D-RPC: Compressing Reasoning Paths for LLM Distillation

A novel technique known as Distillation through Reasoning Path Compression (D-RPC) enhances the transfer of reasoning skills from large language models (LLMs) to smaller counterparts. The rationales provided by teachers for analogous problems frequently differ in their structure and approach, leading to inconsistent supervision. D-RPC limits the teacher's options to a compact, dynamically updated collection of reusable high-level reasoning paths, selecting the most pertinent path for each training query. This approach ensures consistent rationales for similar issues while preserving diversity among various problem types. A PAC-Bayes analysis clarifies the balance between the size of the bank and its coverage: smaller banks lower supervision entropy but may create coverage gaps, with the generalization bound pinpointing an ideal intermediate size.