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arxiv: 2605.24286 · v1 · pith:ZRCPO4RDnew · submitted 2026-05-22 · 💻 cs.LG · cs.CL

Faithfulness as Information Flow: Evaluating and Training Faithful Chain-of-Thought Reasoning

Jinghan Jia , Joe Benton , Eric Easley This is my paper

Pith reviewed 2026-06-30 15:25 UTC · model grok-4.3

classification 💻 cs.LG cs.CL
keywords chain-of-thought reasoningfaithfulnessinformation flowreinforcement learninglanguage modelsshortcut learningmodel monitoringattention masking
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The pith

Training interventions that control information flow produce more faithful chain-of-thought reasoning in language models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that chain-of-thought reasoning can be made faithful by ensuring answer-relevant information flows through the visible reasoning steps rather than bypassing them via direct prompt-to-answer shortcuts. It defines three complementary information-flow properties—sufficiency, completeness, and necessity—and instantiates them with entropy, masked-KL, and gradient diagnostics that recover human judgments of faithfulness on hinted tasks. The authors then introduce update-time interventions for verifier-based reinforcement learning, such as attention masking and backward-only gradient masking, that encourage models to route information through the chain-of-thought. If these controls succeed, the resulting reasoning traces become more transparent for monitoring and less prone to hidden shortcuts or reward hacking.

Core claim

Faithful CoT reasoning routes answer-relevant information through the mediated prompt-to-CoT-to-answer path instead of direct prompt-to-answer shortcuts. This view is captured by a task-agnostic framework of sufficiency, completeness, and necessity properties measured via entropy-based, masked-KL, and gradient-based diagnostics. Update-time interventions including attention masking, backward-only gradient masking, CoT gradients, and adversarial prompt perturbations shift models toward stronger CoT mediation, making shortcut behavior more visible in the trace while improving the structural metrics.

What carries the argument

The structural information-flow perspective instantiated as the three properties of sufficiency, completeness, and necessity that diagnose whether answer-relevant information must pass through the chain-of-thought.

If this is right

  • The entropy, masked-KL, and gradient diagnostics recover externally judged faithfulness differences on hinted reasoning tasks.
  • The interventions increase behavioral and structural indicators of CoT mediation across hinted arithmetic, reward-hackable code repair, and DAPO-Math models.
  • Shortcut and reward-hacking behavior becomes more transparent inside the generated chain-of-thought.
  • Task-agnostic faithfulness metrics improve and wrong-hint susceptibility decreases in some evaluated settings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same information-flow controls could be tested on models trained entirely without hints to check whether monitorability improves on open-ended tasks.
  • Gradient-based diagnostics may remain usable even when entropy-based or KL-based measures become unstable due to low-entropy outputs.
  • Combining these training interventions with process-level supervision might further reduce hidden reliance on prompt shortcuts.

Load-bearing premise

The three information-flow properties accurately capture what counts as faithful reasoning when judged externally, an assumption checked only on hinted-reasoning tasks.

What would settle it

Apply the training interventions to a new model, then measure whether the resulting chain-of-thought traces receive higher human faithfulness ratings than the baseline on tasks that include incorrect hints or no hints at all.

Figures

Figures reproduced from arXiv: 2605.24286 by Eric Easley, Jinghan Jia, Joe Benton.

Figure 1
Figure 1. Figure 1: Information flow in reasoning: faithful CoT vs. short￾cut solutions. Left: A misleading hint changes the model’s answer, while the CoT does not reveal the hint’s influence, indicating a prompt￾to-answer shortcut. Right: In faithful reasoning, answer-relevant information should flow through the mediated path P → C → A. In unfaithful reasoning, the model can additionally rely on a direct shortcut P → A that … view at source ↗
Figure 2
Figure 2. Figure 2: Task-agnostic faithfulness metrics. Left: attention masks isolate full, CoT-mediated, and prompt-only answer distributions. Right: gradient-based metrics compare answer dependence on prompt versus CoT tokens; greater CoT-gradient concentration indicates stronger CoT-mediated reasoning. 4 Measures: Operationalizing Faithfulness We instantiate the properties of Section 3 with three families of task-agnostic … view at source ↗
Figure 3
Figure 3. Figure 3: Validation of the proposed task-agnostic faithfulness metrics. DeepSeek-R1-Distill-14B vs. Qwen3-8B on answer-changing hinted GPQA examples, where an external verbalization criterion indicates Qwen3-8B is more faithful. Bars show mean metric values across validation examples; error bars denote standard error. All metrics significantly distinguish the two models under a two-sided Mann–Whitney U test, but on… view at source ↗
Figure 4
Figure 4. Figure 4: Training dynamics of vanilla RL and faithfulness-oriented interventions (CoT Gradient, Gradient Mask, Update Mask, and FACT) in transparency, robustness to wrong hints, and task performance on hinted arithmetic. The four panels report implicit hint mention rate, wrong-hint following rate, accuracy on wrong-hint-conditioned examples, and overall accuracy vs. training steps. Higher implicit hint mention, low… view at source ↗
Figure 5
Figure 5. Figure 5: Causal-effect and necessity analysis on hinted arithmetic. We report the normalized KL difference between CoT-hint and prompt-hint sensi￾tivity across training steps under sign-flip, scale-2×, and random hint-value changes. Positive values indicate CoT-dominant behavior, while negative val￾ues indicate prompt-dominant shortcut reliance; higher is better. Causal information flow ( [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 6
Figure 6. Figure 6: Faithfulness metrics on hinted arithmetic. We report sufficiency, completeness, and necessity using H(A | C), Grad-DE, and Grad-Nec vs. training steps. Lower H(A | C), lower Grad-DE, and higher Grad-Nec indicate better faithfulness. Under sign-flip, 2× scaling, and random hint changes, vanilla RL trends increas￾ingly negative as training proceeds, con￾sistent with the prompt-dominant short￾cut suggested by… view at source ↗
Figure 7
Figure 7. Figure 7: Behavioral dynamics of vanilla RL and faithfulness-oriented interventions on buggy-code fixing. The four panels report visible/hidden test case pass rate, lookup-table hack rate, and CoT hack verbalization rate vs. training steps. Visible and hidden test pass rates measure reward optimization and generalization, respectively; lookup-table hack rate measures shortcut exploitation of visible tests; and CoT h… view at source ↗
Figure 8
Figure 8. Figure 8: Faithfulness metrics on buggy-code fixing. The three panels report sufficiency, completeness, and necessity using H(A | C), Grad-DE, and Grad-Nec across training steps. Better faithfulness corresponds to more sufficient CoT information, weaker direct prompt-to-answer reliance, and stronger answer dependence on the CoT. Vanilla RL almost never verbalizes the lookup-table strategy despite pro￾ducing such sol… view at source ↗
Figure 9
Figure 9. Figure 9: Behavioral evaluation of vanilla RL and CoT Gradient on DAPO-Math. Models are trained on the DAPO-Math training set and evaluated on 1,000 validation examples. The four panels report no-hint accuracy, wrong-hint follow rate, explicit verbalization rate among hint-following responses, and implicit verbalization rate among hint-following responses vs. training steps. Higher no-hint accuracy indicates stronge… view at source ↗
Figure 10
Figure 10. Figure 10: Faithfulness metrics of vanilla RL and CoT Gradient on DAPO-Math. The three panels report sufficiency, completeness, and ne￾cessity using H(A | C), Grad-DE, and Grad-Nec across training steps, evaluated on 1,000 validation examples. Lower H(A | C), lower Grad-DE, and higher Grad-Nec indicate better faithfulness. Task-agnostic metrics ( [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper claims that CoT faithfulness can be understood and improved via an information-flow lens requiring answer-relevant information to route through the prompt-to-CoT-to-answer path. It defines three properties (sufficiency, completeness, necessity) instantiated as entropy-based, masked-KL, and gradient diagnostics; shows these recover human faithfulness judgments on hinted-reasoning tasks; and introduces on-policy RL interventions (attention masking, backward-only gradient masking, CoT gradients, adversarial prompt perturbations) that shift behavioral and structural indicators toward greater CoT mediation on hinted arithmetic, reward-hackable code repair, and DAPO-Math under wrong-hint injection.

Significance. If the results hold, the work supplies a task-agnostic, information-theoretic framework plus concrete training interventions for producing more monitorable CoT, with open code at the cited GitHub repository strengthening reproducibility. The low-entropy failure mode identified for KL diagnostics and the gradient-based alternative are useful technical contributions.

major comments (2)
  1. [Abstract] Abstract and experiments on hinted reasoning: the three diagnostics are shown to recover externally judged faithfulness differences only on hinted-reasoning tasks, yet the central claim that the RL interventions produce more faithful CoT on code repair and DAPO-Math rests on metric shifts in those settings without reported human faithfulness judgments, so it is unclear whether the observed changes track faithfulness or merely the mechanics of the interventions (e.g., attention masking directly affecting the masked-KL term).
  2. [Abstract] Abstract: the reported shifts in behavioral and structural indicators after interventions are presented without error bars, dataset sizes, or statistical tests, so the strength of evidence that the interventions reliably improve CoT mediation cannot be assessed from the given information.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and experiments on hinted reasoning: the three diagnostics are shown to recover externally judged faithfulness differences only on hinted-reasoning tasks, yet the central claim that the RL interventions produce more faithful CoT on code repair and DAPO-Math rests on metric shifts in those settings without reported human faithfulness judgments, so it is unclear whether the observed changes track faithfulness or merely the mechanics of the interventions (e.g., attention masking directly affecting the masked-KL term).

    Authors: Human judgments are reported only on hinted-reasoning tasks, where controlled external labels are feasible. The three diagnostics are task-agnostic by design (sufficiency/completeness/necessity via information flow) and were validated to recover human distinctions in that setting. On code repair and DAPO-Math, the interventions target information-flow mechanisms (attention masking blocks direct shortcuts; gradient masking and CoT gradients enforce mediation) and produce consistent shifts across multiple diagnostics, including gradient-based ones that are orthogonal to attention masking. This multi-metric pattern indicates the changes reflect the intended structural property rather than artifacts of any single diagnostic. We will add an explicit discussion of the validation scope and metric rationale in the revised manuscript. revision: partial

  2. Referee: [Abstract] Abstract: the reported shifts in behavioral and structural indicators after interventions are presented without error bars, dataset sizes, or statistical tests, so the strength of evidence that the interventions reliably improve CoT mediation cannot be assessed from the given information.

    Authors: We agree that the abstract omits these details. Dataset sizes appear in the experimental sections of the full manuscript. In revision we will add error bars and statistical tests to all reported shifts in figures/tables and update the abstract to reference the strengthened statistical presentation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; metrics defined independently and validated externally

full rationale

The paper defines faithfulness via three information-flow properties (sufficiency, completeness, necessity) instantiated with entropy, masked-KL, and gradient diagnostics drawn from standard information theory. These are validated against external human judgments on hinted-reasoning tasks, and interventions are assessed via on-policy RL with reported behavioral and metric shifts. No load-bearing step reduces by the paper's equations or self-citation to a fitted input or self-defined quantity; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Framework rests on standard transformer gradient attribution and information-theoretic quantities; no new physical entities or ad-hoc fitted constants are introduced in the abstract. Limited visibility into full methods prevents exhaustive enumeration.

axioms (1)
  • domain assumption Entropy, masked KL divergence and gradient attributions can be used to quantify information flow through specific paths in transformer models
    Invoked to define the three diagnostics.

pith-pipeline@v0.9.1-grok · 5830 in / 1390 out tokens · 58957 ms · 2026-06-30T15:25:59.840470+00:00 · methodology

discussion (0)

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Reference graph

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