Should Semantic Vector Composition be Explicit? Can it be Linear?

TL;DR

This paper explores whether semantic vector composition should be explicitly modeled as a linear algebra operation, or learned implicitly within neural networks, and considers potential quantum computing implementations for such models.

Contribution

It surveys the debate on explicit versus implicit semantic composition and discusses the potential for quantum computing to implement compositional models.

Findings

Linear algebra may be sufficient for semantic composition.

Neural networks can implicitly learn compositionality.

Quantum computing could enable new approaches to semantic modeling.

Abstract

Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations for 'wet' and 'fish', how should the concept 'wet fish' be represented? This position paper surveys this question from two points of view. The first considers the question of whether an explicit mathematical representation can be successful using only tools from within linear algebra, or whether other mathematical tools are needed. The second considers whether semantic vector composition should be explicitly described mathematically, or whether it can be a model-internal side-effect of training a neural network. A third and newer question is whether a compositional model can be implemented on a quantum computer. Given the fundamentally linear nature of quantum mechanics, we propose that these questions are related, and that this survey may help to highlight candidate operations for future quantum implementation.