Linear Algebraic Structure of Word Senses, with Applications to Polysemy
Sanjeev Arora, Yuanzhi Li, Yingyu Liang, Tengyu Ma, Andrej Risteski
TL;DR
This paper shows that word senses in standard embeddings such as word2vec and GloVe reside in linear superpositions, formalized as the Linearity Assertion where a word vector is a nonnegative linear combination of its sense vectors. It grounds this in a Gaussian walk (random-discourse) model and derives a linear transform $A$ that links context averages to the target word embedding, then employs sparse coding with ~2000 discourse atoms to extract sense vectors and interrelate senses across words. The authors validate the theory with induced-embedding experiments, pseudoword and sense-subspace tests, and three WSI-oriented tasks, achieving competitive performance and introducing the novel discourse-atom interpretation. A new police-lineup evaluation further demonstrates practical, interpretable sense extraction from off-the-shelf embeddings, suggesting a scalable, theory-driven pathway for polysemy in NLP applications.
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.