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.

References

First, although we observe clear and consistent trajectory structure in GSM8K, MATH-500, and MMLU, it remains an open question whether similar geometric organization arises in other settings, such as open-ended reasoning, multi-hop QA, or program synthesis.

— LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals  (2604.05655 - Sun et al., 7 Apr 2026) in Limitations, paragraph 1

Other open questions are how the center emerges from pre-training (Papyan et al., 2020) and whether the geometry can be extended to reasoning capability.

— The Geometry of Knowledge Accessibility in Large Language Models  (2610.03052 - Chen, 2 Oct 2026) in Section 7, Conclusion