Generality of reasoning‑trajectory geometry beyond studied benchmarks

Determine whether large language models exhibit similar step-indexed reasoning‑trajectory geometric organization—i.e., structured hidden‑state regions that reflect reasoning progress—when applied to other tasks such as open‑ended reasoning, multi‑hop question answering, and program synthesis, beyond the GSM8K, MATH‑500, and MMLU settings in which this structure was observed.

Background

The paper demonstrates that during chain‑of‑thought math and knowledge tasks, hidden activations immediately before step markers and final‑answer markers occupy linearly separable, step‑specific regions, and that these structures organize progressively with layer depth. These findings are shown on GSM8K, MATH‑500, and MMLU.

In the Limitations section, the authors explicitly note uncertainty about whether the same kind of geometric organization of reasoning trajectories appears in other task settings, specifically naming open‑ended reasoning, multi‑hop QA, and program synthesis as examples.