SIFT: Robust Meta-Faithfulness Verification of Chain-of-Thought Reasoning Under Distribution Shift

Noor Islam S. Mohammad, Md. Basim Al Zabir Shammo, Hasan Siddiki, Mahmudul Hasan, Md. Faisal Sheikh +1

Chain-of-Thought (CoT) faithfulness detectors are widely used to audit reasoning models, yet a detector is itself a predictor whose verdicts are treated as stable properties. We ask whether a detector is faithful to itself under distribution shift. We formalize meta-faithfulness as an invariance principle: a valid detector must return identical verdicts on traces that differ only by transformations preserving ground-truth faithfulness. We prove three results: (i) no detector using only intervention-response profiles can separate faithful from epiphenomenal mechanisms with identical signatures; (ii) any detector relying on shift-sensitive features violates invariance at a rate independent of its in-distribution accuracy; (iii) an asymptotic certified selective-risk guarantee enables confident abstention. We operationalize the principle in FaithShift, a stress-test protocol spanning ten shift axes, and propose SIFT, a hidden-state trajectory detector trained with cross-environment invariance objectives and certified abstention. Across 14,996 traces, four domains, and eight models, three findings emerge. First, transfer collapse is real: all existing detectors show gaps $\geq 0.15$…