Compositional Distributional Semantics with Compact Closed Categories and Frobenius Algebras

TL;DR

This thesis advances categorical compositional semantics for natural language by introducing Frobenius algebra-based models, a new ambiguity handling methodology, and a quantum-inspired formalization, improving interpretability and accuracy.

Contribution

It presents a concrete Frobenius algebra instantiation, a novel ambiguity separation method, and a quantum mechanics-inspired formal framework for compositional semantics.

Findings

Improved coverage and interpretability of compositional models.

Enhanced accuracy in semantic composition through ambiguity separation.

Novel quantum-inspired formalization of lexical ambiguity using density matrices.

Abstract

This thesis contributes to ongoing research related to the categorical compositional model for natural language of Coecke, Sadrzadeh and Clark in three ways: Firstly, I propose a concrete instantiation of the abstract framework based on Frobenius algebras (joint work with Sadrzadeh). The theory improves shortcomings of previous proposals, extends the coverage of the language, and is supported by experimental work that improves existing results. The proposed framework describes a new class of compositional models that find intuitive interpretations for a number of linguistic phenomena. Secondly, I propose and evaluate in practice a new compositional methodology which explicitly deals with the different levels of lexical ambiguity (joint work with Pulman). A concrete algorithm is presented, based on the separation of vector disambiguation from composition in an explicit prior step. Extensive experimental work shows that the proposed methodology indeed results in more accurate composite representations for the framework of Coecke et al. in particular and every other class of compositional models in general. As a last contribution, I formalize the explicit treatment of lexical ambiguity in the context of the categorical framework by resorting to categorical quantum mechanics (joint work with Coecke). In the proposed extension, the concept of a distributional vector is replaced with that of a density matrix, which compactly represents a probability distribution over the potential different meanings of the specific word. Composition takes the form of quantum measurements, leading to interesting analogies between quantum physics and linguistics.