  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 lower bounds on the accuracy of 151 small
transformers trained on a Max-of-$K$ task. 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 noise as a key challenge
for using mechanistic interpretability to generate compact proofs on model
performance.
