A Study of Entanglement in a Categorical Framework of Natural Language

TL;DR

This paper explores how entanglement in categorical models of natural language impacts compositional semantics, revealing that many verb tensors are nearly separable, which simplifies interactions, but Frobenius algebras and machine learning can enhance entanglement.

Contribution

It analyzes entanglement levels in categorical NLP models, showing how tensor separability affects compositionality and proposing methods to improve entanglement using Frobenius algebras and machine learning.

Findings

Many verb tensors are nearly separable, simplifying word interactions.

Frobenius algebras help mitigate issues caused by low entanglement.

Machine learning can produce verb tensors with sufficient entanglement.

Abstract

In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the categorical framework of Coecke, Sadrzadeh and Clark (2010) for natural language, from an entanglement perspective. Specifically, our goal is to better understand in what way the level of entanglement of the relational tensors (or the lack of it) affects the compositional structures in practical situations. Our findings reveal that a number of proposals for verb construction lead to almost separable tensors, a fact that considerably simplifies the interactions between the words. We examine the ramifications of this fact, and we show that the use of Frobenius algebras mitigates the potential problems to a great extent. Finally, we briefly examine a machine learning method that creates verb tensors exhibiting a sufficient level of entanglement.