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

arXiv: https://arxiv.org/abs/2605.24286 · HTML: https://mlsanity.com/paper/2605.24286/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 36 references that are in the map.
- First posted on arXiv 22 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 32)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [AI Control: Improving Safety Despite Intentional Subversion](https://mlsanity.com/paper/2312.06942/) (2023)
- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Are DeepSeek R1 And Other Reasoning Models More Faithful?](https://mlsanity.com/paper/2501.08156/) (2025)
- [Monitoring Monitorability](https://mlsanity.com/paper/2512.18311/) (2025)
- [Measuring Chain of Thought Faithfulness by Unlearning Reasoning Steps](https://mlsanity.com/paper/2502.14829/) (2025)
- [FaithCoT-Bench: Benchmarking Instance-Level Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.04040/) (2025)
- [Reasoning Models Struggle to Control their Chains of Thought](https://mlsanity.com/paper/2603.05706/) (2026)
- [Teaching Models to Verbalize Reward Hacking in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.22777/) (2025)
- [Counterfactual Simulation Training for Chain-of-Thought Faithfulness](https://mlsanity.com/paper/2602.20710/) (2026)
- [Analyzing and Improving Chain-of-Thought Monitorability Through Information Theory](https://mlsanity.com/paper/2602.18297/) (2026)
- [Mechanistic Evidence for Faithfulness Decay in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.11201/) (2026)
- [MonitorBench: A Comprehensive Benchmark for Chain-of-Thought Monitorability in Large Language Models](https://mlsanity.com/paper/2603.28590/) (2026)
- [C2-Faith: Benchmarking LLM Judges for Causal and Coverage Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2603.05167/) (2026)

## Built on by (most cited first, 3 of 3)

- [A Removal Based Approach to Improve LLM Faithfulness at Test-Time](https://mlsanity.com/paper/2609.04343/) (2026)
- [Physics as the label for measuring and correcting materials reasoning in multimodal models](https://mlsanity.com/paper/2609.12181/) (2026)
- [Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models](https://mlsanity.com/paper/2610.05472/) (2026)

## Abstract (arXiv)

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.