Measuring Compositionality in Representation Learning

TL;DR

This paper introduces a method to quantify how well learned representations in machine learning models reflect the compositional structure of inputs, bridging linguistic concepts with vector-based representations.

Contribution

It proposes a general procedure for measuring compositionality in vector representations by comparing true models to compositional approximations, with formal and empirical analysis.

Findings

The method effectively quantifies compositionality in various models.

Higher compositionality correlates with better generalization.

Representational primitives can be inferred to understand structure.

Abstract

Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this compositional structure is reflected in the the inputs' learned representations. While the assessment of compositionality in languages has received significant attention in linguistics and adjacent fields, the machine learning literature lacks general-purpose tools for producing graded measurements of compositional structure in more general (e.g. vector-valued) representation spaces. We describe a procedure for evaluating compositionality by measuring how well the true representation-producing model can be approximated by a model that explicitly composes a collection of inferred representational primitives. We use the procedure to provide formal and empirical characterizations of compositional structure in a variety of settings, exploring the relationship between compositionality and learning dynamics, human judgments, representational similarity, and generalization.