Tracking Equivalent Mechanistic Interpretations Across Neural Networks

TL;DR

This paper introduces a formal framework for assessing whether different neural network models share a common underlying interpretation, addressing key challenges in scaling and defining interpretive equivalence.

Contribution

It formalizes the concept of interpretive equivalence, develops an algorithm to estimate it, and provides theoretical guarantees relating interpretations, circuits, and representations.

Findings

Proposed a formal definition of interpretive equivalence.

Developed an algorithm to estimate interpretive equivalence.

Provided theoretical conditions linking representations and interpretations.

Abstract

Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that task. However, MI is difficult to scale and generalize. This stems in part from two key challenges: there is no precise notion of a valid interpretation; and, generating interpretations is often an ad hoc process. In this paper, we address these challenges by defining and studying the problem of interpretive equivalence: determining whether two different models share a common interpretation, without requiring an explicit description of what that interpretation is. At the core of our approach, we propose and formalize the principle that two interpretations of a model are equivalent if all of their possible implementations are also equivalent. We develop an algorithm to estimate interpretive equivalence and case study its use on Transformer-based models. To analyze our algorithm, we introduce necessary and sufficient conditions for interpretive equivalence based on models' representation similarity. We provide guarantees that simultaneously relate a model's algorithmic interpretations, circuits, and representations. Our framework lays a foundation for the development of more rigorous evaluation methods of MI and automated, generalizable interpretation discovery methods.