GloVe, FastText, and Subword Embeddings

> Word2Vec trained one embedding per word. GloVe factorized the co-occurrence matrix. FastText embedded the pieces. BPE bridged to transformers.

Type: Build

Languages: Python

Prerequisites: Phase 5 · 03 (Word2Vec from Scratch)

Time: ~45 minutes

The Problem

Word2Vec left two open questions.

First, there was a parallel line of research that factorized the co-occurrence matrix directly (LSA, HAL) rather than doing online skip-gram updates. Was Word2Vec's iterative approach fundamentally better, or was the difference an artifact of how the two methods handled counts? GloVe answered that: matrix factorization with a thoughtfully chosen loss matches or beats Word2Vec, and costs less to train.

Second, neither method had a story for words it had never seen. Zoomer-approved, dogecoin, any proper noun coined last week, every inflected form of a rare root. FastText fixed this by embedding character n-grams: a word is the sum of its parts, including morphemes, so even out-of-vocabulary words get a sensible vector.

Third, once transformers arrived, the question shifted again. Word-level vocabularies cap out around a million entries; real language is more open than that. Byte-pair encoding (BPE) and its relatives solved this by learning a vocabulary of frequent subword units that covers everything. Every modern tokenizer for every modern LLM is a subword tokenizer.

This lesson walks all three, then explains which to reach for when.

The Concept

GloVe (Global Vectors). Build the word-word co-occurrence matrix X where X[i][j] is how often word j appears in the context of word i. Train vectors such that v_i · v_j + b_i + b_j ≈ log(X[i][j]). Weight the loss so frequent pairs do not dominate. Done.

FastText. A word is the sum of its character n-grams plus the word itself. where becomes , . The word vector is the sum of those component vectors. Train as Word2Vec. Benefit: unseen words (whereupon) compose from known n-grams.

BPE (Byte-Pair Encoding). Start with a vocabulary of individual bytes (or characters). Count every adjacent pair in the corpus. Merge the most frequent pair into a new token. Repeat for k iterations. Result: a vocabulary of k + 256 tokens where frequent sequences (ing, tion, the) are single tokens and rare words are broken into familiar pieces. Every sentence tokenizes into something.

Build It

GloVe: factorize the co-occurrence matrix

import numpy as np
from collections import Counter


def build_cooccurrence(docs, window=5):
    pair_counts = Counter()
    vocab = {}
    for doc in docs:
        for token in doc:
            if token not in vocab:
                vocab[token] = len(vocab)
    for doc in docs:
        indexed = [vocab[t] for t in doc]
        for i, center in enumerate(indexed):
            for j in range(max(0, i - window), min(len(indexed), i + window + 1)):
                if i != j:
                    distance = abs(i - j)
                    pair_counts[(center, indexed[j])] += 1.0 / distance
    return vocab, pair_counts


def glove_train(vocab, pair_counts, dim=16, epochs=100, lr=0.05, x_max=100, alpha=0.75, seed=0):
    n = len(vocab)
    rng = np.random.default_rng(seed)
    W = rng.normal(0, 0.1, size=(n, dim))
    W_tilde = rng.normal(0, 0.1, size=(n, dim))
    b = np.zeros(n)
    b_tilde = np.zeros(n)

    for epoch in range(epochs):
        for (i, j), x_ij in pair_counts.items():
            weight = (x_ij / x_max) ** alpha if x_ij < x_max else 1.0
            diff = W[i] @ W_tilde[j] + b[i] + b_tilde[j] - np.log(x_ij)
            coef = weight * diff

            grad_W_i = coef * W_tilde[j]
            grad_W_tilde_j = coef * W[i]
            W[i] -= lr * grad_W_i
            W_tilde[j] -= lr * grad_W_tilde_j
            b[i] -= lr * coef
            b_tilde[j] -= lr * coef

    return W + W_tilde

Two moving pieces worth naming. The weighting function f(x) = (x/x_max)^alpha downweights very frequent pairs (like (the, and)) so they do not dominate the loss. The final embedding is the sum of W (center) and W_tilde (context) tables. Summing both is a published trick that tends to outperform using just one.

FastText: subword-aware embeddings

def char_ngrams(word, n_min=3, n_max=6):
    wrapped = f"<{word}>"
    grams = {wrapped}
    for n in range(n_min, n_max + 1):
        for i in range(len(wrapped) - n + 1):
            grams.add(wrapped[i:i + n])
    return grams

>>> char_ngrams("where")
{'<where>', '<wh', 'whe', 'her', 'ere', 're>', '<whe', 'wher', 'here', 'ere>', '<wher', 'where', 'here>'}

Each word is represented by its set of n-grams (typically 3 to 6 characters). The word embedding is the sum of its n-gram embeddings. For skip-gram training, plug this in where Word2Vec used a single vector.

def fasttext_vector(word, ngram_table):
    grams = char_ngrams(word)
    vecs = [ngram_table[g] for g in grams if g in ngram_table]
    if not vecs:
        return None
    return np.sum(vecs, axis=0)

For an unseen word, you still get a vector as long as some of its n-grams are known. whereupon shares , her, ere, and with where, so the two land near each other.

def learn_bpe(corpus, k_merges):
    vocab = Counter()
    for word, freq in corpus.items():
        tokens = tuple(word) + ("</w>",)
        vocab[tokens] = freq

    merges = []
    for _ in range(k_merges):
        pair_freq = Counter()
        for tokens, freq in vocab.items():
            for a, b in zip(tokens, tokens[1:]):
                pair_freq[(a, b)] += freq
        if not pair_freq:
            break
        best = pair_freq.most_common(1)[0][0]
        merges.append(best)

        new_vocab = Counter()
        for tokens, freq in vocab.items():
            new_tokens = []
            i = 0
            while i < len(tokens):
                if i + 1 < len(tokens) and (tokens[i], tokens[i + 1]) == best:
                    new_tokens.append(tokens[i] + tokens[i + 1])
                    i += 2
                else:
                    new_tokens.append(tokens[i])
                    i += 1
            new_vocab[tuple(new_tokens)] = freq
        vocab = new_vocab
    return merges


def apply_bpe(word, merges):
    tokens = list(word) + ["</w>"]
    for a, b in merges:
        new_tokens = []
        i = 0
        while i < len(tokens):
            if i + 1 < len(tokens) and tokens[i] == a and tokens[i + 1] == b:
                new_tokens.append(a + b)
                i += 2
            else:
                new_tokens.append(tokens[i])
                i += 1
        tokens = new_tokens
    return tokens

>>> corpus = Counter({"low": 5, "lower": 2, "newest": 6, "widest": 3})
>>> merges = learn_bpe(corpus, k_merges=10)
>>> apply_bpe("lowest", merges)
['low', 'est</w>']

import fasttext.util
fasttext.util.download_model("en", if_exists="ignore")
ft = fasttext.load_model("cc.en.300.bin")
print(ft.get_word_vector("whereupon").shape)
print(ft.get_word_vector("zoomerapproved").shape)

from transformers import AutoTokenizer

tok = AutoTokenizer.from_pretrained("gpt2")
print(tok.tokenize("unbelievably tokenized"))

['un', 'bel', 'iev', 'ably', 'Ġtoken', 'ized']

name: tokenizer-picker
description: Pick a tokenization approach for a new language model or text pipeline.
version: 1.0.0
phase: 5
lesson: 04
tags: [nlp, tokenization, embeddings]
---

Given a task and dataset description, you output:

1. Tokenization strategy (word-level, BPE, WordPiece, SentencePiece, byte-level). One-sentence reason.
2. Vocabulary size target (e.g., 32k for an English-only LM, 64k-100k for multilingual).
3. Library call with the exact training command. Name the library. Quote the arguments.
4. One reproducibility pitfall. Tokenizer-model mismatch is the single most common silent production bug; call out which pair must be used together.

Refuse to recommend training a custom tokenizer when the user is fine-tuning a pretrained LLM. Refuse to recommend word-level tokenization for any model targeting production inference. Flag non-English / multi-script corpora as needing SentencePiece with byte fallback.