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

TL;DR

SCULPT reframes mathematical reasoning as constraint-guided workflow search, integrating six domain-aware constraints into a canonical four-stage MCTS to prune implausible steps. It formalizes constraint aggregation with a weighted geometric mean and employs a depth-aware expansion gate to regulate search, complemented by adaptive constraint weighting and magnitude-aware backpropagation. Across GSM8K, MATH, and GSM-Hard, SCULPT yields higher accuracy with substantially reduced exploration, achieving a 34.2% reduction in implausible branches and a 66% reduction in search variance, while lowering optimization costs by up to ~31%. The approach demonstrates that domain-specific symbolic and pattern-based guidance can substantially improve the reliability and efficiency of long-horizon reasoning in high-precision domains, with potential applicability to formal verification and legal reasoning.

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.

Figures (3)

• Figure 1: SCULPT architectural overview. Upper left: The Instruction Hub decomposes problem requirements into a vector of symbolic constraints (dimensional consistency $C_{\mathcal{U}}$, type compatibility $C_{\mathcal{T}}$, pattern similarity $C_{\mathcal{P}}$, magnitude sanity $C_{\mathcal{M}}$, depth control $C_{\mathcal{D}}$, and diversity $C_{\mathcal{V}}$). Lower left: The Routine Stack executes the MCTS search loop (selection, expansion, simulation, backpropagation) shaped by the aggregate compliance $C_{\text{total}}$. Lower right: Optimized programs are exposed via the Representation Layer, which provides multiple views including symbolic logic graphs and computational flow visualizations.
• Figure 2: Search space transformation via SCULPT. (a) A vanilla MCTS-based workflow search can suffer from a high branching factor due to many admissible but mathematically implausible actions. (b) SCULPT identifies and prunes these nodes early through symbolic constraint checks. (c) The resulting search space is regularized, focusing computational budget on logically consistent reasoning paths.
• Figure 3: Ablation studies on the MATH dataset. (a) Individual constraints: pattern similarity and type compatibility provide strong individual guidance, while dimensional consistency acts as a necessary but restrictive regularizer. (b) Injection stages: full integration across all four stages provides the highest accuracy. (c) Weighting strategy: dynamically updating constraint importance based on performance correlation yields more robust search priors.