Validity-Calibrated Reasoning Distillation

Abstract

Reasoning distillation aims to transfer multi-step reasoning capabilities from large language models to smaller, efficient ones. While recent methods have shown promising gains, they typically rely on static teacher-student hierarchies and frame distillation as trajectory imitation. This is misaligned with the structure of reasoning, where intermediate steps are locally under-specified: global correctness constrains the final answer, but does not uniquely determine each intermediate move. We propose validity-calibrated reasoning distillation, a framework that treats reasoning distillation as a problem of local learning-signal allocation rather than path alignment. Instead of enforcing token-level imitation, we compare the student's and teacher's proposed next-step actions under the same prefix and use their relative local validity to modulate the strength of the distillation update. This yields a dynamic, context-dependent supervision that preserves the teacher's structural guidance while adapting update strength to local reasoning quality. Across math, code, and instruction-following benchmarks, our method outperforms strong distillation baselines. These results indicate that effective LLM reasoning distillation is governed not by rigid trajectory imitation, but by locally calibrated allocation of learning signal.