spoiler-score detector

PPC: Preplan-Plan-CoT Framework for LLM Mathematical Reasoning

This paper introduces PPC (Preplan-Plan-CoT), a reasoning framework that adds an explicit problem-understanding stage (the 'preplan') before the planning and chain-of-thought execution stages in LLM mathematical reasoning. The preplan captures problem type, applicable tools, and foreseeable pitfalls, addressing a gap in existing plan-based methods that only address 'how' to solve without first clarifying 'what' to solve. A three-stage synthesis pipeline with a spoiler-score detector and composite GRPO reward ensures clean preplan supervision and coherent plan generation. Evaluated across four backbones and five math benchmarks, PPC achieves best results on 39 of 40 metrics with +2.23 maj@16 and +3.06 pass@16 improvements over the strongest baseline at no additional inference token cost.