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Pre-trained Word Embeddings

In this notebook, we’ll demonstrate how to use pre-trained word embeddings. To see why word embeddings are useful, it’s worth comparing them to the alternative. Without word embeddings, we may represent each word with a one-hot vector [0, ...,0, 1, 0, ... 0], where at the index corresponding to the appropriate vocabulary word, 1 is placed, and the value 0 occurs everywhere else. The weight matrices connecting our word-level inputs to the network’s hidden layers would each be \(v \times h\), where \(v\) is the size of the vocabulary and \(h\) is the size of the hidden layer. With 100,000 words feeding into an LSTM layer with \(1000\) nodes, the model would need to learn \(4\) different weight matrices (one for each of the LSTM gates), each with 100 million weights, and thus 400 million parameters in total.

Fortunately, it turns out that a number of efficient techniques can quickly discover broadly useful word embeddings in an unsupervised manner. These embeddings map each word onto a low-dimensional vector \(w \in R^d\) with \(d\) commonly chosen to be roughly \(100\). Intuitively, these embeddings are chosen based on the contexts in which words appear. Words that appear in similar contexts, like “tennis” and “racquet,” should have similar embeddings while words that are not alike, like “rat” and “gourmet,” should have dissimilar embeddings.

Practitioners of deep learning for NLP typically initialize their models using pre-trained word embeddings, bringing in outside information, and reducing the number of parameters that a neural network needs to learn from scratch.

Two popular word embeddings are GloVe and fastText.

The following examples use pre-trained word embeddings drawn from the following sources:

To begin, let’s first import a few packages that we’ll need for this example:

In [1]:
import warnings
warnings.filterwarnings('ignore')

from mxnet import gluon
from mxnet import nd
import gluonnlp as nlp
import re

Creating Vocabulary with Word Embeddings

Now we’ll demonstrate how to index words, attach pre-trained word embeddings for them, and use such embeddings in Gluon. First, let’s assign a unique ID and word vector to each word in the vocabulary in just a few lines of code.

Creating Vocabulary from Data Sets

To begin, suppose that we have a simple text data set consisting of newline-separated strings.

In [2]:
text = " hello world \n hello nice world \n hi world \n"

To start, let’s implement a simple tokenizer to separate the words and then count the frequency of each word in the data set. We can use our defined tokenizer to count word frequency in the data set.

In [3]:
def simple_tokenize(source_str, token_delim=' ', seq_delim='\n'):
    return filter(None, re.split(token_delim + '|' + seq_delim, source_str))
counter = nlp.data.count_tokens(simple_tokenize(text))

The obtained counter behaves like a Python dictionary whose key-value pairs consist of words and their frequencies, respectively. We can then instantiate a Vocab object with a counter. Because counter tracks word frequencies, we are able to specify arguments such as max_size (maximum size) and min_freq (minimum frequency) to the Vocab constructor to restrict the size of the resulting vocabulary.

Suppose that we want to build indices for all the keys in counter. If we simply want to construct a Vocab containing every word, then we can supply counter the only argument.

In [4]:
vocab = nlp.Vocab(counter)

A Vocab object associates each word with an index. We can easily access words by their indices using the vocab.idx_to_token attribute.

In [5]:
for word in vocab.idx_to_token:
    print(word)
<unk>
<pad>
<bos>
<eos>
world
hello
hi
nice

Contrarily, we can also grab an index given a token using vocab.token_to_idx.

In [6]:
print(vocab.token_to_idx["<unk>"])
print(vocab.token_to_idx["world"])
0
4

In Gluon NLP, for each word, there are three representations: the index of where it occurred in the original input (idx), the embedding (or vector/vec), and the token (the actual word). At any point, we may use any of the following methods to switch between the three representations: idx_to_vec, idx_to_token, token_to_idx.

Attaching word embeddings

Our next step will be to attach word embeddings to the words indexed by vocab. In this example, we’ll use fastText embeddings trained on the wiki.simple dataset. First, we’ll want to create a word embedding instance by calling nlp.embedding.create, specifying the embedding type fasttext (an unnamed argument) and the source source='wiki.simple' (the named argument).

In [7]:
fasttext_simple = nlp.embedding.create('fasttext', source='wiki.simple')
Embedding file wiki.simple.npz is not found. Downloading from Gluon Repository. This may take some time.
Downloading /root/.mxnet/embedding/fasttext/wiki.simple.npz from https://apache-mxnet.s3-accelerate.dualstack.amazonaws.com/gluon/embeddings/fasttext/wiki.simple.npz...

To attach the newly loaded word embeddings fasttext_simple to indexed words in vocab, we can simply call vocab’s set_embedding method:

In [8]:
vocab.set_embedding(fasttext_simple)

To see other available sources of pretrained word embeddings using the fastText algorithm, we can call text.embedding.list_sources.

In [9]:
nlp.embedding.list_sources('fasttext')[:5]
Out[9]:
['crawl-300d-2M', 'crawl-300d-2M-subword', 'wiki.aa', 'wiki.ab', 'wiki.ace']

The created vocabulary vocab includes four different words and a special unknown token. Let us check the size of vocab.

In [10]:
len(vocab)
Out[10]:
8

By default, the vector of any token that is unknown to vocab is a zero vector. Its length is equal to the vector dimensions of the fastText word embeddings: (300,).

In [11]:
vocab.embedding['beautiful'].shape
Out[11]:
(300,)

The first five elements of the vector of any unknown token are zeros.

In [12]:
vocab.embedding['beautiful'][:5]
Out[12]:

[0. 0. 0. 0. 0.]
<NDArray 5 @cpu(0)>

Let us check the shape of the embedding of the words ‘hello’ and ‘world’ from vocab.

In [13]:
vocab.embedding['hello', 'world'].shape
Out[13]:
(2, 300)

We can access the first five elements of the embedding of ‘hello’ and ‘world’ and see that they are non-zero.

In [14]:
vocab.embedding['hello', 'world'][:, :5]
Out[14]:

[[ 0.39567   0.21454  -0.035389 -0.24299  -0.095645]
 [ 0.10444  -0.10858   0.27212   0.13299  -0.33165 ]]
<NDArray 2x5 @cpu(0)>

Using Pre-trained Word Embeddings in Gluon

To demonstrate how to use pre- trained word embeddings in Gluon, let us first obtain the indices of the words ‘hello’ and ‘world’.

In [15]:
vocab['hello', 'world']
Out[15]:
[5, 4]

We can obtain the vectors for the words ‘hello’ and ‘world’ by specifying their indices (5 and 4) and the weight or embedding matrix, which we get from calling vocab.embedding.idx_to_vec in gluon.nn.Embedding. We initialize a new layer and set the weights using the layer.weight.set_data method. Subsequently, we pull out the indices 5 and 4 from the weight vector and check their first five entries.

In [16]:
input_dim, output_dim = vocab.embedding.idx_to_vec.shape
layer = gluon.nn.Embedding(input_dim, output_dim)
layer.initialize()
layer.weight.set_data(vocab.embedding.idx_to_vec)
layer(nd.array([5, 4]))[:, :5]
Out[16]:

[[ 0.39567   0.21454  -0.035389 -0.24299  -0.095645]
 [ 0.10444  -0.10858   0.27212   0.13299  -0.33165 ]]
<NDArray 2x5 @cpu(0)>

Creating Vocabulary from Pre-trained Word Embeddings

We can also create vocabulary by using vocabulary of pre-trained word embeddings, such as GloVe. Below are a few pre-trained file names under the GloVe word embedding.

In [17]:
nlp.embedding.list_sources('glove')[:5]
Out[17]:
['glove.42B.300d',
 'glove.6B.100d',
 'glove.6B.200d',
 'glove.6B.300d',
 'glove.6B.50d']

For simplicity of demonstration, we use a smaller word embedding file, such as the 50-dimensional one.

In [18]:
glove_6b50d = nlp.embedding.create('glove', source='glove.6B.50d')
Embedding file glove.6B.50d.npz is not found. Downloading from Gluon Repository. This may take some time.
Downloading /root/.mxnet/embedding/glove/glove.6B.50d.npz from https://apache-mxnet.s3-accelerate.dualstack.amazonaws.com/gluon/embeddings/glove/glove.6B.50d.npz...

Now we create vocabulary by using all the tokens from glove_6b50d.

In [19]:
vocab = nlp.Vocab(nlp.data.Counter(glove_6b50d.idx_to_token))
vocab.set_embedding(glove_6b50d)

Below shows the size of vocab including a special unknown token.

In [20]:
len(vocab.idx_to_token)
Out[20]:
400004

We can access attributes of vocab.

In [21]:
print(vocab['beautiful'])
print(vocab.idx_to_token[71424])
71424
beautiful

Applications of Word Embeddings

To apply word embeddings, we need to define cosine similarity. Cosine similarity determines the similarity between two vectors.

In [22]:
from mxnet import nd
def cos_sim(x, y):
    return nd.dot(x, y) / (nd.norm(x) * nd.norm(y))

The range of cosine similarity between two vectors can be between -1 and 1. The larger the value, the larger the similarity between the two vectors.

In [23]:
x = nd.array([1, 2])
y = nd.array([10, 20])
z = nd.array([-1, -2])

print(cos_sim(x, y))
print(cos_sim(x, z))

[1.]
<NDArray 1 @cpu(0)>

[-1.]
<NDArray 1 @cpu(0)>

Word Similarity

Given an input word, we can find the nearest \(k\) words from the vocabulary (400,000 words excluding the unknown token) by similarity. The similarity between any given pair of words can be represented by the cosine similarity of their vectors.

We first must normalize each row, followed by taking the dot product of the entire vocabulary embedding matrix and the single word embedding (dot_prod). We can then find the indices for which the dot product is greatest (topk), which happens to be the indices of the most similar words.

In [24]:
def norm_vecs_by_row(x):
    return x / nd.sqrt(nd.sum(x * x, axis=1) + 1E-10).reshape((-1,1))

def get_knn(vocab, k, word):
    word_vec = vocab.embedding[word].reshape((-1, 1))
    vocab_vecs = norm_vecs_by_row(vocab.embedding.idx_to_vec)
    dot_prod = nd.dot(vocab_vecs, word_vec)
    indices = nd.topk(dot_prod.reshape((len(vocab), )), k=k+1, ret_typ='indices')
    indices = [int(i.asscalar()) for i in indices]
    # Remove unknown and input tokens.
    return vocab.to_tokens(indices[1:])

Let us find the 5 most similar words to ‘baby’ from the vocabulary (size: 400,000 words).

In [25]:
get_knn(vocab, 5, 'baby')
Out[25]:
['babies', 'boy', 'girl', 'newborn', 'pregnant']

We can verify the cosine similarity of the vectors of ‘baby’ and ‘babies’.

In [26]:
cos_sim(vocab.embedding['baby'], vocab.embedding['babies'])
Out[26]:

[0.83871305]
<NDArray 1 @cpu(0)>

Let us find the 5 most similar words to ‘computers’ from the vocabulary.

In [27]:
get_knn(vocab, 5, 'computers')
Out[27]:
['computer', 'phones', 'pcs', 'machines', 'devices']

Let us find the 5 most similar words to ‘run’ from the given vocabulary.

In [28]:
get_knn(vocab, 5, 'run')
Out[28]:
['running', 'runs', 'went', 'start', 'ran']

Let us find the 5 most similar words to ‘beautiful’ from the vocabulary.

In [29]:
get_knn(vocab, 5, 'beautiful')
Out[29]:
['lovely', 'gorgeous', 'wonderful', 'charming', 'beauty']

Word Analogy

We can also apply pre-trained word embeddings to the word analogy problem. For example, “man : woman :: son : daughter” is an analogy. This sentence can also be read as “A man is to a woman as a son is to a daughter.”

The word analogy completion problem is defined concretely as: for analogy ‘a : b :: c : d’, given the first three words ‘a’, ‘b’, ‘c’, find ‘d’. The idea is to find the most similar word vector for vec(‘c’) + (vec(‘b’)-vec(‘a’)).

In this example, we will find words that are analogous from the 400,000 indexed words in vocab.

In [30]:
def get_top_k_by_analogy(vocab, k, word1, word2, word3):
    word_vecs = vocab.embedding[word1, word2, word3]
    word_diff = (word_vecs[1] - word_vecs[0] + word_vecs[2]).reshape((-1, 1))
    vocab_vecs = norm_vecs_by_row(vocab.embedding.idx_to_vec)
    dot_prod = nd.dot(vocab_vecs, word_diff)
    indices = nd.topk(dot_prod.reshape((len(vocab), )), k=k, ret_typ='indices')
    indices = [int(i.asscalar()) for i in indices]
    return vocab.to_tokens(indices)

We leverage this method to find the word to complete the analogy ‘man : woman :: son :’.

In [31]:
get_top_k_by_analogy(vocab, 1, 'man', 'woman', 'son')
Out[31]:
['daughter']

Let us verify the cosine similarity between vec(‘son’)+vec(‘woman’)-vec(‘man’) and vec(‘daughter’).

In [32]:
def cos_sim_word_analogy(vocab, word1, word2, word3, word4):
    words = [word1, word2, word3, word4]
    vecs = vocab.embedding[words]
    return cos_sim(vecs[1] - vecs[0] + vecs[2], vecs[3])

cos_sim_word_analogy(vocab, 'man', 'woman', 'son', 'daughter')
Out[32]:

[0.9658341]
<NDArray 1 @cpu(0)>

And to perform some more tests, let’s try the following analogy: ‘beijing : china :: tokyo : ‘.

In [33]:
get_top_k_by_analogy(vocab, 1, 'beijing', 'china', 'tokyo')
Out[33]:
['japan']

And another word analogy: ‘bad : worst :: big : ‘.

In [34]:
get_top_k_by_analogy(vocab, 1, 'bad', 'worst', 'big')
Out[34]:
['biggest']

And the last analogy: ‘do : did :: go :’.

In [35]:
get_top_k_by_analogy(vocab, 1, 'do', 'did', 'go')
Out[35]:
['went']