通过推理空间压缩实现结构性理性提炼
Structural Rationale Distillation via Reasoning Space Compression
AI总结：
本文提出D-RPC方法，通过压缩推理空间约束教师模型生成一致且多样化的推理路径，提升学生模型在数学和常识推理任务中的表现，优于多种基线方法。
摘要：
当从大型语言模型（LLMs）中提炼推理过程到小型模型时，教师模型对相似问题的推理路径结构和策略往往差异显著。本文提出Distillation through Reasoning Path Compression（D-RPC），通过约束教师模型遵循一个动态维护的可重用高层次推理路径库。对于每个训练问题，D-RPC检索最相关的路径并约束教师模型遵循它，生成在相似问题间一致但能覆盖不同问题类型的推理路径。PAC-Bayes分析正式化了银行大小与覆盖范围之间的权衡：较小的银行减少监督熵但可能造成覆盖缺口，而泛化界确定了一个最优的中间大小，通过消融实验得到验证。在五个数学和常识推理基准测试中，使用两个学生模型，D-RPC在表现上优于链式推理提炼、自由生成推理路径、直接提炼和结构化监督基线方法，同时使用的token数量少于模板密集型替代方法。
英文摘要：
When distilling reasoning from large language models (LLMs) into smaller ones, teacher rationales for similar problems often vary wildly in structure and strategy. Like a chef who makes the same dish differently each time, this inconsistency burdens the student with noisy supervision that is hard to internalize. We propose Distillation through Reasoning Path Compression (D-RPC), which constrains the teacher to follow a compact, dynamically maintained bank of reusable high-level reasoning paths. For each training question, D-RPC retrieves the most relevant path and conditions the teacher to follow it, producing rationales that are consistent across similar problems yet diverse enough to cover different problem types. A PAC-Bayes analysis formalizes the resulting trade-off between bank size and coverage: smaller banks reduce supervision entropy but risk coverage gaps, and the generalization bound identifies an optimal intermediate size confirmed by our ablations. Across five math and commonsense reasoning benchmarks with two student models, D-RPC consistently outperforms chain-of-thought distillation, freeform rationale generation, direct distillation, and structured-supervision baselines, while using fewer tokens than template-heavy alternatives.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
