word2vec

word2vec is not a singular algorithm, rather, it is a family of model architectures and optimizations that can be used to learn word embeddings from large datasets. Embeddings learned through word2vec have proven to be successful on a variety of downstream natural language processing tasks.

These papers proposed two methods for learning representations of words:

Continuous bag-of-words model: predicts the middle word based on surrounding context words. The context consists of a few words before and after the current (middle) word. This architecture is called a bag-of-words model as the order of words in the context is not important.
Continuous skip-gram model: predicts words within a certain range before and after the current word in the same sentence. A worked example of this is given below.

You'll use the skip-gram approach in this tutorial. First, you'll explore skip-grams and other concepts using a single sentence for illustration. Next, you'll train your own word2vec model on a small dataset. This tutorial also contains code to export the trained embeddings and visualize them in the TensorFlow Embedding Projector.

Skip-gram and negative sampling

While a bag-of-words model predicts a word given the neighboring context, a skip-gram model predicts the context (or neighbors) of a word, given the word itself. The model is trained on skip-grams, which are n-grams that allow tokens to be skipped (see the diagram below for an example). The context of a word can be represented through a set of skip-gram pairs of (target_word, context_word) where context_word appears in the neighboring context of target_word.

Consider the following sentence of eight words:

The wide road shimmered in the hot sun.

The context words for each of the 8 words of this sentence are defined by a window size. The window size determines the span of words on either side of a target_word that can be considered a context word. Below is a table of skip-grams for target words based on different window sizes.

$word2vec_skipgrams$

The training objective of the skip-gram model is to maximize the probability of predicting context words given the target word. For a sequence of words w₁, w₂, ... w_T, the objective can be written as the average log probability

$word2vec_skipgram_objective$

where c is the size of the training context. The basic skip-gram formulation defines this probability using the softmax function.

$word2vec_full_softmax$

where v and v^' are target and context vector representations of words and W is vocabulary size.

Computing the denominator of this formulation involves performing a full softmax over the entire vocabulary words, which are often large (10⁵-10⁷) terms.

The noise contrastive estimation (NCE) loss function is an efficient approximation for a full softmax. With an objective to learn word embeddings instead of modeling the word distribution, the NCE loss can be simplified to use negative sampling.

The simplified negative sampling objective for a target word is to distinguish the context word from num_ns negative samples drawn from noise distribution P_n(w) of words. More precisely, an efficient approximation of full softmax over the vocabulary is, for a skip-gram pair, to pose the loss for a target word as a classification problem between the context word and num_ns negative samples.

A negative sample is defined as a (target_word, context_word) pair such that the context_word does not appear in the window_size neighborhood of the target_word. For the example sentence, these are a few potential negative samples (when window_size is 2).

(hot, shimmered)
(wide, hot)
(wide, sun)

In the next section, you'll generate skip-grams and negative samples for a single sentence. You'll also learn about subsampling techniques and train a classification model for positive and negative training examples later in the tutorial.

Setup

import io
import re
import string
import tqdm

import numpy as np

import tensorflow as tf
from tensorflow.keras import layers

2024-07-19 11:19:50.266209: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2024-07-19 11:19:50.287751: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2024-07-19 11:19:50.294095: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered

# Load the TensorBoard notebook extension
%load_ext tensorboard

SEED = 42
AUTOTUNE = tf.data.AUTOTUNE

Vectorize an example sentence

Consider the following sentence:

The wide road shimmered in the hot sun.

Tokenize the sentence:

sentence = "The wide road shimmered in the hot sun"
tokens = list(sentence.lower().split())
print(len(tokens))

Create a vocabulary to save mappings from tokens to integer indices:

vocab, index = {}, 1  # start indexing from 1
vocab['<pad>'] = 0  # add a padding token
for token in tokens:
  if token not in vocab:
    vocab[token] = index
    index += 1
vocab_size = len(vocab)
print(vocab)

{'<pad>': 0, 'the': 1, 'wide': 2, 'road': 3, 'shimmered': 4, 'in': 5, 'hot': 6, 'sun': 7}

Create an inverse vocabulary to save mappings from integer indices to tokens:

inverse_vocab = {index: token for token, index in vocab.items()}
print(inverse_vocab)

{0: '<pad>', 1: 'the', 2: 'wide', 3: 'road', 4: 'shimmered', 5: 'in', 6: 'hot', 7: 'sun'}

Vectorize your sentence:

example_sequence = [vocab[word] for word in tokens]
print(example_sequence)

[1, 2, 3, 4, 5, 1, 6, 7]

Generate skip-grams from one sentence

The tf.keras.preprocessing.sequence module provides useful functions that simplify data preparation for word2vec. You can use the tf.keras.preprocessing.sequence.skipgrams to generate skip-gram pairs from the example_sequence with a given window_size from tokens in the range [0, vocab_size).

window_size = 2
positive_skip_grams, _ = tf.keras.preprocessing.sequence.skipgrams(
      example_sequence,
      vocabulary_size=vocab_size,
      window_size=window_size,
      negative_samples=0)
print(len(positive_skip_grams))

Print a few positive skip-grams:

for target, context in positive_skip_grams[:5]:
  print(f"({target}, {context}): ({inverse_vocab[target]}, {inverse_vocab[context]})")

(2, 1): (wide, the)
(2, 3): (wide, road)
(1, 6): (the, hot)
(3, 5): (road, in)
(1, 7): (the, sun)

Negative sampling for one skip-gram

The skipgrams function returns all positive skip-gram pairs by sliding over a given window span. To produce additional skip-gram pairs that would serve as negative samples for training, you need to sample random words from the vocabulary. Use the tf.random.log_uniform_candidate_sampler function to sample num_ns number of negative samples for a given target word in a window. You can call the function on one skip-grams's target word and pass the context word as true class to exclude it from being sampled.

# Get target and context words for one positive skip-gram.
target_word, context_word = positive_skip_grams[0]

# Set the number of negative samples per positive context.
num_ns = 4

context_class = tf.reshape(tf.constant(context_word, dtype="int64"), (1, 1))
negative_sampling_candidates, _, _ = tf.random.log_uniform_candidate_sampler(
    true_classes=context_class,  # class that should be sampled as 'positive'
    num_true=1,  # each positive skip-gram has 1 positive context class
    num_sampled=num_ns,  # number of negative context words to sample
    unique=True,  # all the negative samples should be unique
    range_max=vocab_size,  # pick index of the samples from [0, vocab_size]
    seed=SEED,  # seed for reproducibility
    name="negative_sampling"  # name of this operation
)
print(negative_sampling_candidates)
print([inverse_vocab[index.numpy()] for index in negative_sampling_candidates])

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1721387992.808839    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.812783    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.816433    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.819973    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.831306    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.834967    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.838234    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.841501    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.844863    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.848342    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.851679    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387992.855085    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.077319    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.079463    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.081515    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.083524    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.085555    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.087555    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.089481    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.091388    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.093328    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.095306    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.097243    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.099177    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.136509    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.138618    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.140595    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.142565    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.144526    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.146537    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.148480    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
tf.Tensor([2 1 4 3], shape=(4,), dtype=int64)
['wide', 'the', 'shimmered', 'road']
I0000 00:00:1721387994.150422    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.152419    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.154834    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.157208    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1721387994.159570    9940 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355

Construct one training example

For a given positive (target_word, context_word) skip-gram, you now also have num_ns negative sampled context words that do not appear in the window size neighborhood of target_word. Batch the 1 positive context_word and num_ns negative context words into one tensor. This produces a set of positive skip-grams (labeled as 1) and negative samples (labeled as 0) for each target word.

# Reduce a dimension so you can use concatenation (in the next step).
squeezed_context_class = tf.squeeze(context_class, 1)

# Concatenate a positive context word with negative sampled words.
context = tf.concat([squeezed_context_class, negative_sampling_candidates], 0)

# Label the first context word as `1` (positive) followed by `num_ns` `0`s (negative).
label = tf.constant([1] + [0]*num_ns, dtype="int64")
target = target_word

Check out the context and the corresponding labels for the target word from the skip-gram example above:

print(f"target_index    : {target}")
print(f"target_word     : {inverse_vocab[target_word]}")
print(f"context_indices : {context}")
print(f"context_words   : {[inverse_vocab[c.numpy()] for c in context]}")
print(f"label           : {label}")

target_index    : 2
target_word     : wide
context_indices : [1 2 1 4 3]
context_words   : ['the', 'wide', 'the', 'shimmered', 'road']
label           : [1 0 0 0 0]

A tuple of (target, context, label) tensors constitutes one training example for training your skip-gram negative sampling word2vec model. Notice that the target is of shape (1,) while the context and label are of shape (1+num_ns,)