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

arXiv: https://arxiv.org/abs/2601.12842 · HTML: https://mlsanity.com/paper/2601.12842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 17 of 17)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [AFlow: Automating Agentic Workflow Generation](https://mlsanity.com/paper/2410.10762/) (2024)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Can Generalist Foundation Models Outcompete Special-Purpose Tuning? Case Study in Medicine](https://mlsanity.com/paper/2311.16452/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [TextGrad: Automatic "Differentiation" via Text](https://mlsanity.com/paper/2406.07496/) (2024)
- [From LLM Reasoning to Autonomous AI Agents: A Comprehensive Review](https://mlsanity.com/paper/2504.19678/) (2025)
- [Towards Making the Most of ChatGPT for Machine Translation](https://mlsanity.com/paper/2303.13780/) (2023)
- [Symbolic Learning Enables Self-Evolving Agents](https://mlsanity.com/paper/2406.18532/) (2024)
- [AutoFlow: Automated Workflow Generation for Large Language Model Agents](https://mlsanity.com/paper/2407.12821/) (2024)
- [Archon: An Architecture Search Framework for Inference-Time Techniques](https://mlsanity.com/paper/2409.15254/) (2024)
- [VerifAI: Verified Generative AI](https://mlsanity.com/paper/2307.02796/) (2023)
- [HoTPP Benchmark: Are We Good at the Long Horizon Events Forecasting?](https://mlsanity.com/paper/2406.14341/) (2024)
- [Symskill: Symbol and Skill Co-Invention for Data-Efficient and Reactive Long-Horizon Manipulation](https://mlsanity.com/paper/2510.01661/) (2025)

## Abstract (arXiv)

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.