How can a computer do arithmetic with the meaning of words?

A computer can do arithmetic with meaning thanks to word embeddings. Each word becomes a long list of numbers, called a vector. The vectors are arranged so that words with similar meanings sit close together. Subtract one word's vector from another, add a third, and you land near a fourth word that makes the same kind of sense to a human.

The idea goes back to 1957. The English linguist John Rupert Firth proposed that a word is characterized by the company it keeps: words used in the same contexts tend to mean similar things. In 2013, a team at Google turned that idea into numbers with Word2vec, a small neural network trained on huge amounts of text. It gives every word a vector, usually a few hundred numbers long, based only on the words that tend to surround it.

What made Word2vec famous was that its vectors captured relationships, not just similarity. Take the vector for "Brother", subtract "Man", add "Woman", and the result is closest to "Sister". The same arithmetic works for countries and their capitals, and even for verb tenses. Nobody told the model what a sister or a capital city is. It learned the pattern from raw text.

That sensitivity to the company words keep has a dark side. In 2016, researchers showed that a popular word2vec model trained on Google News text produced the analogy "man is to computer programmer as woman is to homemaker". It had absorbed gender stereotypes from the articles it learned from. Later research found that using such embeddings without careful oversight can carry society's biases into the systems built on them, and can even amplify them.