Minimal Free Resolution Guided Adaptive Tree Reasoning

Dynamic reasoning trees can help large language models solve complex tasks by explicitly structuring intermediate decisions. However, existing approaches often rely on manually specified subproblems or predefined decomposition patterns, which limits the effectiveness of reasoning and generalization. To solve this problem, we propose SyRA, a hierarchical reasoning framework based on MFR theory that supports the construction of adaptive reasoning trees and reliable error correction within a single LLM. Specifically, SyRA focuses on reasoning-tree construction, dynamically controlling branching and expansion using MFR principles to enable informative, non-redundant subproblem decomposition. In addition, it introduces a residual backtracking mechanism for adaptive cross-layer error correction, allowing the model to revise earlier reasoning decisions based on downstream feedback. Across eight reasoning benchmarks, SyRA significantly reduces logical errors and improves reasoning accuracy, while achieving a better balance between accuracy and reasoning time than the Chain-of-Thought, Decompose-Analyze-Rethink and Tree-of-Thought. Our code and dataset are available at https://github.com/ Tim798-art/SyRA/tree/main/SyRA .