Cited by 186Topic ModelingNatural Language Processing TechniquesSentiment Analysis and Opinion Mining

Linear Algebraic Structure of Word Senses, with Applications to Polysemy

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Arora, Sanjeev, Li, Yuanzhi, Liang, Yingyu, Ma, Tengyu, Risteski, Andrej·2018·Transactions of the Association for Computational Linguistics

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.

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  • Documents can be conceived of as a random walk in a discourse space, where words are more likely to follow other words if they are closer in an embedding space.

    “Those papers conceive of documents being a "random walk" in a discourse space, where words are more likely to follow other words if they are closer to them in an embedding space.”

    From Embedding Regression: Models for Context-Specific Description and Inference (2023) · cites this paper as Arora et al. 2018

    Section 2, “Justification for Linearity Assertion” (page not provided), describes a slow random walk through discourse space that generates nearby words. But it says word probabilities depend on closeness to the current discourse vector, not directly on closeness to the preceding word’s embedding. (LLM, conf=0.85)

    Experimental — accuracy not yet measured
  • Under the random walk model, a particular relationship follows for the embedding of a word and the embeddings of the words that appear in its contexts.

    “Crucially for ALC, Arora et al. (2018) also proves that under this model, a particular relationship will follow for the embedding of a word and the embeddings of the words that appear in the contexts around it.”

    From Embedding Regression: Models for Context-Specific Description and Inference (2023) · cites this paper as Arora et al. 2018

  • The matrix A downweights the contributions of very common but uninformative words when averaging.

    “That A serves to downweight the contributions of very common (but uninformative) words when averaging.”

    From Embedding Regression: Models for Context-Specific Description and Inference (2023) · cites this paper as Arora et al. 2018

  • If the random walk model holds, a researcher can obtain an embedding for a word by averaging the embeddings of the words around it and multiplying them by a particular square matrix A.

    “The main result from Arora et al. (2018) shows the following: if the random walk model holds, the researcher can obtain an embedding for word w (e.g., "bill") by taking the average of the embeddings of the words around w (u w Þ and multiplying them by a particular square matrix A .”

    From Embedding Regression: Models for Context-Specific Description and Inference (2023) · cites this paper as Arora et al. 2018

  • Embedding representations can be used to solve analogy reasoning tasks, which implies that the vectors capture relational meaning between words.

    “For example, embedding representations can be used to solve analogy reasoning tasks, implying the vectors do indeed capture relational meaning between words (e.g., Arora et al. 2018;Mikolov et al. 2013).”

    From Embedding Regression: Models for Context-Specific Description and Inference (2023) · cites this paper as Arora et al. 2018

    The Introduction and Section 4.2 discuss how embeddings represent word senses and test that structure, but they do not address solving word-analogy tasks. Searches for analogy reasoning and relational meaning found no passage in our copy supporting the cited example or its inference. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 14

  1. Sanjeev Arora, Yingyu Liang, and Tengyu Ma. 2017. A simple but tough-to-beat baseline for sentence embed- dings. In In Proceedings of International Conference on Learning Representations.
  2. Yoshua Bengio, Réjean Ducharme, Pascal Vincent, and Christian Jauvin. 2003. A neural probabilistic lan- guage model. Journal of Machine Learning Research, pages 1137-1155.
  3. Samuel Brody and Mirella Lapata. 2009. Bayesian word sense induction. In Proceedings of the 12th Confer- ence of the European Chapter of the Association for Computational Linguistics, pages 103-111.
  4. Kenneth Ward Church and Patrick Hanks. 1990. Word association norms, mutual information, and lexicogra- phy. Computational linguistics, pages 22-29.
  5. Christiane Fellbaum. 1998. WordNet: An Electronic Lexical Database. MIT Press.
  6. Ignacio Iacobacci, Mohammad Taher Pilehvar, and Roberto Navigli. 2015. SensEmbed: Learning sense embeddings for word and relational similarity. In Pro- ceedings of Association for Computational Linguis- tics, pages 95-105.
  7. Suresh Manandhar, Ioannis P Klapaftis, Dmitriy Dligach, and Sameer S Pradhan. 2010. SemEval 2010: Task 14: Word sense induction & disambiguation. In Pro- ceedings of the 5th International Workshop on Seman- tic Evaluation, pages 63-68.
  8. Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S. Cor- rado, and Jeff Dean. 2013a. Distributed represen- tations of words and phrases and their composition- ality. In Advances in Neural Information Processing Systems, pages 3111-3119.
  9. Jiaqi Mu, Suma Bhat, and Pramod Viswanath. 2017. Ge- ometry of polysemy. In Proceedings of International Conference on Learning Representations.
  10. Brian Murphy, Partha Pratim Talukdar, and Tom M. Mitchell. 2012. Learning effective and interpretable semantic models using non-negative sparse embed- ding. In Proceedings of the 24th International Confer- ence on Computational Linguistics, pages 1933-1950.
  11. Arvind Neelakantan, Jeevan Shankar, Re Passos, and Andrew Mccallum. 2014. Efficient nonparametric estimation of multiple embeddings per word in vec- tor space. In Proceedings of Conference on Empiri- cal Methods in Natural Language Processing, pages 1059-1069.
  12. Andrew Rosenberg and Julia Hirschberg. 2007. V- measure: A conditional entropy-based external clus- ter evaluation measure. In Conference on Empirical Methods in Natural Language Processing and Confer- ence on Computational Natural Language Learning, pages 410-420.
  13. Hinrich Schutze. 1998. Automatic word sense discrimi- nation. Computational Linguistics, pages 97-123.
  14. Peter D. Turney and Patrick Pantel. 2010. From fre- quency to meaning: Vector space models of seman- tics. Journal of Artificial Intelligence Research, pages 141-188. Wikimedia. 2012. English Wikipedia dump. Accessed March 2015.

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Authors
Arora, S., Li, Y., Liang, Y., Ma, T., & Risteski, A.
Affiliations
Princeton University (US)
Venue
Transactions of the Association for Computational Linguistics
Publisher
MIT Press
Published
2018-12
Volume
6
Pages
483-495
ISSN
2307-387X (ISSN-L)
OpenAlex
W2295508206
Cited by
186
References
31
Citations by year
2026: 6 · 2025: 14 · 2024: 9 · 2023: 13 · 2022: 14 · 2021: 26 · 2020: 32 · 2019: 30 · 2018: 23 · 2017: 12 · 2016: 4 · 2015: 3
FWCI
15.53
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Transactions of the Association for Computational Linguistics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1527371, 1317308)
  • Office of Naval Research (ONR-N00014, N00014)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
  • Physical Sciences › Computer Science › Artificial Intelligence › Natural Language Processing Techniques
  • Physical Sciences › Computer Science › Artificial Intelligence › Sentiment Analysis and Opinion Mining
Keywords
word embeddings, polysemy, word senses, linear superposition, sparse coding, co-occurrence

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