Compact Proofs of Model Performance via Mechanistic Interpretability

TL;DR

This paper introduces a novel approach that employs mechanistic interpretability to derive compact, formal performance guarantees for models, validated through proofs on a small transformer trained on Max-of-K.

Contribution

It demonstrates how mechanistic interpretability can be used to produce formal performance proofs, establishing links between interpretability, proof length, and bound tightness.

Findings

Shorter proofs correlate with better mechanistic understanding.

More faithful mechanistic understanding yields tighter bounds.

Identified structureless errors as a challenge for compact proofs.

Abstract

We propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving accuracy lower bounds for a small transformer trained on Max-of-K, validating proof transferability across 151 random seeds and four values of K. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless errors as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.