Certified Interventional Fidelity: Anytime-Valid, Adaptive Evaluation of Causal Claims in Mechanistic Interpretability

Mechanistic interpretability often evaluates explanations by intervening on a model: swapping hidden states, patching activations, ablating components, or comparing a compressed model to the original one. These experiments are usually summarized by a point estimate, even though the evaluation may be monitored while it runs or adapted toward suspected failures. This makes it hard to tell whether a reported fidelity or patching effect is a stable causal claim or a consequence of finite sampling and evaluation choices. We introduce Certified Interventional Fidelity (CIF), a statistical layer for interventional interpretability evaluations. CIF first writes the quantity being reported as a causal estimand: an expectation of a bounded score over a stated input distribution and a stated intervention distribution. It then provides confidence intervals and anytime-valid confidence sequences for this estimand, including under adaptive intervention sampling via bounded mixture importance weighting. We instantiate CIF with Hoeffding-style sequences and variance-adaptive betting sequences, the latter reducing certification cost by 10-30x in our experiments. On MNIST abstractions and GPT-2 Small IOI circuits, CIF certifies high-fidelity claims, shows when apparent method differences are not statistically supported, and makes sensitivity to the intervention distribution explicit.