SCULPT: Constraint-Guided Pruned MCTS that Carves Efficient Paths for Mathematical Reasoning

• URL: http://arxiv.org/abs/2601.12842v1
• Date: Mon, 19 Jan 2026 08:55:46 GMT
• Title: SCULPT: Constraint-Guided Pruned MCTS that Carves Efficient Paths for Mathematical Reasoning
• Authors: Qitong Fang, Haotian Li, Xu Wang,
• Abstract summary: This paper introduces SCULPT, a constraint-guided approach for Monte Carlo Tree Search (MCTS)<n>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.<n>Overall, domain-aware constraints can improve accuracy while maintaining efficiency and stability.
• Score: 11.991985041067638
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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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