Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.

翻译：大型语言模型（LLMs）在复杂推理任务（如数学应用题）中展现出令人瞩目的推理能力，尤其是在特定设计的提示引导下。这些模型通常采用思维链方法求解任务，不仅增强了其推理能力，还为其问题求解过程提供了有价值的见解。然而，提升LLMs的推理能力仍有显著空间。部分研究表明，集成LLM输出验证器可在无需额外模型训练的情况下提升推理准确性。本文沿袭这些研究，提出一种新颖的基于图的方法以进一步增强LLMs的推理能力。我们认为，LLM生成的同一推理任务的多个解，因其不同推理路径中间步骤间的逻辑关联，可表示为推理图。为此，我们提出推理图验证器（RGV）来分析并验证LLM生成的解。通过对这些图进行评估，模型能够产生更准确可靠的结果。我们的实验结果表明，基于图的验证方法不仅显著增强了LLMs的推理能力，且在提升这些模型推理性能方面优于现有验证器方法。