer()
Warning: tf.examples.tutorials.mnist is deprecated. We will use tf.keras.datasets.mnist instead.
In [35]:
(X_train, y_train), (X_test, y_test) = tf.keras.datasets.mnist.load_data()
X_train = X_train.astype(np.float32).reshape(-1, 28*28) / 255.0
X_test = X_test.astype(np.float32).reshape(-1, 28*28) / 255.0
y_train = y_train.astype(np.int32)
y_test = y_test.astype(np.int32)
X_valid, X_train = X_train[:5000], X_train[5000:]
y_valid, y_train = y_train[:5000], y_train[5000:]
In [36]:
def shuffle_batch(X, y, batch_size):
rnd_idx = np.random.permutation(len(X))
n_batches = len(X) // batch_size
for batch_idx in np.array_split(rnd_idx, n_batches):
X_batch, y_batch = X[batch_idx], y[batch_idx]
yield X_batch, y_batch
In [37]:
X_test = X_test.reshape((-1, n_steps, n_inputs))
In [38]:
n_epochs = 100
batch_size = 150
with tf.Session() as sess:
init.run()
for epoch in range(n_epochs):
for X_batch, y_batch in shuffle_batch(X_train, y_train, batch_size):
X_batch = X_batch.reshape((-1, n_steps, n_inputs))
sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
acc_batch = accuracy.eval(feed_dict={X: X_batch, y: y_batch})
acc_test = accuracy.eval(feed_dict={X: X_test, y: y_test})
print(epoch, "Last batch accuracy:", acc_batch, "Test accuracy:", acc_test)
In [39]:
reset_graph()
n_steps = 28
n_inputs = 28
n_outputs = 10
learning_rate = 0.001
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.int32, [None])
In [40]:
n_neurons = 100
n_layers = 3
layers = [tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons,
activation=tf.nn.relu)
for layer in range(n_layers)]
multi_layer_cell = tf.nn.rnn_cell.MultiRNNCell(layers)
outputs, states = tf.nn.dynamic_rnn(multi_layer_cell, X, dtype=tf.float32)
In [41]:
states_concat = tf.concat(axis=1, values=states)
logits = tf.layers.dense(states_concat, n_outputs)
xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
loss = tf.reduce_mean(xentropy)
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
correct = tf.nn.in_top_k(logits, y, 1)
accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))
init = tf.global_variables_initializer()
In [42]:
n_epochs = 10
batch_size = 150
with tf.Session() as sess:
init.run()
for epoch in range(n_epochs):
for X_batch, y_batch in shuffle_batch(X_train, y_train, batch_size):
X_batch = X_batch.reshape((-1, n_steps, n_inputs))
sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
acc_batch = accuracy.eval(feed_dict={X: X_batch, y: y_batch})
acc_test = accuracy.eval(feed_dict={X: X_test, y: y_test})
print(epoch, "Last batch accuracy:", acc_batch, "Test accuracy:", acc_test)
In [43]:
t_min, t_max = 0, 30
resolution = 0.1
def time_series(t):
return t * np.sin(t) / 3 + 2 * np.sin(t*5)
def next_batch(batch_size, n_steps):
t0 = np.random.rand(batch_size, 1) * (t_max - t_min - n_steps * resolution)
Ts = t0 + np.arange(0., n_steps + 1) * resolution
ys = time_series(Ts)
return ys[:, :-1].reshape(-1, n_steps, 1), ys[:, 1:].reshape(-1, n_steps, 1)
In [44]:
t = np.linspace(t_min, t_max, int((t_max - t_min) / resolution))
n_steps = 20
t_instance = np.linspace(12.2, 12.2 + resolution * (n_steps + 1), n_steps + 1)
plt.figure(figsize=(11,4))
plt.subplot(121)
plt.title("A time series (generated)", fontsize=14)
plt.plot(t, time_series(t), label=r"$t . \sin(t) / 3 + 2 . \sin(5t)$")
plt.plot(t_instance[:-1], time_series(t_instance[:-1]), "b-", linewidth=3, label="A training instance")
plt.legend(loc="lower left", fontsize=14)
plt.axis([0, 30, -17, 13])
plt.xlabel("Time")
plt.ylabel("Value")
plt.subplot(122)
plt.title("A training instance", fontsize=14)
plt.plot(t_instance[:-1], time_series(t_instance[:-1]), "bo", markersize=10, label="instance")
plt.plot(t_instance[1:], time_series(t_instance[1:]), "w*", markersize=10, label="target")
plt.legend(loc="upper left")
plt.xlabel("Time")
save_fig("time_series_plot")
plt.show()
In [45]:
X_batch, y_batch = next_batch(1, n_steps)
In [46]:
np.c_[X_batch[0], y_batch[0]]
Out[46]:
Let's create the RNN. It will contain 100 recurrent neurons and we will unroll it over 20 time steps since each training instance will be 20 inputs long. Each input will contain only one feature (the value at that time). The targets are also sequences of 20 inputs, each containing a single value:
In [47]:
reset_graph()
n_steps = 20
n_inputs = 1
n_neurons = 100
n_outputs = 1
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.float32, [None, n_steps, n_outputs])
cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons, activation=tf.nn.relu)
outputs, states = tf.nn.dynamic_rnn(cell, X, dtype=tf.float32)
At each time step we now have an output vector of size 100. But what we actually want is a single output value at each time step. The simplest solution is to wrap the cell in an OutputProjectionWrapper.
In [48]:
reset_graph()
n_steps = 20
n_inputs = 1
n_neurons = 100
n_outputs = 1
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.float32, [None, n_steps, n_outputs])
In [49]:
cell = tf.contrib.rnn.OutputProjectionWrapper(
tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons, activation=tf.nn.relu),
output_size=n_outputs)
In [50]:
outputs, states = tf.nn.dynamic_rnn(cell, X, dtype=tf.float32)
In [51]:
learning_rate = 0.001
loss = tf.reduce_mean(tf.square(outputs - y)) # MSE
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
init = tf.global_variables_initializer()
In [52]:
saver = tf.train.Saver()
In [53]:
n_iterations = 1500
batch_size = 50
with tf.Session() as sess:
init.run()
for iteration in range(n_iterations):
X_batch, y_batch = next_batch(batch_size, n_steps)
sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
if iteration % 100 == 0:
mse = loss.eval(feed_dict={X: X_batch, y: y_batch})
print(iteration, "\tMSE:", mse)
saver.save(sess, "./my_time_series_model") # not shown in the book
In [54]:
with tf.Session() as sess: # not shown in the book
saver.restore(sess, "./my_time_series_model") # not shown
X_new = time_series(np.array(t_instance[:-1].reshape(-1, n_steps, n_inputs)))
y_pred = sess.run(outputs, feed_dict={X: X_new})
In [55]:
y_pred
Out[55]:
In [56]:
plt.title("Testing the model", fontsize=14)
plt.plot(t_instance[:-1], time_series(t_instance[:-1]), "bo", markersize=10, label="instance")
plt.plot(t_instance[1:], time_series(t_instance[1:]), "w*", markersize=10, label="target")
plt.plot(t_instance[1:], y_pred[0,:,0], "r.", markersize=10, label="prediction")
plt.legend(loc="upper left")
plt.xlabel("Time")
save_fig("time_series_pred_plot")
plt.show()
In [57]:
reset_graph()
n_steps = 20
n_inputs = 1
n_neurons = 100
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.float32, [None, n_steps, n_outputs])
In [58]:
cell = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons, activation=tf.nn.relu)
rnn_outputs, states = tf.nn.dynamic_rnn(cell, X, dtype=tf.float32)
In [59]:
n_outputs = 1
learning_rate = 0.001
In [60]:
stacked_rnn_outputs = tf.reshape(rnn_outputs, [-1, n_neurons])
stacked_outputs = tf.layers.dense(stacked_rnn_outputs, n_outputs)
outputs = tf.reshape(stacked_outputs, [-1, n_steps, n_outputs])
In [61]:
loss = tf.reduce_mean(tf.square(outputs - y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
init = tf.global_variables_initializer()
saver = tf.train.Saver()
In [62]:
n_iterations = 1500
batch_size = 50
with tf.Session() as sess:
init.run()
for iteration in range(n_iterations):
X_batch, y_batch = next_batch(batch_size, n_steps)
sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
if iteration % 100 == 0:
mse = loss.eval(feed_dict={X: X_batch, y: y_batch})
print(iteration, "\tMSE:", mse)
X_new = time_series(np.array(t_instance[:-1].reshape(-1, n_steps, n_inputs)))
y_pred = sess.run(outputs, feed_dict={X: X_new})
saver.save(sess, "./my_time_series_model")
In [63]:
y_pred
Out[63]:
In [64]:
plt.title("Testing the model", fontsize=14)
plt.plot(t_instance[:-1], time_series(t_instance[:-1]), "bo", markersize=10, label="instance")
plt.plot(t_instance[1:], time_series(t_instance[1:]), "w*", markersize=10, label="target")
plt.plot(t_instance[1:], y_pred[0,:,0], "r.", markersize=10, label="prediction")
plt.legend(loc="upper left")
plt.xlabel("Time")
plt.show()
In [65]:
with tf.Session() as sess: # not shown in the book
saver.restore(sess, "./my_time_series_model") # not shown
sequence = [0.] * n_steps
for iteration in range(300):
X_batch = np.array(sequence[-n_steps:]).reshape(1, n_steps, 1)
y_pred = sess.run(outputs, feed_dict={X: X_batch})
sequence.append(y_pred[0, -1, 0])
In [66]:
plt.figure(figsize=(8,4))
plt.plot(np.arange(len(sequence)), sequence, "b-")
plt.plot(t[:n_steps], sequence[:n_steps], "b-", linewidth=3)
plt.xlabel("Time")
plt.ylabel("Value")
plt.show()
In [67]:
with tf.Session() as sess:
saver.restore(sess, "./my_time_series_model")
sequence1 = [0. for i in range(n_steps)]
for iteration in range(len(t) - n_steps):
X_batch = np.array(sequence1[-n_steps:]).reshape(1, n_steps, 1)
y_pred = sess.run(outputs, feed_dict={X: X_batch})
sequence1.append(y_pred[0, -1, 0])
sequence2 = [time_series(i * resolution + t_min + (t_max-t_min/3)) for i in range(n_steps)]
for iteration in range(len(t) - n_steps):
X_batch = np.array(sequence2[-n_steps:]).reshape(1, n_steps, 1)
y_pred = sess.run(outputs, feed_dict={X: X_batch})
sequence2.append(y_pred[0, -1, 0])
plt.figure(figsize=(11,4))
plt.subplot(121)
plt.plot(t, sequence1, "b-")
plt.plot(t[:n_steps], sequence1[:n_steps], "b-", linewidth=3)
plt.xlabel("Time")
plt.ylabel("Value")
plt.subplot(122)
plt.plot(t, sequence2, "b-")
plt.plot(t[:n_steps], sequence2[:n_steps], "b-", linewidth=3)
plt.xlabel("Time")
save_fig("creative_sequence_plot")
plt.show()
In [68]:
reset_graph()
n_inputs = 2
n_steps = 5
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
In [69]:
n_neurons = 100
n_layers = 3
layers = [tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
for layer in range(n_layers)]
multi_layer_cell = tf.nn.rnn_cell.MultiRNNCell(layers)
outputs, states = tf.nn.dynamic_rnn(multi_layer_cell, X, dtype=tf.float32)
In [70]:
init = tf.global_variables_initializer()
In [71]:
X_batch = np.random.rand(2, n_steps, n_inputs)
In [72]:
with tf.Session() as sess:
init.run()
outputs_val, states_val = sess.run([outputs, states], feed_dict={X: X_batch})
In [73]:
outputs_val.shape
Out[73]:
Do NOT do this:
In [74]:
with tf.device("/gpu:0"): # BAD! This is ignored.
layer1 = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
with tf.device("/gpu:1"): # BAD! Ignored again.
layer2 = tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
Instead, you need a DeviceCellWrapper:
In [75]:
import tensorflow as tf
class DeviceCellWrapper(tf.nn.rnn_cell.RNNCell):
def __init__(self, device, cell):
self._cell = cell
self._device = device
@property
def state_size(self):
return self._cell.state_size
@property
def output_size(self):
return self._cell.output_size
def __call__(self, inputs, state, scope=None):
with tf.device(self._device):
return self._cell(inputs, state, scope)
In [76]:
reset_graph()
n_inputs = 5
n_steps = 20
n_neurons = 100
X = tf.placeholder(tf.float32, shape=[None, n_steps, n_inputs])
In [77]:
devices = ["/cpu:0", "/cpu:0", "/cpu:0"] # replace with ["/gpu:0", "/gpu:1", "/gpu:2"] if you have 3 GPUs
cells = [DeviceCellWrapper(dev,tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons))
for dev in devices]
multi_layer_cell = tf.nn.rnn_cell.MultiRNNCell(cells)
outputs, states = tf.nn.dynamic_rnn(multi_layer_cell, X, dtype=tf.float32)
Alternatively, since TensorFlow 1.1, you can use the tf.contrib.rnn.DeviceWrapper class (alias tf.nn.rnn_cell.DeviceWrapper since TF 1.2).
In [78]:
init = tf.global_variables_initializer()
In [79]:
with tf.Session() as sess:
init.run()
print(sess.run(outputs, feed_dict={X: np.random.rand(2, n_steps, n_inputs)}))
In [80]:
reset_graph()
n_inputs = 1
n_neurons = 100
n_layers = 3
n_steps = 20
n_outputs = 1
In [81]:
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.float32, [None, n_steps, n_outputs])
Note: the input_keep_prob parameter can be a placeholder, making it possible to set it to any value you want during training, and to 1.0 during testing (effectively turning dropout off). This is a much more elegant solution than what was recommended in earlier versions of the book (i.e., writing your own wrapper class or having a separate model for training and testing). Thanks to Shen Cheng for bringing this to my attention.
In [82]:
keep_prob = tf.placeholder_with_default(1.0, shape=())
cells = [tf.nn.rnn_cell.BasicRNNCell(num_units=n_neurons)
for layer in range(n_layers)]
cells_drop = [tf.nn.rnn_cell.DropoutWrapper(cell, input_keep_prob=keep_prob)
for cell in cells]
multi_layer_cell = tf.nn.rnn_cell.MultiRNNCell(cells_drop)
rnn_outputs, states = tf.nn.dynamic_rnn(multi_layer_cell, X, dtype=tf.float32)
In [83]:
learning_rate = 0.01
stacked_rnn_outputs = tf.reshape(rnn_outputs, [-1, n_neurons])
stacked_outputs = tf.layers.dense(stacked_rnn_outputs, n_outputs)
outputs = tf.reshape(stacked_outputs, [-1, n_steps, n_outputs])
loss = tf.reduce_mean(tf.square(outputs - y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
init = tf.global_variables_initializer()
saver = tf.train.Saver()
In [84]:
n_iterations = 1500
batch_size = 50
train_keep_prob = 0.5
with tf.Session() as sess:
init.run()
for iteration in range(n_iterations):
X_batch, y_batch = next_batch(batch_size, n_steps)
_, mse = sess.run([training_op, loss],
feed_dict={X: X_batch, y: y_batch,
keep_prob: train_keep_prob})
if iteration % 100 == 0: # not shown in the book
print(iteration, "Training MSE:", mse) # not shown
saver.save(sess, "./my_dropout_time_series_model")
In [85]:
with tf.Session() as sess:
saver.restore(sess, "./my_dropout_time_series_model")
X_new = time_series(np.array(t_instance[:-1].reshape(-1, n_steps, n_inputs)))
y_pred = sess.run(outputs, feed_dict={X: X_new})
In [86]:
plt.title("Testing the model", fontsize=14)
plt.plot(t_instance[:-1], time_series(t_instance[:-1]), "bo", markersize=10, label="instance")
plt.plot(t_instance[1:], time_series(t_instance[1:]), "w*", markersize=10, label="target")
plt.plot(t_instance[1:], y_pred[0,:,0], "r.", markersize=10, label="prediction")
plt.legend(loc="upper left")
plt.xlabel("Time")
plt.show()
Oops, it seems that Dropout does not help at all in this particular case. :/
In [87]:
reset_graph()
lstm_cell = tf.nn.rnn_cell.BasicLSTMCell(num_units=n_neurons)
In [88]:
n_steps = 28
n_inputs = 28
n_neurons = 150
n_outputs = 10
n_layers = 3
learning_rate = 0.001
X = tf.placeholder(tf.float32, [None, n_steps, n_inputs])
y = tf.placeholder(tf.int32, [None])
lstm_cells = [tf.nn.rnn_cell.BasicLSTMCell(num_units=n_neurons)
for layer in range(n_layers)]
multi_cell = tf.nn.rnn_cell.MultiRNNCell(lstm_cells)
outputs, states = tf.nn.dynamic_rnn(multi_cell, X, dtype=tf.float32)
top_layer_h_state = states[-1][1]
logits = tf.layers.dense(top_layer_h_state, n_outputs, name="softmax")
xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
loss = tf.reduce_mean(xentropy, name="loss")
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
correct = tf.nn.in_top_k(logits, y, 1)
accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))
init = tf.global_variables_initializer()
In [89]:
states
Out[89]:
In [90]:
top_layer_h_state
Out[90]:
In [91]:
n_epochs = 10
batch_size = 150
with tf.Session() as sess:
init.run()
for epoch in range(n_epochs):
for X_batch, y_batch in shuffle_batch(X_train, y_train, batch_size):
X_batch = X_batch.reshape((-1, n_steps, n_inputs))
sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
acc_batch = accuracy.eval(feed_dict={X: X_batch, y: y_batch})
acc_test = accuracy.eval(feed_dict={X: X_test, y: y_test})
print(epoch, "Last batch accuracy:", acc_batch, "Test accuracy:", acc_test)
In [92]:
lstm_cell = tf.nn.rnn_cell.LSTMCell(num_units=n_neurons, use_peepholes=True)
In [93]:
gru_cell = tf.nn.rnn_cell.GRUCell(num_units=n_neurons)
This section is based on TensorFlow's Word2Vec tutorial.
In [94]:
from six.moves import urllib
import errno
import os
import zipfile
WORDS_PATH = "datasets/words"
WORDS_URL = 'http://mattmahoney.net/dc/text8.zip'
def mkdir_p(path):
"""Create directories, ok if they already exist.
This is for python 2 support. In python >=3.2, simply use:
>>> os.makedirs(path, exist_ok=True)
"""
try:
os.makedirs(path)
except OSError as exc:
if exc.errno == errno.EEXIST and os.path.isdir(path):
pass
else:
raise
def fetch_words_data(words_url=WORDS_URL, words_path=WORDS_PATH):
os.makedirs(words_path, exist_ok=True)
zip_path = os.path.join(words_path, "words.zip")
if not os.path.exists(zip_path):
urllib.request.urlretrieve(words_url, zip_path)
with zipfile.ZipFile(zip_path) as f:
data = f.read(f.namelist()[0])
return data.decode("ascii").split()
In [95]:
words = fetch_words_data()
In [96]:
words[:5]
Out[96]:
In [97]:
from collections import Counter
vocabulary_size = 50000
vocabulary = [("UNK", None)] + Counter(words).most_common(vocabulary_size - 1)
vocabulary = np.array([word for word, _ in vocabulary])
dictionary = {word: code for code, word in enumerate(vocabulary)}
data = np.array([dictionary.get(word, 0) for word in words])
In [98]:
" ".join(words[:9]), data[:9]
Out[98]:
In [99]:
" ".join([vocabulary[word_index] for word_index in [5241, 3081, 12, 6, 195, 2, 3134, 46, 59]])
Out[99]:
In [100]:
words[24], data[24]
Out[100]:
In [101]:
from collections import deque
def generate_batch(batch_size, num_skips, skip_window):
global data_index
assert batch_size % num_skips == 0
assert num_skips <= 2 * skip_window
batch = np.ndarray(shape=[batch_size], dtype=np.int32)
labels = np.ndarray(shape=[batch_size, 1], dtype=np.int32)
span = 2 * skip_window + 1 # [ skip_window target skip_window ]
buffer = deque(maxlen=span)
for _ in range(span):
buffer.append(data[data_index])
data_index = (data_index + 1) % len(data)
for i in range(batch_size // num_skips):
target = skip_window # target label at the center of the buffer
targets_to_avoid = [ skip_window ]
for j in range(num_skips):
while target in targets_to_avoid:
target = np.random.randint(0, span)
targets_to_avoid.append(target)
batch[i * num_skips + j] = buffer[skip_window]
labels[i * num_skips + j, 0] = buffer[target]
buffer.append(data[data_index])
data_index = (data_index + 1) % len(data)
return batch, labels
In [102]:
np.random.seed(42)
In [103]:
data_index = 0
batch, labels = generate_batch(8, 2, 1)
In [104]:
batch, [vocabulary[word] for word in batch]
Out[104]:
In [105]:
labels, [vocabulary[word] for word in labels[:, 0]]
Out[105]:
In [106]:
batch_size = 128
embedding_size = 128 # Dimension of the embedding vector.
skip_window = 1 # How many words to consider left and right.
num_skips = 2 # How many times to reuse an input to generate a label.
# We pick a random validation set to sample nearest neighbors. Here we limit the
# validation samples to the words that have a low numeric ID, which by
# construction are also the most frequent.
valid_size = 16 # Random set of words to evaluate similarity on.
valid_window = 100 # Only pick dev samples in the head of the distribution.
valid_examples = np.random.choice(valid_window, valid_size, replace=False)
num_sampled = 64 # Number of negative examples to sample.
learning_rate = 0.01
In [107]:
reset_graph()
# Input data.
train_labels = tf.placeholder(tf.int32, shape=[batch_size, 1])
valid_dataset = tf.constant(valid_examples, dtype=tf.int32)
In [108]:
vocabulary_size = 50000
embedding_size = 150
# Look up embeddings for inputs.
init_embeds = tf.random_uniform([vocabulary_size, embedding_size], -1.0, 1.0)
embeddings = tf.Variable(init_embeds)
In [109]:
train_inputs = tf.placeholder(tf.int32, shape=[None])
embed = tf.nn.embedding_lookup(embeddings, train_inputs)
In [110]:
# Construct the variables for the NCE loss
nce_weights = tf.Variable(
tf.truncated_normal([vocabulary_size, embedding_size],
stddev=1.0 / np.sqrt(embedding_size)))
nce_biases = tf.Variable(tf.zeros([vocabulary_size]))
# Compute the average NCE loss for the batch.
# tf.nce_loss automatically draws a new sample of the negative labels each
# time we evaluate the loss.
loss = tf.reduce_mean(
tf.nn.nce_loss(nce_weights, nce_biases, train_labels, embed,
num_sampled, vocabulary_size))
# Construct the Adam optimizer
optimizer = tf.train.AdamOptimizer(learning_rate)
training_op = optimizer.minimize(loss)
# Compute the cosine similarity between minibatch examples and all embeddings.
norm = tf.sqrt(tf.reduce_sum(tf.square(embeddings), axis=1, keepdims=True))
normalized_embeddings = embeddings / norm
valid_embeddings = tf.nn.embedding_lookup(normalized_embeddings, valid_dataset)
similarity = tf.matmul(valid_embeddings, normalized_embeddings, transpose_b=True)
# Add variable initializer.
init = tf.global_variables_initializer()
In [111]:
num_steps = 10001
with tf.Session() as session:
init.run()
average_loss = 0
for step in range(num_steps):
print("\rIteration: {}".format(step), end="\t")
batch_inputs, batch_labels = generate_batch(batch_size, num_skips, skip_window)
feed_dict = {train_inputs : batch_inputs, train_labels : batch_labels}
# We perform one update step by evaluating the training op (including it
# in the list of returned values for session.run()
_, loss_val = session.run([training_op, loss], feed_dict=feed_dict)
average_loss += loss_val
if step % 2000 == 0:
if step > 0:
average_loss /= 2000
# The average loss is an estimate of the loss over the last 2000 batches.
print("Average loss at step ", step, ": ", average_loss)
average_loss = 0
# Note that this is expensive (~20% slowdown if computed every 500 steps)
if step % 10000 == 0:
sim = similarity.eval()
for i in range(valid_size):
valid_word = vocabulary[valid_examples[i]]
top_k = 8 # number of nearest neighbors
nearest = (-sim[i, :]).argsort()[1:top_k+1]
log_str = "Nearest to %s:" % valid_word
for k in range(top_k):
close_word = vocabulary[nearest[k]]
log_str = "%s %s," % (log_str, close_word)
print(log_str)
final_embeddings = normalized_embeddings.eval()
Let's save the final embeddings (of course you can use a TensorFlow Saver if you prefer):
In [112]:
np.save("./my_final_embeddings.npy", final_embeddings)
In [113]:
def plot_with_labels(low_dim_embs, labels):
assert low_dim_embs.shape[0] >= len(labels), "More labels than embeddings"
plt.figure(figsize=(18, 18)) #in inches
for i, label in enumerate(labels):
x, y = low_dim_embs[i,:]
plt.scatter(x, y)
plt.annotate(label,
xy=(x, y),
xytext=(5, 2),
textcoords='offset points',
ha='right',
va='bottom')
In [114]:
from sklearn.manifold import TSNE
tsne = TSNE(perplexity=30, n_components=2, init='pca', n_iter=5000)
plot_only = 500
low_dim_embs = tsne.fit_transform(final_embeddings[:plot_only,:])
labels = [vocabulary[i] for i in range(plot_only)]
plot_with_labels(low_dim_embs, labels)
The basic_rnn_seq2seq() function creates a simple Encoder/Decoder model: it first runs an RNN to encode encoder_inputs into a state vector, then runs a decoder initialized with the last encoder state on decoder_inputs. Encoder and decoder use the same RNN cell type but they don't share parameters.
In [115]:
import tensorflow as tf
reset_graph()
n_steps = 50
n_neurons = 200
n_layers = 3
num_encoder_symbols = 20000
num_decoder_symbols = 20000
embedding_size = 150
learning_rate = 0.01
X = tf.placeholder(tf.int32, [None, n_steps]) # English sentences
Y = tf.placeholder(tf.int32, [None, n_steps]) # French translations
W = tf.placeholder(tf.float32, [None, n_steps - 1, 1])
Y_input = Y[:, :-1]
Y_target = Y[:, 1:]
encoder_inputs = tf.unstack(tf.transpose(X)) # list of 1D tensors
decoder_inputs = tf.unstack(tf.transpose(Y_input)) # list of 1D tensors
lstm_cells = [tf.nn.rnn_cell.BasicLSTMCell(num_units=n_neurons)
for layer in range(n_layers)]
cell = tf.nn.rnn_cell.MultiRNNCell(lstm_cells)
output_seqs, states = tf.contrib.legacy_seq2seq.embedding_rnn_seq2seq(
encoder_inputs,
decoder_inputs,
cell,
num_encoder_symbols,
num_decoder_symbols,
embedding_size)
logits = tf.transpose(tf.unstack(output_seqs), perm=[1, 0, 2])
In [116]:
logits_flat = tf.reshape(logits, [-1, num_decoder_symbols])
Y_target_flat = tf.reshape(Y_target, [-1])
W_flat = tf.reshape(W, [-1])
xentropy = W_flat * tf.nn.sparse_softmax_cross_entropy_with_logits(labels=Y_target_flat, logits=logits_flat)
loss = tf.reduce_mean(xentropy)
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
init = tf.global_variables_initializer()
See Appendix A.
First we need to build a function that generates strings based on a grammar. The grammar will be represented as a list of possible transitions for each state. A transition specifies the string to output (or a grammar to generate it) and the next state.
In [117]:
np.random.seed(42)
default_reber_grammar = [
[("B", 1)], # (state 0) =B=>(state 1)
[("T", 2), ("P", 3)], # (state 1) =T=>(state 2) or =P=>(state 3)
[("S", 2), ("X", 4)], # (state 2) =S=>(state 2) or =X=>(state 4)
[("T", 3), ("V", 5)], # and so on...
[("X", 3), ("S", 6)],
[("P", 4), ("V", 6)],
[("E", None)]] # (state 6) =E=>(terminal state)
embedded_reber_grammar = [
[("B", 1)],
[("T", 2), ("P", 3)],
[(default_reber_grammar, 4)],
[(default_reber_grammar, 5)],
[("T", 6)],
[("P", 6)],
[("E", None)]]
def generate_string(grammar):
state = 0
output = []
while state is not None:
index = np.random.randint(len(grammar[state]))
production, state = grammar[state][index]
if isinstance(production, list):
production = generate_string(grammar=production)
output.append(production)
return "".join(output)
Let's generate a few strings based on the default Reber grammar:
In [118]:
for _ in range(25):
print(generate_string(default_reber_grammar), end=" ")
Looks good. Now let's generate a few strings based on the embedded Reber grammar:
In [119]:
for _ in range(25):
print(generate_string(embedded_reber_grammar), end=" ")
Okay, now we need a function to generate strings that do not respect the grammar. We could generate a random string, but the task would be a bit too easy, so instead we will generate a string that respects the grammar, and we will corrupt it by changing just one character:
In [120]:
def generate_corrupted_string(grammar, chars="BEPSTVX"):
good_string = generate_string(grammar)
index = np.random.randint(len(good_string))
good_char = good_string[index]
bad_char = np.random.choice(sorted(set(chars) - set(good_char)))
return good_string[:index] + bad_char + good_string[index + 1:]
Let's look at a few corrupted strings:
In [121]:
for _ in range(25):
print(generate_corrupted_string(embedded_reber_grammar), end=" ")
It's not possible to feed a string directly to an RNN: we need to convert it to a sequence of vectors, first. Each vector will represent a single letter, using a one-hot encoding. For example, the letter "B" will be represented as the vector [1, 0, 0, 0, 0, 0, 0], the letter E will be represented as [0, 1, 0, 0, 0, 0, 0] and so on. Let's write a function that converts a string to a sequence of such one-hot vectors. Note that if the string is shorted than n_steps, it will be padded with zero vectors (later, we will tell TensorFlow how long each string actually is using the sequence_length parameter).
In [122]:
def string_to_one_hot_vectors(string, n_steps, chars="BEPSTVX"):
char_to_index = {char: index for index, char in enumerate(chars)}
output = np.zeros((n_steps, len(chars)), dtype=np.int32)
for index, char in enumerate(string):
output[index, char_to_index[char]] = 1.
return output
In [123]:
string_to_one_hot_vectors("BTBTXSETE", 12)
Out[123]:
We can now generate the dataset, with 50% good strings, and 50% bad strings:
In [124]:
def generate_dataset(size):
good_strings = [generate_string(embedded_reber_grammar)
for _ in range(size // 2)]
bad_strings = [generate_corrupted_string(embedded_reber_grammar)
for _ in range(size - size // 2)]
all_strings = good_strings + bad_strings
n_steps = max([len(string) for string in all_strings])
X = np.array([string_to_one_hot_vectors(string, n_steps)
for string in all_strings])
seq_length = np.array([len(string) for string in all_strings])
y = np.array([[1] for _ in range(len(good_strings))] +
[[0] for _ in range(len(bad_strings))])
rnd_idx = np.random.permutation(size)
return X[rnd_idx], seq_length[rnd_idx], y[rnd_idx]
In [125]:
X_train, l_train, y_train = generate_dataset(10000)
Let's take a look at the first training instances:
In [126]:
X_train[0]
Out[126]:
It's padded with a lot of zeros because the longest string in the dataset is that long. How long is this particular string?
In [127]:
l_train[0]
Out[127]:
What class is it?
In [128]:
y_train[0]
Out[128]:
Perfect! We are ready to create the RNN to identify good strings. We build a sequence classifier very similar to the one we built earlier to classify MNIST images, with two main differences:
sequence_length when calling the dynamic_rnn() function.sparse_softmax_cross_entropy_with_logits() but for binary classification we use sigmoid_cross_entropy_with_logits().
In [129]:
reset_graph()
possible_chars = "BEPSTVX"
n_inputs = len(possible_chars)
n_neurons = 30
n_outputs = 1
learning_rate = 0.02
momentum = 0.95
X = tf.placeholder(tf.float32, [None, None, n_inputs], name="X")
seq_length = tf.placeholder(tf.int32, [None], name="seq_length")
y = tf.placeholder(tf.float32, [None, 1], name="y")
gru_cell = tf.nn.rnn_cell.GRUCell(num_units=n_neurons)
outputs, states = tf.nn.dynamic_rnn(gru_cell, X, dtype=tf.float32,
sequence_length=seq_length)
logits = tf.layers.dense(states, n_outputs, name="logits")
y_pred = tf.cast(tf.greater(logits, 0.), tf.float32, name="y_pred")
y_proba = tf.nn.sigmoid(logits, name="y_proba")
xentropy = tf.nn.sigmoid_cross_entropy_with_logits(labels=y, logits=logits)
loss = tf.reduce_mean(xentropy, name="loss")
optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,
momentum=momentum,
use_nesterov=True)
training_op = optimizer.minimize(loss)
correct = tf.equal(y_pred, y, name="correct")
accuracy = tf.reduce_mean(tf.cast(correct, tf.float32), name="accuracy")
init = tf.global_variables_initializer()
saver = tf.train.Saver()
Now let's generate a validation set so we can track progress during training:
In [130]:
X_val, l_val, y_val = generate_dataset(5000)
In [131]:
n_epochs = 50
batch_size = 50
with tf.Session() as sess:
init.run()
for epoch in range(n_epochs):
X_batches = np.array_split(X_train, len(X_train) // batch_size)
l_batches = np.array_split(l_train, len(l_train) // batch_size)
y_batches = np.array_split(y_train, len(y_train) // batch_size)
for X_batch, l_batch, y_batch in zip(X_batches, l_batches, y_batches):
loss_val, _ = sess.run(
[loss, training_op],
feed_dict={X: X_batch, seq_length: l_batch, y: y_batch})
acc_train = accuracy.eval(feed_dict={X: X_batch, seq_length: l_batch, y: y_batch})
acc_val = accuracy.eval(feed_dict={X: X_val, seq_length: l_val, y: y_val})
print("{:4d} Train loss: {:.4f}, accuracy: {:.2f}% Validation accuracy: {:.2f}%".format(
epoch, loss_val, 100 * acc_train, 100 * acc_val))
saver.save(sess, "./my_reber_classifier")
Now let's test our RNN on two tricky strings: the first one is bad while the second one is good. They only differ by the second to last character. If the RNN gets this right, it shows that it managed to notice the pattern that the second letter should always be equal to the second to last letter. That requires a fairly long short-term memory (which is the reason why we used a GRU cell).
In [132]:
test_strings = [
"BPBTSSSSSSSXXTTVPXVPXTTTTTVVETE",
"BPBTSSSSSSSXXTTVPXVPXTTTTTVVEPE"]
l_test = np.array([len(s) for s in test_strings])
max_length = l_test.max()
X_test = [string_to_one_hot_vectors(s, n_steps=max_length)
for s in test_strings]
with tf.Session() as sess:
saver.restore(sess, "./my_reber_classifier")
y_proba_val = y_proba.eval(feed_dict={X: X_test, seq_length: l_test})
print()
print("Estimated probability that these are Reber strings:")
for index, string in enumerate(test_strings):
print("{}: {:.2f}%".format(string, 100 * y_proba_val[index][0]))
Ta-da! It worked fine. The RNN found the correct answers with high confidence. :)
Coming soon...
In [ ]: