14.7. Word Similarity and Analogy
Open the notebook in Colab
Open the notebook in Colab
Open the notebook in Colab

In Section 14.4, we trained a word2vec model on a small dataset, and applied it to find semantically similar words for an input word. In practice, word vectors that are pretrained on large corpora can be applied to downstream natural language processing tasks, which will be covered later in Section 15. To demonstrate semantics of pretrained word vectors from large corpora in a straightforward way, let us apply them in the word similarity and analogy tasks.

import os
from mxnet import np, npx
from d2l import mxnet as d2l

npx.set_np()
import os
import torch
from torch import nn
from d2l import torch as d2l

14.7.1. Loading Pretrained Word Vectors

Below lists pretrained GloVe embeddings of dimension 50, 100, and 300, which can be downloaded from the GloVe website. The pretrained fastText embeddings are available in multiple languages. Here we consider one English version (300-dimensional “wiki.en”) that can be downloaded from the fastText website.

#@save
d2l.DATA_HUB['glove.6b.50d'] = (d2l.DATA_URL + 'glove.6B.50d.zip',
                                '0b8703943ccdb6eb788e6f091b8946e82231bc4d')

#@save
d2l.DATA_HUB['glove.6b.100d'] = (d2l.DATA_URL + 'glove.6B.100d.zip',
                                 'cd43bfb07e44e6f27cbcc7bc9ae3d80284fdaf5a')

#@save
d2l.DATA_HUB['glove.42b.300d'] = (d2l.DATA_URL + 'glove.42B.300d.zip',
                                  'b5116e234e9eb9076672cfeabf5469f3eec904fa')

#@save
d2l.DATA_HUB['wiki.en'] = (d2l.DATA_URL + 'wiki.en.zip',
                           'c1816da3821ae9f43899be655002f6c723e91b88')
#@save
d2l.DATA_HUB['glove.6b.50d'] = (d2l.DATA_URL + 'glove.6B.50d.zip',
                                '0b8703943ccdb6eb788e6f091b8946e82231bc4d')

#@save
d2l.DATA_HUB['glove.6b.100d'] = (d2l.DATA_URL + 'glove.6B.100d.zip',
                                 'cd43bfb07e44e6f27cbcc7bc9ae3d80284fdaf5a')

#@save
d2l.DATA_HUB['glove.42b.300d'] = (d2l.DATA_URL + 'glove.42B.300d.zip',
                                  'b5116e234e9eb9076672cfeabf5469f3eec904fa')

#@save
d2l.DATA_HUB['wiki.en'] = (d2l.DATA_URL + 'wiki.en.zip',
                           'c1816da3821ae9f43899be655002f6c723e91b88')

To load these pretrained GloVe and fastText embeddings, we define the following TokenEmbedding class.

#@save
class TokenEmbedding:
    """Token Embedding."""
    def __init__(self, embedding_name):
        self.idx_to_token, self.idx_to_vec = self._load_embedding(
            embedding_name)
        self.unknown_idx = 0
        self.token_to_idx = {token: idx for idx, token in
                             enumerate(self.idx_to_token)}

    def _load_embedding(self, embedding_name):
        idx_to_token, idx_to_vec = ['<unk>'], []
        data_dir = d2l.download_extract(embedding_name)
        # GloVe website: https://nlp.stanford.edu/projects/glove/
        # fastText website: https://fasttext.cc/
        with open(os.path.join(data_dir, 'vec.txt'), 'r') as f:
            for line in f:
                elems = line.rstrip().split(' ')
                token, elems = elems[0], [float(elem) for elem in elems[1:]]
                # Skip header information, such as the top row in fastText
                if len(elems) > 1:
                    idx_to_token.append(token)
                    idx_to_vec.append(elems)
        idx_to_vec = [[0] * len(idx_to_vec[0])] + idx_to_vec
        return idx_to_token, np.array(idx_to_vec)

    def __getitem__(self, tokens):
        indices = [self.token_to_idx.get(token, self.unknown_idx)
                   for token in tokens]
        vecs = self.idx_to_vec[np.array(indices)]
        return vecs

    def __len__(self):
        return len(self.idx_to_token)
#@save
class TokenEmbedding:
    """Token Embedding."""
    def __init__(self, embedding_name):
        self.idx_to_token, self.idx_to_vec = self._load_embedding(
            embedding_name)
        self.unknown_idx = 0
        self.token_to_idx = {token: idx for idx, token in
                             enumerate(self.idx_to_token)}

    def _load_embedding(self, embedding_name):
        idx_to_token, idx_to_vec = ['<unk>'], []
        data_dir = d2l.download_extract(embedding_name)
        # GloVe website: https://nlp.stanford.edu/projects/glove/
        # fastText website: https://fasttext.cc/
        with open(os.path.join(data_dir, 'vec.txt'), 'r') as f:
            for line in f:
                elems = line.rstrip().split(' ')
                token, elems = elems[0], [float(elem) for elem in elems[1:]]
                # Skip header information, such as the top row in fastText
                if len(elems) > 1:
                    idx_to_token.append(token)
                    idx_to_vec.append(elems)
        idx_to_vec = [[0] * len(idx_to_vec[0])] + idx_to_vec
        return idx_to_token, torch.tensor(idx_to_vec)

    def __getitem__(self, tokens):
        indices = [self.token_to_idx.get(token, self.unknown_idx)
                   for token in tokens]
        vecs = self.idx_to_vec[torch.tensor(indices)]
        return vecs

    def __len__(self):
        return len(self.idx_to_token)

Below we load the 50-dimensional GloVe embeddings (pretrained on a Wikipedia subset). When creating the TokenEmbedding instance, the specified embedding file has to be downloaded if it was not yet.

glove_6b50d = TokenEmbedding('glove.6b.50d')
glove_6b50d = TokenEmbedding('glove.6b.50d')

Output the vocabulary size. The vocabulary contains 400000 words (tokens) and a special unknown token.

len(glove_6b50d)
400001
len(glove_6b50d)
400001

We can get the index of a word in the vocabulary, and vice versa.

glove_6b50d.token_to_idx['beautiful'], glove_6b50d.idx_to_token[3367]
(3367, 'beautiful')
glove_6b50d.token_to_idx['beautiful'], glove_6b50d.idx_to_token[3367]
(3367, 'beautiful')

14.7.2. Applying Pretrained Word Vectors

Using the loaded GloVe vectors, we will demonstrate their semantics by applying them in the following word similarity and analogy tasks.

14.7.2.1. Word Similarity

Similar to Section 14.4.3, in order to find semantically similar words for an input word based on cosine similarities between word vectors, we implement the following knn (\(k\)-nearest neighbors) function.

def knn(W, x, k):
    # Add 1e-9 for numerical stability
    cos = np.dot(W, x.reshape(-1,)) / (
        np.sqrt(np.sum(W * W, axis=1) + 1e-9) * np.sqrt((x * x).sum()))
    topk = npx.topk(cos, k=k, ret_typ='indices')
    return topk, [cos[int(i)] for i in topk]
def knn(W, x, k):
    # Add 1e-9 for numerical stability
    cos = torch.mv(W, x.reshape(-1,)) / (
        torch.sqrt(torch.sum(W * W, axis=1) + 1e-9) *
        torch.sqrt((x * x).sum()))
    _, topk = torch.topk(cos, k=k)
    return topk, [cos[int(i)] for i in topk]

Then, we search for similar words using the pretrained word vectors from the TokenEmbedding instance embed.

def get_similar_tokens(query_token, k, embed):
    topk, cos = knn(embed.idx_to_vec, embed[[query_token]], k + 1)
    for i, c in zip(topk[1:], cos[1:]):  # Exclude the input word
        print(f'cosine sim={float(c):.3f}: {embed.idx_to_token[int(i)]}')
def get_similar_tokens(query_token, k, embed):
    topk, cos = knn(embed.idx_to_vec, embed[[query_token]], k + 1)
    for i, c in zip(topk[1:], cos[1:]):  # Exclude the input word
        print(f'cosine sim={float(c):.3f}: {embed.idx_to_token[int(i)]}')

The vocabulary of the pretrained word vectors in glove_6b50d contains 400000 words and a special unknown token. Excluding the input word and unknown token, among this vocabulary let us find three most semantically similar words to word “chip”.

get_similar_tokens('chip', 3, glove_6b50d)
cosine sim=0.856: chips
cosine sim=0.749: intel
cosine sim=0.749: electronics
get_similar_tokens('chip', 3, glove_6b50d)
cosine sim=0.856: chips
cosine sim=0.749: intel
cosine sim=0.749: electronics

Below outputs similar words to “baby” and “beautiful”.

get_similar_tokens('baby', 3, glove_6b50d)
cosine sim=0.839: babies
cosine sim=0.800: boy
cosine sim=0.792: girl
get_similar_tokens('beautiful', 3, glove_6b50d)
cosine sim=0.921: lovely
cosine sim=0.893: gorgeous
cosine sim=0.830: wonderful
get_similar_tokens('baby', 3, glove_6b50d)
cosine sim=0.839: babies
cosine sim=0.800: boy
cosine sim=0.792: girl
get_similar_tokens('beautiful', 3, glove_6b50d)
cosine sim=0.921: lovely
cosine sim=0.893: gorgeous
cosine sim=0.830: wonderful

14.7.2.2. Word Analogy

Besides finding similar words, we can also apply word vectors to word analogy tasks. For example, “man”:“woman”::“son”:“daughter” is the form of a word analogy: “man” is to “woman” as “son” is to “daughter”. Specifically, the word analogy completion task can be defined as: for a word analogy \(a : b :: c : d\), given the first three words \(a\), \(b\) and \(c\), find \(d\). Denote the vector of word \(w\) by \(\text{vec}(w)\). To complete the analogy, we will find the word whose vector is most similar to the result of \(\text{vec}(c)+\text{vec}(b)-\text{vec}(a)\).

def get_analogy(token_a, token_b, token_c, embed):
    vecs = embed[[token_a, token_b, token_c]]
    x = vecs[1] - vecs[0] + vecs[2]
    topk, cos = knn(embed.idx_to_vec, x, 1)
    return embed.idx_to_token[int(topk[0])]  # Remove unknown words
def get_analogy(token_a, token_b, token_c, embed):
    vecs = embed[[token_a, token_b, token_c]]
    x = vecs[1] - vecs[0] + vecs[2]
    topk, cos = knn(embed.idx_to_vec, x, 1)
    return embed.idx_to_token[int(topk[0])]  # Remove unknown words

Let us verify the “male-female” analogy using the loaded word vectors.

get_analogy('man', 'woman', 'son', glove_6b50d)
'daughter'
get_analogy('man', 'woman', 'son', glove_6b50d)
'daughter'

Below completes a “capital-country” analogy: “beijing”:“china”::“tokyo”:“japan”. This demonstrates semantics in the pretrained word vectors.

get_analogy('beijing', 'china', 'tokyo', glove_6b50d)
'japan'
get_analogy('beijing', 'china', 'tokyo', glove_6b50d)
'japan'

For the “adjective-superlative adjective” analogy such as “bad”:“worst”::“big”:“biggest”, we can see that the pretrained word vectors may capture the syntactic information.

get_analogy('bad', 'worst', 'big', glove_6b50d)
'biggest'
get_analogy('bad', 'worst', 'big', glove_6b50d)
'biggest'

To show the captured notion of past tense in the pretrained word vectors, we can test the syntax using the “present tense-past tense” analogy: “do”:“did”::“go”:“went”.

get_analogy('do', 'did', 'go', glove_6b50d)
'went'
get_analogy('do', 'did', 'go', glove_6b50d)
'went'

14.7.3. Summary

  • In practice, word vectors that are pretrained on large corpora can be applied to downstream natural language processing tasks.

  • Pretrained word vectors can be applied to the word similarity and analogy tasks.

14.7.4. Exercises

  1. Test the fastText results using TokenEmbedding('wiki.en').

  2. When the vocabulary is extremely large, how can we find similar words or complete a word analogy faster?