Recurrent Neural Networks
Introduction
Take a look at this great article for an introduction to recurrent neural networks and LSTMs in particular.
Language Modeling
In this tutorial we will show how to train a recurrent neural network on a challenging task of language modeling. The goal of the problem is to fit a probabilistic model which assigns probabilities to sentences. It does so by predicting next words in a text given a history of previous words. For this purpose we will use the Penn Tree Bank (PTB) dataset, which is a popular benchmark for measuring the quality of these models, whilst being small and relatively fast to train.
Language modeling is key to many interesting problems such as speech recognition, machine translation, or image captioning. It is also fun -- take a look here.
For the purpose of this tutorial, we will reproduce the results from Zaremba et al., 2014 (pdf), which achieves very good quality on the PTB dataset.
Tutorial Files
This tutorial references the following files from models/tutorials/rnn/ptb
in the TensorFlow models repo:
File | Purpose |
---|---|
ptb_word_lm.py |
The code to train a language model on the PTB dataset. |
reader.py |
The code to read the dataset. |
Download and Prepare the Data
The data required for this tutorial is in the data/
directory of the
PTB dataset from Tomas Mikolov's webpage.
The dataset is already preprocessed and contains overall 10000 different words,
including the end-of-sentence marker and a special symbol (\reader.py
, we convert each word to a unique integer identifier,
in order to make it easy for the neural network to process the data.
The Model
LSTM
The core of the model consists of an LSTM cell that processes one word at a
time and computes probabilities of the possible values for the next word in the
sentence. The memory state of the network is initialized with a vector of zeros
and gets updated after reading each word. For computational reasons, we will
process data in mini-batches of size batch_size
. In this example, it is important
to note that current_batch_of_words
does not correspond to a "sentence" of words.
Every word in a batch should correspond to time t. Tensorflow will automatically sum
the gradients of each batch for you.
For example:
t=0 t=1 t=2 t=3 t=4
[The, brown, fox, is, quick]
[The, red, fox, jumped, high]
words_in_dataset[0] = [The, The]
words_in_dataset[1] = [fox, fox]
words_in_dataset[2] = [is, jumped]
words_in_dataset[3] = [quick, high]
num_batches = 4, batch_size = 2, time_steps = 5
The basic pseudocode is as follows:
words_in_dataset = tf.placeholder(tf.float32, [num_batches, batch_size, num_features])
lstm = tf.contrib.rnn.BasicLSTMCell(lstm_size)
# Initial state of the LSTM memory.
hidden_state = tf.zeros([batch_size, lstm.state_size])
current_state = tf.zeros([batch_size, lstm.state_size])
state = hidden_state, current_state
probabilities = []
loss = 0.0
for current_batch_of_words in words_in_dataset:
# The value of state is updated after processing each batch of words.
output, state = lstm(current_batch_of_words, state)
# The LSTM output can be used to make next word predictions
logits = tf.matmul(output, softmax_w) + softmax_b
probabilities.append(tf.nn.softmax(logits))
loss += loss_function(probabilities, target_words)
Truncated Backpropagation
By design, the output of a recurrent neural network (RNN) depends on arbitrarily
distant inputs. Unfortunately, this makes backpropagation computation difficult.
In order to make the learning process tractable, it is common practice to create
an "unrolled" version of the network, which contains a fixed number
(num_steps
) of LSTM inputs and outputs. The model is then trained on this
finite approximation of the RNN. This can be implemented by feeding inputs of
length num_steps
at a time and performing a backward pass after each
such input block.
Here is a simplified block of code for creating a graph which performs truncated backpropagation:
# Placeholder for the inputs in a given iteration.
words = tf.placeholder(tf.int32, [batch_size, num_steps])
lstm = tf.contrib.rnn.BasicLSTMCell(lstm_size)
# Initial state of the LSTM memory.
initial_state = state = tf.zeros([batch_size, lstm.state_size])
for i in range(num_steps):
# The value of state is updated after processing each batch of words.
output, state = lstm(words[:, i], state)
# The rest of the code.
# ...
final_state = state
And this is how to implement an iteration over the whole dataset:
# A numpy array holding the state of LSTM after each batch of words.
numpy_state = initial_state.eval()
total_loss = 0.0
for current_batch_of_words in words_in_dataset:
numpy_state, current_loss = session.run([final_state, loss],
# Initialize the LSTM state from the previous iteration.
feed_dict={initial_state: numpy_state, words: current_batch_of_words})
total_loss += current_loss
Inputs
The word IDs will be embedded into a dense representation (see the Vector Representations Tutorial) before feeding to the LSTM. This allows the model to efficiently represent the knowledge about particular words. It is also easy to write:
# embedding_matrix is a tensor of shape [vocabulary_size, embedding size]
word_embeddings = tf.nn.embedding_lookup(embedding_matrix, word_ids)
The embedding matrix will be initialized randomly and the model will learn to differentiate the meaning of words just by looking at the data.
Loss Function
We want to minimize the average negative log probability of the target words:
It is not very difficult to implement but the function
sequence_loss_by_example
is already available, so we can just use it here.
The typical measure reported in the papers is average per-word perplexity (often just called perplexity), which is equal to
and we will monitor its value throughout the training process.
Stacking multiple LSTMs
To give the model more expressive power, we can add multiple layers of LSTMs to process the data. The output of the first layer will become the input of the second and so on.
We have a class called MultiRNNCell
that makes the implementation seamless:
def lstm_cell():
return tf.contrib.rnn.BasicLSTMCell(lstm_size)
stacked_lstm = tf.contrib.rnn.MultiRNNCell(
[lstm_cell() for _ in range(number_of_layers)])
initial_state = state = stacked_lstm.zero_state(batch_size, tf.float32)
for i in range(num_steps):
# The value of state is updated after processing each batch of words.
output, state = stacked_lstm(words[:, i], state)
# The rest of the code.
# ...
final_state = state
Run the Code
Before running the code, download the PTB dataset, as discussed at the beginning of this tutorial. Then, extract the PTB dataset underneath your home directory as follows:
tar xvfz simple-examples.tgz -C $HOME
(Note: On Windows, you may need to use other tools.)
Now, clone the TensorFlow models repo from GitHub. Run the following commands:
cd models/tutorials/rnn/ptb
python ptb_word_lm.py --data_path=$HOME/simple-examples/data/ --model=small
There are 3 supported model configurations in the tutorial code: "small", "medium" and "large". The difference between them is in size of the LSTMs and the set of hyperparameters used for training.
The larger the model, the better results it should get. The small
model should
be able to reach perplexity below 120 on the test set and the large
one below
80, though it might take several hours to train.
What Next?
There are several tricks that we haven't mentioned that make the model better, including:
- decreasing learning rate schedule,
- dropout between the LSTM layers.
Study the code and modify it to improve the model even further.