Graph of Verification: Structured Verification of LLM Reasoning with Directed Acyclic Graphs

Verifying the complex and multi-step reasoning of Large Language Models (LLMs) is a critical challenge, as holistic methods often overlook localized flaws. Step-by-step validation is a promising alternative, yet existing methods are often rigid. They struggle to adapt to diverse reasoning structures, from formal proofs to informal natural language narratives. To address this adaptability gap, we propose the Graph of Verification (GoV), a novel framework for adaptable and multi-granular verification. GoV's core innovation is its flexible "node block" architecture. This mechanism allows GoV to adaptively adjust its verification granularity--from atomic steps for formal tasks to entire paragraphs for natural language--to match the native structure of the reasoning process. This flexibility allows GoV to resolve the fundamental trade-off between verification precision and robustness. Experiments on both well-structured and loosely-structured benchmarks demonstrate GoV's versatility. The results show that GoV's adaptive approach significantly outperforms both holistic baselines and other state-of-the-art decomposition-based methods, establishing a new standard for training-free reasoning verification.