# Analyzing and Improving Chain-of-Thought Monitorability Through Information Theory

arXiv: https://arxiv.org/abs/2602.18297 · HTML: https://mlsanity.com/paper/2602.18297/

## Key facts

- Cited by 10 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 34 of its 48 references that are in the map.
- First posted on arXiv 20 Feb 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 34)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [Alignment faking in large language models](https://mlsanity.com/paper/2412.14093/) (2024)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Frontier Models are Capable of In-context Scheming](https://mlsanity.com/paper/2412.04984/) (2024)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety](https://mlsanity.com/paper/2507.11473/) (2025)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [Large Language Models can Strategically Deceive their Users when Put Under Pressure](https://mlsanity.com/paper/2311.07590/) (2023)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [When Chain of Thought is Necessary, Language Models Struggle to Evade Monitors](https://mlsanity.com/paper/2507.05246/) (2025)
- [Hidden in Plain Text: Emergence & Mitigation of Steganographic Collusion in LLMs](https://mlsanity.com/paper/2410.03768/) (2024)
- [On the Hardness of Faithful Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2406.10625/) (2024)
- [Understanding Chain-of-Thought in LLMs through Information Theory](https://mlsanity.com/paper/2411.11984/) (2024)
- [Preferences Implicit in the State of the World](https://mlsanity.com/paper/1902.04198/) (2019)
- [Large language models can learn and generalize steganographic chain-of-thought under process supervision](https://mlsanity.com/paper/2506.01926/) (2025)
- [Adaptive Attacks on Trusted Monitors Subvert AI Control Protocols](https://mlsanity.com/paper/2510.09462/) (2025)
- [Is It Thinking or Cheating? Detecting Implicit Reward Hacking by Measuring Reasoning Effort](https://mlsanity.com/paper/2510.01367/) (2025)
- [MONA: Myopic Optimization with Non-myopic Approval Can Mitigate Multi-step Reward Hacking](https://mlsanity.com/paper/2501.13011/) (2025)
- [Early Signs of Steganographic Capabilities in Frontier LLMs](https://mlsanity.com/paper/2507.02737/) (2025)

## Built on by (most cited first, 10 of 10)

- [Do Androids Dream of Breaking the Game? Systematically Auditing AI Agent Benchmarks with BenchJack](https://mlsanity.com/paper/2605.12673/) (2026)
- [Faithfulness as Information Flow: Evaluating and Training Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2605.24286/) (2026)
- [Tandem Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2606.28166/) (2026)
- [Does Out-of-Sight Equal Out-of-Mind in CoT Monitorability?](https://mlsanity.com/paper/2608.04928/) (2026)
- [Beyond Training: A Feasibility Taxonomy for Inference-Time AI Governance](https://mlsanity.com/paper/2609.10105/) (2026)
- [Corrupt Plans, Clean Traces: Evading Chain-of-Thought Monitoring with Plan Injection](https://mlsanity.com/paper/2609.15989/) (2026)
- [Taming CoT Obfuscation in VLMs: From Mechanistic Evidence to Activation Enforcement](https://mlsanity.com/paper/2609.24243/) (2026)
- [Training LLMs to Verbalize Evaluation Awareness](https://mlsanity.com/paper/2609.36316/) (2026)
- [Hidden Reasoning Must Leak, but Need Not Be Readable: Fundamental Opportunities and Limits for Chain-of-Thought Monitoring](https://mlsanity.com/paper/2609.37312/) (2026)
- [On the Monitorability of Natural Language Autoencoders: Identification vs Discrimination](https://mlsanity.com/paper/2610.18727/) (2026)

## Abstract (arXiv)

Chain-of-thought (CoT) monitors are LLM-based systems that analyze reasoning traces to detect when outputs may exhibit attributes of interest, such as test-hacking behavior during code generation. In this paper, we use information-theoretic analysis to show that non-zero mutual information between CoT and output is a necessary but not sufficient condition for CoT monitorability. We identify two sources of approximation error that may undermine the performance of CoT monitors in practice: information gap, which measures the extent to which the monitor can extract the information available in CoT, and elicitation error, which measures the extent to which the monitor approximates the optimal monitoring function. We further demonstrate that CoT monitorability can be systematically improved through targeted training objectives. To this end, we propose two complementary approaches: (a) an oracle-based method that directly rewards the monitored model for producing CoTs that maximize monitor accuracy, and (b) a more practical, label-free approach that maximizes conditional mutual information between outputs and CoTs. Across multiple different environments, we show both methods significantly improve monitor accuracy while preventing CoT degeneration even when training against a monitor, thereby mitigating reward hacking when the task reward is imperfectly specified.