Knowing What to Solve Before How: Preplan Empowered LLM Mathematical Reasoning

Problem
This preprint addresses a significant gap in the existing literature on plan-based reasoning methods for large language models (LLMs). Current methodologies typically follow a question → plan → chain of thought (CoT) paradigm, where both planning and execution stages are intertwined. However, the critical initial step of recognizing the problem type, identifying applicable tools, and anticipating potential pitfalls is implicit. This oversight can lead to suboptimal reasoning outcomes. The authors propose a new framework, PPC (Preplan-Plan-CoT), which introduces an explicit problem-understanding stage, thereby enhancing the reasoning process.

Method
The PPC framework consists of a three-stage synthesis pipeline: preplan, plan, and CoT. The preplan stage explicitly identifies the problem type and relevant tools, ensuring a clear understanding before proceeding to the planning phase. To maintain the integrity of the preplan, the authors implement a spoiler-score detector that filters out irrelevant information and potential failures, thereby ensuring clean supervision for the preplan. Additionally, a composite GRPO (Generalized Reward for Planning Optimization) reward mechanism is employed to ensure that the generated plan is logically derived from the preplan. The authors evaluate PPC across four different backbone architectures and five mathematical reasoning benchmarks, demonstrating its versatility and effectiveness.

Results
PPC outperforms existing methods significantly, achieving the best results on 39 out of 40 metrics across the evaluated benchmarks. Notably, it improves the major accuracy at 16 (maj@16) and pass rate at 16 (pass@16) by +2.23 and +3.06, respectively, compared to the strongest baseline. Importantly, these improvements are achieved without incurring additional inference token overhead, indicating that the framework is both efficient and effective.

Limitations
The authors acknowledge that while PPC enhances reasoning capabilities, it may still be limited by the quality of the preplan stage, which relies on the model’s ability to accurately identify problem types and relevant tools. Additionally, the framework’s performance may vary depending on the complexity of the mathematical problems presented. The study does not address potential scalability issues when applied to more diverse or complex problem domains beyond the tested benchmarks. Furthermore, as a preprint, the findings have not undergone peer review, which may affect their robustness.

Why it matters
The introduction of the PPC framework has significant implications for the development of more sophisticated LLMs capable of advanced reasoning tasks. By explicitly incorporating a problem-understanding stage, this work paves the way for future research to explore similar paradigms in other domains, potentially leading to more effective AI systems in areas requiring complex decision-making and reasoning. The findings suggest that enhancing the initial understanding of a problem can lead to substantial improvements in overall performance, which could influence the design of future LLM architectures and training methodologies.

Authors: Shaojie Wang, Liang Zhang
Source: arXiv:2605.30245
URL: https://arxiv.org/abs/2605.30245v1