Beneath the Surface of Chains-of-Thought: A Mechanistic Interpretation of Reasoning Operations in LLMs

Reasoning is no longer just an emergent behavior of LLMs; it is increasingly becoming a training objective. Yet we still know little about how reasoning is represented and organized inside the model.

Beneath the Surface of Chains-of-Thought addresses this question by decomposing Chain-of-Thought into operations based on Pólya’s problem-solving framework and examining their hidden states.

Across three models and two reasoning datasets, we find that the eight reasoning operations form separable geometric structures in hidden space. On Qwen3-8B, one-vs-rest probes achieve AUROC of 0.927–0.998 and AUPRC of 0.648–0.988 across operations, with separability consistently strongest in intermediate layers. Smaller-scale generalization experiments replicate this structure on an additional model and show that probes transfer to unseen reasoning datasets without task-specific retraining.

Crucially, this structure is not explained by surface wording or position alone: operation signals become distributed across spans, and even identical tokens are represented differently depending on the reasoning context.

Together, these findings suggest that the functional structure of reasoning traces is reflected in the model’s internal geometry, opening a path toward directly analyzing and intervening in reasoning representations to better understand and control LLM reasoning.