Topology of Word Embeddings: Singularities Reflect Polysemy

Alexander Jakubowski, Milica Gasic, Marcus Zibrowius


Abstract
The manifold hypothesis suggests that word vectors live on a submanifold within their ambient vector space. We argue that we should, more accurately, expect them to live on a <i>pinched</i> manifold: a singular quotient of a manifold obtained by identifying some of its points. The identified, singular points correspond to polysemous words, i.e. words with multiple meanings. Our point of view suggests that monosemous and polysemous words can be distinguished based on the topology of their neighbourhoods. We present two kinds of empirical evidence to support this point of view: (1) We introduce a topological measure of polysemy based on persistent homology that correlates well with the actual number of meanings of a word. (2) We propose a simple, topologically motivated solution to the SemEval-2010 task on <i>Word Sense Induction & Disambiguation</i> that produces competitive results.
Anthology ID:
2020.starsem-1.11
Volume:
Proceedings of the Ninth Joint Conference on Lexical and Computational Semantics
Month:
December
Year:
2020
Address:
Barcelona, Spain (Online)
Venue:
*SEM
SIGs:
SIGLEX | SIGSEM
Publisher:
Association for Computational Linguistics
Note:
Pages:
103–113
Language:
URL:
https://aclanthology.org/2020.starsem-1.11
DOI:
Bibkey:
Cite (ACL):
Alexander Jakubowski, Milica Gasic, and Marcus Zibrowius. 2020. Topology of Word Embeddings: Singularities Reflect Polysemy. In Proceedings of the Ninth Joint Conference on Lexical and Computational Semantics, pages 103–113, Barcelona, Spain (Online). Association for Computational Linguistics.
Cite (Informal):
Topology of Word Embeddings: Singularities Reflect Polysemy (Jakubowski et al., *SEM 2020)
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PDF:
https://aclanthology.org/2020.starsem-1.11.pdf