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

• URL: http://arxiv.org/abs/2605.30245v1
• Date: Thu, 28 May 2026 17:11:43 GMT
• Title: Knowing What to Solve Before How: Preplan Empowered LLM Mathematical Reasoning
• Abstract summary: We propose PPC (Preplan-Plan-CoT), a framework that introduces an explicit problem-understanding stage, the preplan.<n>We show that PPC achieves the best results on 39 of 40 metrics, improving maj@16 and pass@16 by +2.23 and +3.06 over the strongest baseline.
• Score: 5.703029996279753
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Current plan-based reasoning methods improve large language models (LLMs) by inserting a planning stage before execution, giving rise to the question $\rightarrow$ plan $\rightarrow$ cot paradigm. While effective, a closer examination reveals an inherent paradigm-level gap: both the planning and its execution stages decide how to solve a problem, while the prior question of what to solve; recognizing the problem type, the applicable tools, and the foreseeable pitfalls; remains entirely implicit. To bridge this gap, we propose PPC (Preplan-Plan-CoT), a framework that introduces an explicit problem-understanding stage, the preplan, yielding a new question $\rightarrow$ preplan $\rightarrow$ plan $\rightarrow$ cot paradigm. Realizing this paradigm requires safeguarding the conceptual integrity of preplan at both ends. Specifically, we design a three-stage synthesis pipeline with a spoiler-score detector that filters out leakage and spoiler failures to build clean preplan supervision, and a composite GRPO reward enforces that the generated plan genuinely follows from the preplan. Experiments across four backbones and five mathematical reasoning benchmarks show that PPC achieves the best results on 39 of 40 metrics, improving maj@16 and pass@16 by +2.23 and +3.06 over the strongest baseline without introducing additional inference token overhead.

Related papers

• Finding Optimal Cost-Bounded Plan Reductions: Refined Model [0.0]
  We study the problem of extracting, from a precomputed plan, a valid subplan that maximizes utility while respecting a cost bound.<n>We show the decision variant is NP-complete and propose two exact methods to solve it: one via oversubscription planning (OSP) and another via Linear Programming (ILP)
  arXiv  Detail & Related papers  (2026-07-28T09:21:19Z)
• PPA-Plan: Proactive Pitfall Avoidance for Reliable Planning in Long-Context LLM Reasoning [8.87747076871578]
  Large language models (LLMs) struggle with reasoning over long contexts where relevant information is sparsely distributed.<n>We propose PPA-Plan, a proactive planning strategy for long-context reasoning that focuses on preventing such failures before plan generation.<n>Experiments on long-context QA benchmarks show that executing plans generated by PPA-Plan consistently outperforms existing plan-and-execute methods and direct prompting.
  arXiv  Detail & Related papers  (2026-01-17T04:48:36Z)
• Satisficing and Optimal Generalised Planning via Goal Regression (Extended Version) [16.43772461453855]
  Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems.<n>We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal plan for each goal atom in some order.<n>We formalise and prove the conditions under which our method is guaranteed to learn valid generalised plans and state space pruning axioms for search.
  arXiv  Detail & Related papers  (2025-11-14T09:16:32Z)
• DeepPlanner: Scaling Planning Capability for Deep Research Agents via Advantage Shaping [74.34061104176554]
  We propose DeepPlanner, an end-to-end RL framework that effectively enhances the planning capabilities of deep research agents.<n>Our approach shapes token-level advantage with an entropy-based term to allocate larger updates to high entropy tokens, and selectively upweights sample-level advantages for planning-intensive rollouts.
  arXiv  Detail & Related papers  (2025-10-14T20:47:05Z)
• HyperTree Planning: Enhancing LLM Reasoning via Hierarchical Thinking [109.09735490692202]
  We propose HyperTree Planning (HTP), a novel reasoning paradigm that constructs hypertree-structured planning outlines for effective planning.<n> Experiments demonstrate the effectiveness of HTP, achieving state-of-the-art accuracy on the TravelPlanner benchmark with Gemini-1.5-Pro, resulting in a 3.6 times performance improvement over o1-preview.
  arXiv  Detail & Related papers  (2025-05-05T02:38:58Z)
• Thinking Forward and Backward: Effective Backward Planning with Large Language Models [19.05496894766632]
  Large language models (LLMs) have exhibited remarkable reasoning and planning capabilities. Many planning problems exhibit an inherent asymmetry such that planning backward from the goal is significantly easier. We propose a backward planning algorithm for LLMs that first flips the problem and then plans forward in the flipped problem.
  arXiv  Detail & Related papers  (2024-11-04T04:26:03Z)
• Symbolic Numeric Planning with Patterns [1.450144681559089]
  We encode the problem of finding a plan for $Pi$ with bound $n$ as a formula with fewer variables and/or clauses than the state-of-the-art rolled-up and relaxed-relaxed-$exists$ encodings. We show that our planner Patty has remarkably good comparative performances on this year's International Planning Competition.
  arXiv  Detail & Related papers  (2023-12-15T17:20:25Z)
• Planning as In-Painting: A Diffusion-Based Embodied Task Planning Framework for Environments under Uncertainty [56.30846158280031]
  Task planning for embodied AI has been one of the most challenging problems. We propose a task-agnostic method named 'planning as in-painting' The proposed framework achieves promising performances in various embodied AI tasks.
  arXiv  Detail & Related papers  (2023-12-02T10:07:17Z)
• Tree-Planner: Efficient Close-loop Task Planning with Large Language Models [63.06270302774049]
  Tree-Planner reframes task planning with Large Language Models into three distinct phases. Tree-Planner achieves state-of-the-art performance while maintaining high efficiency.
  arXiv  Detail & Related papers  (2023-10-12T17:59:50Z)
• Guiding Language Model Reasoning with Planning Tokens [122.43639723387516]
  Large language models (LLMs) have recently attracted considerable interest for their ability to perform complex reasoning tasks. We propose a hierarchical generation scheme to encourage a more structural generation of chain-of-thought steps. Our approach requires a negligible increase in trainable parameters (0.001%) and can be applied through either full fine-tuning or a more parameter-efficient scheme.
  arXiv  Detail & Related papers  (2023-10-09T13:29:37Z)
• Describe, Explain, Plan and Select: Interactive Planning with Large Language Models Enables Open-World Multi-Task Agents [26.78244595330595]
  "$underlineD$escribe" is an interactive planning approach based on Large Language Models (LLMs) DEPS facilitates better error correction on initial LLM-generated $textitplan$ by integrating $textitdescription$ of the plan execution process. Experiments mark the milestone of the first zero-shot multi-task agent that can robustly accomplish 70+ Minecraft tasks.
  arXiv  Detail & Related papers  (2023-02-03T06:06:27Z)
• Divide-and-Conquer Monte Carlo Tree Search For Goal-Directed Planning [78.65083326918351]
  We consider alternatives to an implicit sequential planning assumption. We propose Divide-and-Conquer Monte Carlo Tree Search (DC-MCTS) for approximating the optimal plan. We show that this algorithmic flexibility over planning order leads to improved results in navigation tasks in grid-worlds.
  arXiv  Detail & Related papers  (2020-04-23T18:08:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.