Legibility is Not Interpretability: Comparing Judged and Actual Importance in Chain-Of-Thought Reasoning
Authors: Kevin Du, Alexander Hoyle, Laura Ruis, Acyr Locatelli
Abstract
Reasoning traces from chain-of-thought models appear to offer a legible window into how a model arrives at its answer. A growing body of work treats them as such, using LLM judges to diagnose errors, evaluate faithfulness, and provide step-level supervision via process reward models and generative critics. These practices rely on the text of a reasoning step carrying information about its functional role. But does the text actually encode information about which reasoning steps matter? We operationalize the importance of a reasoning step as its advantage: the change in expected reward, e.g., producing the correct final answer, from including that step, estimated via Monte Carlo rollouts. Basing ground truth on these estimates, we evaluate whether LLM judges can identify high-advantage steps and find that sufficiently capable LLMs can outperform a prevalence baseline but fall well short of a noise ceiling. Fine-tuning a model as a step-level critic yields strong improvement for incorrect responses but remains distant from ceiling for correct responses, suggesting that step importance is only partially recoverable from the text of the reasoning trace. Our findings contribute to a growing body of chain-of-thought faithfulness work that cautions against treating the legibility of reasoning traces as interpretability, especially with implications for process reward modeling.
Chain-of-thought (CoT) traces are increasingly used both to improve language model capability and to audit model behavior, implicitly assuming that the visible trace remains synchronized with the computation that determines the answer. We test this assumption with a step-level Detect-Classify-Compare framework built around an answer-commitment proxy that is cross-validated with Patchscopes, tuned-lens probes, and causal direction ablation. Across nine models and seven reasoning benchmarks, latent commitment and explicit answer arrival align on only 61.9% of steps on average. The dominant mismatch pattern is confabulated continuation: 58.0% of detected mismatch events occur after the answer-commitment proxy has already stabilized while the trace continues producing deliberative-looking text, and a vacuousness analysis shows that the committed answer does not change during these steps. In architecture-matched Qwen2.5/DeepSeek-R1-Distill comparisons, the reasoning pipeline changes failure composition more than aggregate alignment, most clearly at 32B where confabulated steps decrease as contradictory states increase. Lower step-level alignment is also associated with larger CoT utility, suggesting that the settings that benefit most from CoT are often the least temporally faithful. Paired truncation and a complementary donor-corruption test further indicate that much post-commitment text is not load-bearing for the final answer. These findings suggest that CoT can remain useful while still being an unreliable report of when the answer was formed.
Language models often solve complex tasks by generating long reasoning chains, consisting of many steps with varying importance. While some steps are crucial for generating the final answer, others are removable. Determining which steps matter most, and why, remains an open question central to understanding how models process reasoning. We investigate if this question is best approached through model internals or through tokens of the reasoning chain itself. We find that model activations contain more information than tokens for identifying important reasoning steps. Crucially, by training probes on model activations to predict importance, we show that models encode an internal representation of step importance, even prior to the generation of subsequent steps. The internal representations of importance in different models yield high agreement on which steps are important. The representation is distributed across layers, and does not correlate with surface-level features, such as a step's relative position or its length. Our findings suggest that analyzing activations can reveal aspects of reasoning that surface-level approaches fundamentally miss, indicating that reasoning analyses should look into model internals.
Understanding how computational effort is allocated across individual chain-of-thought (CoT) reasoning steps remains an open challenge: existing interpretability methods rely on output-level signals or collapse processing depth into a single trajectory-level scalar, leaving step-wise effort opaque. We propose Step-Aware Reasoning Energy (SARE), a geometric framework that quantifies effort at the granularity of individual CoT steps via Centered Kernel Alignment (CKA) between Gram matrices of token hidden states across adjacent transformer layers, capturing inter-token relational structure without requiring eigenvector alignment or cluster correspondence. SARE further contextualizes this energy within reasoning's semantic progression by modeling CoT trajectories as transitions among latent semantic states. Across six reasoning benchmarks and three open-weight LLMs, we find that reasoning energy is highly non-uniform across step types, exhibiting phase-like transitions invisible to trajectory-level metrics; incorrect trajectories show systematically lower energy at critical reasoning junctions; and SARE-based features match or outperform output-based confidence baselines in most settings, indicating that internal geometric dynamics encode predictive information beyond surface-level signals.