Rethinking Reasoning Paths as Phase-Structured Trajectories

The paper proposes PAIR, a method that treats reasoning paths of large language models as phase‑structured trajectories within each question. By sampling multiple trajectories per question, aligning them to shared relative phases, and comparing successful versus unsuccessful paths only within the same phase, PAIR isolates path‑quality signals from question‑level variation. Experiments show that standard correctness probes lose predictive power under this within‑question evaluation, while PAIR improves trajectory ranking, Best‑of‑N selection, and enables phase‑wise steering of generation outcomes.

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