From Mechanistic to Compositional Interpretability

TL;DR

This paper introduces a formal, compositional framework for neural interpretability using category theory, enabling systematic, verifiable, and concise explanations of model behavior.

Contribution

It develops a novel formal framework for interpretability, connecting mechanistic explanations with compositionality and minimum description length, and introduces methods for model simplification.

Findings

Framework unifies mechanistic interpretability with compositionality.

Proves a parsimony criterion for concise explanations.

Situates existing methods as special cases within the framework.

Abstract

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be objectively verified, compared, or composed. We introduce compositional interpretability, a category-theoretic framework grounded in the principles of compositionality and minimum description length. Compositional interpretations are pairs of syntactic and semantic mappings that must commute to enforce consistency between a model's decomposition and its observed behaviour. We deconstruct explanation quality into measures of faithfulness and complexity to cast interpretability as a constrained optimisation problem, and introduce compressive refinement to systematically restructure models into simpler parts without altering their function. Finally, we prove a parsimony criterion under which syntactic compression theoretically guarantees more concise, human-aligned explanations. Our framework situates prominent mechanistic methods as subclasses of refinement, and clarifies why their compressibility heuristics tend to align with human interpretability. Our work provides a measurable, optimisable foundation for automating the discovery and evaluation of mechanistic explanations.