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

TL;DR

SCULPT introduces a constraint-guided Monte Carlo Tree Search method that integrates domain-aware symbolic checks to improve the efficiency and accuracy of mathematical reasoning in large language models.

Contribution

It presents a novel constraint-guided MCTS framework that enhances search efficiency and reasoning stability by incorporating symbolic domain checks into the exploration process.

Findings

SCULPT improves accuracy across multiple datasets.

The approach maintains efficiency while enhancing reasoning stability.

Results with GPT-5.2 demonstrate transferability and frontier performance.

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.