Linear Algebraic Structure of Word Senses, with Applications to Polysemy

TL;DR

This paper reveals that multiple word senses are embedded in a linear superposition within word vectors and introduces a sparse coding method to recover these senses, supported by a mathematical model and empirical validation.

Contribution

It demonstrates that word senses can be linearly separated in embeddings and introduces a novel sparse coding technique with discourse atoms for sense extraction.

Findings

Multiple senses reside in linear superposition within embeddings

Sparse coding can recover approximate sense vectors

Discourse atoms provide succinct sense descriptions

Abstract

Word embeddings are ubiquitous in NLP and information retrieval, but it is unclear what they represent when the word is polysemous. Here it is shown that multiple word senses reside in linear superposition within the word embedding and simple sparse coding can recover vectors that approximately capture the senses. The success of our approach, which applies to several embedding methods, is mathematically explained using a variant of the random walk on discourses model (Arora et al., 2016). A novel aspect of our technique is that each extracted word sense is accompanied by one of about 2000 "discourse atoms" that gives a succinct description of which other words co-occur with that word sense. Discourse atoms can be of independent interest, and make the method potentially more useful. Empirical tests are used to verify and support the theory.