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.

The pretraining of code LLMs typically begins with general data and progresses to domain-specific data through sequential stages. In the latter stages, a challenging issue is that the data of a target domain can be limited in size, and conventional approach of increasing the number of epochs does not lead to a performance gain. In this paper, we propose a novel packing method, which is extracting overlapping contexts from the training data using variable-length stride. Our method can mitigate the data-scarcity issue by providing more diverse and abundant examples of next token prediction than non-overlapping contexts. While the training time of our approach is increased proportionally to the amount of augmented examples, we present space-efficient implementations to store overlapping contexts. Extensive experiments with real datasets show that our approach outperforms the conventional approach of controlling the number of epochs in terms of the pass@k rate.