Faithfulness Metrics Don't Measure Faithfulness: A Meta-Evaluation with Ground Truth

Chain-of-thought (CoT) reasoning is useful for monitoring language models only when the reasoning trace faithfully reflects the computation that produces the final answer. However, models can rely on prompt-to-answer shortcuts that bypass the CoT, making the visible reasoning trace misleading even when it appears plausible. We study CoT faithfulness through a structural information-flow perspective: faithful reasoning should route answer-relevant information through the mediated path from prompt to CoT to answer, rather than through a direct prompt-to-answer shortcut. This perspective yields a task-agnostic framework based on three complementary properties, sufficiency, completeness, and necessity, which we instantiate with entropy-based, masked-KL, and gradient-based diagnostics. We show that these metrics recover externally judged faithfulness differences in hinted reasoning, and identify a low-entropy failure mode of KL-based diagnostics where gradient-based measures remain more stable. Building on this analysis, we introduce update-time interventions for verifier-based on-policy RL, including attention masking, backward-only gradient masking, CoT gradients, and adversarial perturbations of prompt representations. Across hinted arithmetic, reward-hackable code repair, and DAPO-Math models trained without hints but evaluated under wrong-hint injection, our interventions shift behavioral and structural indicators toward stronger CoT mediation. In particular, they make shortcut and reward-hacking behavior more transparent in the CoT and improve task-agnostic faithfulness metrics, while in some settings also reducing wrong-hint susceptibility. Our results suggest that controlling information flow during training is a practical route toward more faithful and monitorable CoT reasoning. Code is available at https://github.com/safety-research/faithful-cot.

Chain-of-thought (CoT) explanations support oversight only if they are faithful: the stated reasoning must actually produce the answer. Auditing black-box (behavioral) detection of unfaithful CoT against FaithCoT-Bench's human annotations, we find answer correctness structures the problem at every level. Answer incorrectness alone (an oracle diagnostic, not a deployable detector) outperforms every purpose-built signal (AUROC 0.696), because 69% of annotated unfaithfulness occurs on incorrect answers. Stratifying by correctness splits detection into two regimes: on correct answers, behavioral signals moderately separate faithful from post-hoc reasoning (0.63-0.67); on incorrect answers, where most unfaithfulness lives, no tested signal is detectably above chance (replicated on all four models for benchmark-wide signals). The standard step-removal metric anti-correlates with human labels; this inversion reproduces on the benchmark's released scores and on hint-dependent counterfactually labeled traces. Linear probes decode the behaviorally blind regime in Llama-3.1-8B and the correct-answer regime in Qwen-2.5-7B, with no shared, positively aligned direction detected across regimes; instructed answer-first traces (7 models) transfer to neither annotated regime, while hint-induced unverbalized answer flips do, in model- and source-dependent settings. We also independently verify and resolve a documentation-data mismatch in the benchmark's label semantics.

Chain-of-Thought (CoT) faithfulness, i.e., whether CoTs genuinely reflect large language models' (LLM) underlying behavior, is typically evaluated under two disjoint paradigms: contextual faithfulness, measured by perturbing the input or CoT trace, and parametric faithfulness, assessed by intervening on a model's parametric knowledge. Yet prior work compares them only descriptively. We fill this gap by proposing FaithMate, a unified preference-alignment interface for optimizing models towards either faithfulness paradigm. It enables us to investigate the interplay between the two paradigms, examining whether and to what extent faithfulness gains generalize within and across paradigms. Across three models, two datasets, and six faithfulness metrics, we find that the two paradigms are positively coupled, yet asymmetric: optimizing towards parametric faithfulness yields consistent gains across both paradigms, whereas the contextual counterpart delivers more variable gains. Within the contextual paradigm, faithfulness gains on one metric do not consistently transfer to others, implying that existing contextual metrics capture disjoint facets of faithfulness and exposing inherent trade-offs. These findings imply that CoT faithfulness is not a monolithic objective and therefore requires multifaceted optimization and evaluation.