Interpretability in Parameter Space: Minimizing Mechanistic Description Length with Attribution-based Parameter Decomposition

TL;DR

This paper introduces Attribution-based Parameter Decomposition (APD), a novel method for decomposing neural network parameters into minimal, faithful, and simple components to enhance mechanistic interpretability.

Contribution

It presents APD, a new approach that optimally decomposes neural network parameters into mechanistic components with minimal description length, validated on toy models.

Findings

Successfully identified ground truth mechanisms in toy models

Recovered features from superposition and separated computations

Provided a foundation for minimal circuit identification

Abstract

Mechanistic interpretability aims to understand the internal mechanisms learned by neural networks. Despite recent progress toward this goal, it remains unclear how best to decompose neural network parameters into mechanistic components. We introduce Attribution-based Parameter Decomposition (APD), a method that directly decomposes a neural network's parameters into components that (i) are faithful to the parameters of the original network, (ii) require a minimal number of components to process any input, and (iii) are maximally simple. Our approach thus optimizes for a minimal length description of the network's mechanisms. We demonstrate APD's effectiveness by successfully identifying ground truth mechanisms in multiple toy experimental settings: Recovering features from superposition; separating compressed computations; and identifying cross-layer distributed representations. While challenges remain to scaling APD to non-toy models, our results suggest solutions to several open problems in mechanistic interpretability, including identifying minimal circuits in superposition, offering a conceptual foundation for 'features', and providing an architecture-agnostic framework for neural network decomposition.