Recurrent Neural Networks with Word Embeddings¶

Recurrent Neural Networks with Word Embeddings

Summary

In this tutorial, you will learn how to:
learn Word Embeddings
using Recurrent Neural Networks architectures
with Context Windows
in order to perform Semantic Parsing / Slot-Filling (Spoken Language Understanding)

Code - Citations - Contact

Code

Directly running experiments is also possible using this github repository.

Papers

If you use this tutorial, cite the following papers:
[pdf] Grégoire Mesnil, Xiaodong He, Li Deng and Yoshua Bengio. Investigation of Recurrent-Neural-Network
Architectures and Learning Methods for Spoken Language Understanding. Interspeech, 2013.
[pdf] Gokhan Tur, Dilek Hakkani-Tur and Larry Heck. What is left to be understood in ATIS?
[pdf] Christian Raymond and Giuseppe Riccardi. Generative and discriminative
algorithms for spoken language understanding. Interspeech, 2007.
[pdf] Bastien, Frédéric, Lamblin, Pascal, Pascanu, Razvan, Bergstra, James, Goodfellow,
Ian, Bergeron, Arnaud, Bouchard, Nicolas, and Bengio, Yoshua. Theano: new features and speed improvements. NIPS Workshop on Deep Learning and Unsupervised Feature Learning, 2012.
[pdf] Bergstra, James, Breuleux, Olivier, Bastien, Frédéric, Lamblin, Pascal, Pascanu, Razvan, Desjardins,
Guillaume, Turian, Joseph, Warde-Farley, David, and Bengio, Yoshua. Theano: a CPU and GPU math expression compiler. In Proceedings of the Python for Scientific Computing Conference (SciPy), June 2010.
Thank you!

Contact

Please email to 

Grégoire Mesnil (first-add-a-dot-last-add-at-gmail-add-a-dot-com)

 for
any problem report or feedback. We will be glad to hear from you.

Task

The Slot-Filling (Spoken Language Understanding) consists in assigning a label to each word given a sentence. It’s a classification task.

Dataset

An old and small benchmark for this task is the ATIS (Airline Travel Information System) dataset collected by DARPA. Here is a sentence (or utterance) example using the Inside
Outside Beginning (IOB) representation.

Input (words)	show	flights	from	Boston	to	New	York	today
Output (labels)	O	O	O	B-dept	O	B-arr	I-arr	B-date

The ATIS offical split contains 4,978/893 sentences for a total of 56,590/9,198 words (average sentence length is 15) in the train/test set. The number of classes (different slots) is 128 including the O label
(NULL).
As Microsoft Research people, we deal with
unseen words in the test set by marking any words with only one single occurrence in the training set as 

<UNK>

 and
use this token to represent those unseen words in the test set. As Ronan Collobert and colleagues, we converted sequences
of numbers with the string 

DIGIT

 i.e. 

1984

 is
converted to

DIGITDIGITDIGITDIGIT

.
We split the official train set into a training and validation set that contain respectively 80% and 20% of the official training sentences. Significant
performance improvement difference has to be greater than 0.6% in F1 measure at the 95% level due to the small size of the dataset. For evaluation purpose, experiments have to report the following metrics:
Precision
Recall
F1 score
We will use the conlleval PERL script to measure the performance
of our models.

Recurrent Neural Network Model

Raw input encoding

A token corresponds to a word. Each token in the ATIS vocabulary is associated to an index. Each sentence is a array of indexes (

int32

).
Then, each set (train, valid, test) is a list of arrays of indexes. A python dictionary is defined for mapping the space of indexes to the space of words.

>>> sentence
array([383, 189,  13, 193, 208, 307, 195, 502, 260, 539,
7,  60,  72, 8, 350, 384], dtype=int32)
>>> map(lambda x: index2word[x], sentence)
['please', 'find', 'a', 'flight', 'from', 'miami', 'florida',
'to', 'las', 'vegas', '<UNK>', 'arriving', 'before', 'DIGIT', "o'clock", 'pm']

Same thing for labels corresponding to this particular sentence.

>>> labels
array([126, 126, 126, 126, 126,  48,  50, 126,  78, 123,  81, 126,  15,
14,  89,  89], dtype=int32)
>>> map(lambda x: index2label[x], labels)
['O', 'O', 'O', 'O', 'O', 'B-fromloc.city_name', 'B-fromloc.state_name',
'O', 'B-toloc.city_name', 'I-toloc.city_name', 'B-toloc.state_name',
'O', 'B-arrive_time.time_relative', 'B-arrive_time.time',
'I-arrive_time.time', 'I-arrive_time.time']

Context window

Given a sentence i.e. an array of indexes, and a window size i.e. 1,3,5,..., we need to convert each word in the sentence to a context window surrounding this particular word. In details, we have:

def contextwin(l, win):
'''
win :: int corresponding to the size of the window
given a list of indexes composing a sentence

l :: array containing the word indexes

it will return a list of list of indexes corresponding
to context windows surrounding each word in the sentence
'''
assert (win % 2) == 1
assert win >= 1
l = list(l)

lpadded = win // 2 * [-1] + l + win // 2 * [-1]
out = [lpadded[i:(i + win)] for i in range(len(l))]

assert len(out) == len(l)
return out

The index 

-1

 corresponds
to the 

PADDING

 index
we insert at the beginning/end of the sentence.
Here is a sample:

>>> x
array([0, 1, 2, 3, 4], dtype=int32)
>>> contextwin(x, 3)
[[-1, 0, 1],
[ 0, 1, 2],
[ 1, 2, 3],
[ 2, 3, 4],
[ 3, 4,-1]]
>>> contextwin(x, 7)
[[-1, -1, -1, 0, 1, 2, 3],
[-1, -1,  0, 1, 2, 3, 4],
[-1,  0,  1, 2, 3, 4,-1],
[ 0,  1,  2, 3, 4,-1,-1],
[ 1,  2,  3, 4,-1,-1,-1]]

To summarize, we started with an array of indexes and ended with a matrix of indexes. Each line corresponds to the context window surrounding this word.

Word embeddings

Once we have the sentence converted to context windows i.e. a matrix of indexes, we have to associate these indexes to the embeddings (real-valued vector associated to each word). Using Theano, it gives:

import theano, numpy
from theano import tensor as T

# nv :: size of our vocabulary
# de :: dimension of the embedding space
# cs :: context window size
nv, de, cs = 1000, 50, 5

embeddings = theano.shared(0.2 * numpy.random.uniform(-1.0, 1.0, \
(nv+1, de)).astype(theano.config.floatX)) # add one for PADDING at the end

idxs = T.imatrix() # as many columns as words in the context window and as many lines as words in the sentence
x    = self.emb[idxs].reshape((idxs.shape[0], de*cs))

The x symbolic variable corresponds to a matrix of shape (number of words in the sentences, dimension of the embedding space X context window size).
Let’s compile a theano function to do so

>>> sample
array([0, 1, 2, 3, 4], dtype=int32)
>>> csample = contextwin(sample, 7)
[[-1, -1, -1, 0, 1, 2, 3],
[-1, -1,  0, 1, 2, 3, 4],
[-1,  0,  1, 2, 3, 4,-1],
[ 0,  1,  2, 3, 4,-1,-1],
[ 1,  2,  3, 4,-1,-1,-1]]
>>> f = theano.function(inputs=[idxs], outputs=x)
>>> f(csample)
array([[-0.08088442,  0.08458307,  0.05064092, ...,  0.06876887,
-0.06648078, -0.15192257],
[-0.08088442,  0.08458307,  0.05064092, ...,  0.11192625,
0.08745284,  0.04381778],
[-0.08088442,  0.08458307,  0.05064092, ..., -0.00937143,
0.10804889,  0.1247109 ],
[ 0.11038255, -0.10563177, -0.18760249, ..., -0.00937143,
0.10804889,  0.1247109 ],
[ 0.18738101,  0.14727569, -0.069544  , ..., -0.00937143,
0.10804889,  0.1247109 ]], dtype=float32)
>>> f(csample).shape
(5, 350)

We now have a sequence (of length 5 which is corresponds to the length of the sentence) of context window word embeddings which is easy to feed to a simple recurrent neural network to iterate
with.

Elman recurrent neural network

The followin (Elman) recurrent neural network (E-RNN) takes as input the current input (time 

t

)
and the previous hiddent state (time 

t-1

).
Then it iterates.
In the previous section, we processed the input to fit this sequential/temporal structure. It consists in a matrix where the row 

0

 corresponds
to the time step 

t=0

,
the row 

1

 corresponds
to the time step 

t=1

,
etc.
The parameters of the E-RNN to be learned are:
the word embeddings (real-valued matrix)
the initial hidden state (real-value vector)
two matrices for the linear projection of the input 

t

 and
the previous hidden layer state 

t-1

(optional) bias. Recommendation: don’t use it.
softmax classification layer on top
The hyperparameters define the whole architecture:
dimension of the word embedding
size of the vocabulary
number of hidden units
number of classes
random seed + way to initialize the model
It gives the following code:

class RNNSLU(object):
''' elman neural net model '''
def __init__(self, nh, nc, ne, de, cs):
'''
nh :: dimension of the hidden layer
nc :: number of classes
ne :: number of word embeddings in the vocabulary
de :: dimension of the word embeddings
cs :: word window context size
'''
# parameters of the model
self.emb = theano.shared(name='embeddings',
value=0.2 * numpy.random.uniform(-1.0, 1.0,
(ne+1, de))
# add one for padding at the end
.astype(theano.config.floatX))
self.wx = theano.shared(name='wx',
value=0.2 * numpy.random.uniform(-1.0, 1.0,
(de * cs, nh))
.astype(theano.config.floatX))
self.wh = theano.shared(name='wh',
value=0.2 * numpy.random.uniform(-1.0, 1.0,
(nh, nh))
.astype(theano.config.floatX))
self.w = theano.shared(name='w',
value=0.2 * numpy.random.uniform(-1.0, 1.0,
(nh, nc))
.astype(theano.config.floatX))
self.bh = theano.shared(name='bh',
value=numpy.zeros(nh,
dtype=theano.config.floatX))
self.b = theano.shared(name='b',
value=numpy.zeros(nc,
dtype=theano.config.floatX))
self.h0 = theano.shared(name='h0',
value=numpy.zeros(nh,
dtype=theano.config.floatX))

# bundle
self.params = [self.emb, self.wx, self.wh, self.w,
self.bh, self.b, self.h0]

Then we integrate the way to build the input from the embedding matrix:

idxs = T.imatrix()
x = self.emb[idxs].reshape((idxs.shape[0], de*cs))
y_sentence = T.ivector('y_sentence')  # labels

We use the scan operator to construct the recursion, works like a charm:

def recurrence(x_t, h_tm1):
h_t = T.nnet.sigmoid(T.dot(x_t, self.wx)
+ T.dot(h_tm1, self.wh) + self.bh)
s_t = T.nnet.softmax(T.dot(h_t, self.w) + self.b)
return [h_t, s_t]

[h, s], _ = theano.scan(fn=recurrence,
sequences=x,
outputs_info=[self.h0, None],
n_steps=x.shape[0])

p_y_given_x_sentence = s[:, 0, :]
y_pred = T.argmax(p_y_given_x_sentence, axis=1)

Theano will then compute all the gradients automatically to maximize the log-likelihood:

lr = T.scalar('lr')

sentence_nll = -T.mean(T.log(p_y_given_x_sentence)
[T.arange(x.shape[0]), y_sentence])
sentence_gradients = T.grad(sentence_nll, self.params)
sentence_updates = OrderedDict((p, p - lr*g)
for p, g in
zip(self.params, sentence_gradients))

Next compile those functions:

self.classify = theano.function(inputs=[idxs], outputs=y_pred)
self.sentence_train = theano.function(inputs=[idxs, y_sentence, lr],
outputs=sentence_nll,
updates=sentence_updates)

We keep the word embeddings on the unit sphere by normalizing them after each update:

self.normalize = theano.function(inputs=[],
updates={self.emb:
self.emb /
T.sqrt((self.emb**2)
.sum(axis=1))
.dimshuffle(0, 'x')})

And that’s it!

Evaluation

With the previous defined functions, you can compare the predicted labels with the true labels and compute some metrics. In this repo,
we build a wrapper around the conlleval PERL script. It’s not trivial to compute those metrics due to the Inside
Outside Beginning (IOB) representation i.e. a prediction is considered correct if the word-beginningand the word-inside and the word-outside predictions are all correct. Note that the extension is 

 and
you will have to change it to 

.

Training

Updates

For stochastic gradient descent (SGD) update, we consider the whole sentence as a mini-batch and perform one update per sentence. It is possible to perform a pure SGD (contrary to mini-batch) where the update
is done on only one single word at a time.
After each iteration/update, we normalize the word embeddings to keep them on a unit sphere.

Stopping Criterion

Early-stopping on a validation set is our regularization technique: the training is run for a given number of epochs (a single pass through the whole dataset) and keep the best model along with respect to the
F1 score computed on the validation set after each epoch.

Hyper-Parameter Selection

Although there is interesting research/code on the topic of automatic hyper-parameter
selection, we use the KISSrandom search.
The following intervals can give you some starting point:
learning rate : uniform([0.05,0.01])
window size : random value from {3,...,19}
number of hidden units : random value from {100,200}
embedding dimension : random value from {50,100}

Running the Code

After downloading the data using 

,
the user can then run the code by calling:

python code/rnnslu.py

('NEW BEST: epoch', 25, 'valid F1', 96.84, 'best test F1', 93.79)
[learning] epoch 26 >> 100.00% completed in 28.76 (sec) <<
[learning] epoch 27 >> 100.00% completed in 28.76 (sec) <<
...
('BEST RESULT: epoch', 57, 'valid F1', 97.23, 'best test F1', 94.2, 'with the model', 'rnnslu')

Timing

Running experiments on ATIS using this repository will run one epoch in less than 40 seconds
on i7 CPU 950 @ 3.07GHz using less than 200 Mo of RAM:

[learning] epoch 0 >> 100.00% completed in 34.48 (sec) <<

After a few epochs, you obtain decent performance 94.48 % of F1 score.:

NEW BEST: epoch 28 valid F1 96.61 best test F1 94.19
NEW BEST: epoch 29 valid F1 96.63 best test F1 94.42
[learning] epoch 30 >> 100.00% completed in 35.04 (sec) <<
[learning] epoch 31 >> 100.00% completed in 34.80 (sec) <<
[...]
NEW BEST: epoch 40 valid F1 97.25 best test F1 94.34
[learning] epoch 41 >> 100.00% completed in 35.18 (sec) <<
NEW BEST: epoch 42 valid F1 97.33 best test F1 94.48
[learning] epoch 43 >> 100.00% completed in 35.39 (sec) <<
[learning] epoch 44 >> 100.00% completed in 35.31 (sec) <<
[...]

Word Embedding Nearest Neighbors

We can check the k-nearest neighbors of the learned embeddings. L2 and cosine distance gave the same results so we plot them for the cosine distance.

atlanta	back	ap80	but	aircraft	business	a	august	actually	cheap
phoenix	live	ap57	if	plane	coach	people	september	provide	weekday
denver	lives	ap	up	service	first	do	january	prices	weekdays
tacoma	both	connections	a	airplane	fourth	but	june	stop	am
columbus	how	tomorrow	now	seating	thrift	numbers	december	number	early
seattle	me	before	amount	stand	tenth	abbreviation	november	flight	sfo
minneapolis	out	earliest	more	that	second	if	april	there	milwaukee
pittsburgh	other	connect	abbreviation	on	fifth	up	july	serving	jfk
ontario	plane	thrift	restrictions	turboprop	third	serve	jfk	thank	shortest
montreal	service	coach	mean	mean	twelfth	database	october	ticket	bwi
philadelphia	fare	today	interested	amount	sixth	passengers	may	are	lastest

As you can judge, the limited size of the vocabulary (about 500 words) gives us mitigated performance. According to human judgement: some are good, some are bad.