Towards Verifiable Transformers: Solver-Checkable Circuit Explanations

Abstract

Mechanistic interpretability typically discovers circuits and then argues what they do from examples and ablations. We introduce Verifiable Transformers, a framework for turning task-localized circuits into bounded, solver-checkable claims: projected functional equivalence, task-relevant invariance, edge necessity, and robustness to continuous final-residual perturbations. At small scale, we directly verify all four properties for quote-closing and bracket-type circuits, including program-mediated circuits whose attention selection is entirely symbolic. At GPT-2 scale, we remove LayerNorm from a sparsemax/LeakyReLU model after training with a +0.0087 OpenWebText loss increase, replace retained attention heads with synthesized restricted-DSL programs, and calibrate only program-local readouts while freezing and hashing every other parameter. The resulting three-edge quote circuit (embedding $\to$ MLP 0 $\to$ program head $\to$ logits) verifies all four properties over a hash-pinned 1,280-prompt domain in linear real arithmetic: 1,280/1,280 equivalence and invariance, 640 edge-necessity witnesses per edge, and robustness at $ε= 0.01$