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This paper investigates whether high-level functional reasoning operations in chain-of-thought traces鈥攕uch as problem formulation, goal decomposition, and deduction鈥攃orrespond to distinct geometric structures within LLM hidden representation spaces. Probing reveals that reasoning operations are geometrically separable in held-out representations, peaking in middle layers and remaining robust against lexical and positional confounds. Furthermore, identical tokens are encoded differently based on their functional chunk, with attention-masking interventions confirming that these operation-aligned representations causally depend on preceding reasoning context.
Chain-of-thought is far more than surface imitation: LLMs carve out discrete, context-dependent geometric subspaces for functional operations like deduction and decomposition, with middle layers encoding the abstract reasoning step rather than the literal tokens.
Reasoning in large language models unfolds through diverse functional operations, such as problem formulation, goal decomposition, and deduction. Although these operations are explicitly distinguished in text, little is known about how they are geometrically organized in representation spaces. To this end, we investigate whether distinct reasoning operations exhibit corresponding geometric structure in hidden representations. We find that operations are separable in held-out representations, with separability peaking in middle layers, and verify that this structure is not explained by lexical or positional confounds. Across layers, token-wise operation-alignment becomes more distributed over spans, while identical surface tokens are represented differently depending on the operation of its surrounding chunk. Attention-masking interventions further show that operation-aligned representations at chunk onset depend on preceding reasoning context. Consequently, our work demonstrates that language models maintain representational correspondence between linguistic reasoning expressions and their internal geometric structures. Code and project materials are available at https://github.com/naver-ai/beneath-cot.
