arXiv Computation and Language August 28, 2026 By Zhuochun Li, Yuelyu Ji, Yiming Zeng, Daqing He

SPEAR: Distilling Domain-Adaptive Reasoning Skeletons via Sequential Symbolic Alignment in Reinforcement Learning

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SPEAR (Symbolic Process Evaluation and Alignment Reward) is a training‑free, plug‑and‑play reward method for on‑policy distillation in reinforcement learning. It converts natural‑language reasoning traces into domain‑adaptive symbolic milestones and uses the longest common subsequence to align student exploration with teacher milestones, producing a dense, order‑aware reward that enforces logical consistency without an external neural verifier. Experiments on math, science, and commonsense reasoning tasks show that SPEAR effectively bridges the reasoning gap between student and teacher models through sequence‑level distillation with efficient dense process rewards.

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