Distributional Sentence Entailment Using Density Matrices

TL;DR

This paper extends a distributional semantics model by representing words as density matrices to better capture entailment relations, enabling sentence-level entailment analysis with quantum-inspired measures.

Contribution

It introduces density matrix representations for words in a compositional distributional model to quantify entailment using von Neumann entropy.

Findings

Density matrices effectively model lexical entailment.

The model combines grammatical composition with probabilistic entailment measures.

Empirical examples demonstrate the approach's applicability.

Abstract

Categorical compositional distributional model of Coecke et al. (2010) suggests a way to combine grammatical composition of the formal, type logical models with the corpus based, empirical word representations of distributional semantics. This paper contributes to the project by expanding the model to also capture entailment relations. This is achieved by extending the representations of words from points in meaning space to density operators, which are probability distributions on the subspaces of the space. A symmetric measure of similarity and an asymmetric measure of entailment is defined, where lexical entailment is measured using von Neumann entropy, the quantum variant of Kullback-Leibler divergence. Lexical entailment, combined with the composition map on word representations, provides a method to obtain entailment relations on the level of sentences. Truth theoretic and corpus-based examples are provided.