Analyzing and Improving Chain-of-Thought Monitorability Through Information Theory
This work addresses the challenge of reliably monitoring reasoning traces in LLMs for tasks like code generation, which is incremental as it builds on existing CoT monitoring approaches by refining them with theoretical insights and practical improvements.
The paper tackled the problem of improving the monitorability of chain-of-thought (CoT) reasoning in LLMs by analyzing it through information theory, identifying sources of error like information gap and elicitation error, and proposing training methods that increased monitor accuracy significantly across multiple environments while preventing CoT degeneration.
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.