Title: Constraints-of-Thought: A Framework for Constrained Reasoning in Language-Model-Guided Search
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Monte Carlo Tree Search (MCTS), planning, search, LLMs

Abstract: Large language models (LLMs) have shown substantial progress in generating reasoning traces and candidate plans. However, the LLMs struggle to ensure that those plans align with high-level user intent and satisfy symbolic constraints, especially in complex, multi-step domains. Unconstrained reasoning approaches, such as Chain-of-Thought (CoT), expand the search space but frequently produce infeasible actions or hallucinations. We propose Constraints-of-Thought (Const-o-T), a framework that provides a structured prior that helps Monte Carlo Tree Search (MCTS) focus search on semantically meaningful paths. Each reasoning step is represented as an intent, constraint pair, which serves both to compress the search space and enforce validity. Unlike CoT, ToT, or verifier-guided methods that merely narrate reasoning or validate outputs post hoc, Const-o-T uses intent–constraint pairs as symbolic controllers that actively prune the action space during search. We integrate Const-o-T into  MCTS using a structured representation of intent–constraint pairs: constraints prune infeasible branches and guide exploration toward semantically valid actions, improving planning efficiency and verifiable decision-making. We evaluate Const-o-T on three domains: Risk game, CAD code generation, and arithmetic reasoning, and consistently outperformed the baselines, yielding higher accuracy and stronger structural alignment. We also analyze how constraint-guided reasoning reduces branching factors and description length while balancing bias–variance tradeoffs. Our contribution is the demonstration that intent–constraint representations provide a generalizable foundation for constraint-guided reasoning, yielding more efficient, verifiable, and domain-adaptable planning with LLMs.

TL;DR: We propose Constraints-of-Thought (Const-o-T), a framework that provides a structured prior that helps Monte Carlo Tree Search (MCTS) focus search on semantically meaningful paths.