
TL;DR
This paper explores the geometric and mathematical foundations of semantic spaces, particularly vector space models, to bridge natural language understanding in human brains and computational systems.
Contribution
It introduces a geometric framework using Grassmannians and projective spaces to model semantics and relates latent semantics to geometric flows, advancing the mathematical understanding of semantic spaces.
Findings
Geometric interpretation of latent semantics as flows on Grassmannians
Relation between vector space models and semantic spaces via projectability
Mathematical formulation of G"ardenfors' 'meeting of minds' concept
Abstract
Any natural language can be considered as a tool for producing large databases (consisting of texts, written, or discursive). This tool for its description in turn requires other large databases (dictionaries, grammars etc.). Nowadays, the notion of database is associated with computer processing and computer memory. However, a natural language resides also in human brains and functions in human communication, from interpersonal to intergenerational one. We discuss in this survey/research paper mathematical, in particular geometric, constructions, which help to bridge these two worlds. In particular, in this paper we consider the Vector Space Model of semantics based on frequency matrices, as used in Natural Language Processing. We investigate underlying geometries, formulated in terms of Grassmannians, projective spaces, and flag varieties. We formulate the relation between vector…
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Taxonomy
TopicsNatural Language Processing Techniques · Constraint Satisfaction and Optimization · Spatial Cognition and Navigation
