用约束引导搜索，让大模型解题更高效准确
SCULPT: Constraint-Guided Pruned MCTS that Carves Efficient Paths for Mathematical Reasoning
- 引入领域约束评分机制，指导MCTS的每一步选择与剪枝
- 在多个数据集上提升解题准确率，且推理更稳定
- 适合需要可靠数学推理的AI系统开发者
自动化代理工作流可增强大语言模型（LLMs）的问题求解能力，但现有搜索策略依赖随机探索，常陷入不合理的推理路径。这是因为当前流程从通用提示或学习策略中采样候选步骤，缺乏强领域先验，导致近似随机遍历运算符、单位和格式。本文提出SCULPT，一种基于约束引导的蒙特卡洛树搜索方法，将领域感知评分融入选择、扩展、仿真和反向传播全过程。SCULPT通过符号检查（维度一致性、类型兼容性、量级合理性、深度控制、多样性）与结构模式引导，对动作进行评分并剪枝，从而引导搜索走向合理推理路径。在相同LLM配置下，SCULPT在多个数据集上实现稳定性能提升；额外实验使用GPT-5.2评估执行器迁移能力及在前沿推理模型上的表现。结果表明，领域感知约束可在保持效率的同时提升准确性与推理稳定性。
原文摘要 · Abstract (English)
Automated agent workflows can enhance the problem-solving ability of large language models (LLMs), but common search strategies rely on stochastic exploration and often traverse implausible branches. This occurs because current pipelines sample candidate steps from generic prompts or learned policies with weak domain priors, yielding near-random walks over operators, units, and formats. To promote ordered exploration, this paper introduces SCULPT, a constraint-guided approach for Monte Carlo Tree Search (MCTS) that integrates domain-aware scoring into selection, expansion, simulation, and backpropagation. SCULPT scores and prunes actions using a combination of symbolic checks (dimensional consistency, type compatibility, magnitude sanity, depth control, and diversity) and structural pattern guidance, thereby steering the search toward plausible reasoning paths. Under matched LLM configurations, SCULPT yields stable improvements on multiple datasets; additional results with GPT-5.2 assess executor transferability and performance on frontier reasoning models. Overall, domain-aware constraints can improve accuracy while maintaining efficiency and reasoning stability.
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