Researchers at Hugging Face have published a paper titled "Beneath the Surface of Chains-of-Thought: A Mechanistic Interpretation of Reasoning Operations in LLMs," which investigates how reasoning operations are geometrically organized within the hidden representations of large language models. The study decomposes Chain-of-Thought reasoning into eight distinct operations based on Pólya's problem-solving framework, including problem formulation, goal decomposition, and deduction.
The authors find that these operations are separable in held-out representations, with separability peaking in middle layers across three models and two reasoning datasets. For instance, on Qwen3-8B, one-vs-rest probes achieve AUROC scores between 0.927 and 0.998 and AUPRC scores between 0.648 and 0.988 across operations. Smaller-scale generalization experiments replicate this structure on an additional model and show that probes transfer to unseen reasoning datasets without task-specific retraining.
Importantly, the observed structure is not explained by lexical or positional confounds. The researchers demonstrate that operation-aligned representations at chunk onset depend on preceding reasoning context, and that identical surface tokens are represented differently depending on the operation of the surrounding chunk. Attention-masking interventions further confirm that these representations rely on contextual reasoning context.
The findings suggest that language models maintain a representational correspondence between linguistic reasoning expressions and their internal geometric structures. This opens a path toward directly analyzing and intervening in reasoning representations to better understand and control LLM reasoning. Code and project materials are available at https://github.com/naver-ai/beneath-cot.