The Misery of Mechanistic Interpretability: A Formal Perspective

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Mechanistic interpretability has become the dominant lens for understanding frontier language models, as their inner workings are complex and inherently black boxes. To gain insights into these models, interpretable replacement networks (IRNs) are trained at all layers, exposing interpretable features through sparsely activated neurons. However, the faithfulness of an IRN is usually evaluated only empirically on clean data, and we show that even semantically minor input perturbations flip the dominant IRN features-and thus the human-understandable interpretation-across five open-weight model families (GPT-2 small, Gemma 2 2B, Gemma 3 1B, Llama 3.2 1B, R1-Distill-Qwen 1.5B). We propose the first formal verification framework for the faithfulness of an IRN, where reachability analysis certifies a sound upper bound of the faithfulness gap in adversarial scenarios. Moreover, we show that verification-aware training of IRNs substantially tightens this certified bound, restoring a feature-level interpretation that safety auditors can act on. Together, these results give, to the best of our knowledge, the first formal guarantees for mechanistic interpretability of large language models.