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：大型语言模型在复杂推理任务（如数学应用题）中展现了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解决任务，这不仅增强了其推理能力，还为其问题解决过程提供了宝贵见解。然而，大型语言模型的推理能力仍有显著提升空间。部分研究表明，集成大型语言模型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。本文延续这一研究方向，提出了一种新颖的基于图的方法，以进一步增强大型语言模型的推理能力。我们认为，大型语言模型生成的同一推理任务的多个解，由于不同推理路径中间步骤之间存在逻辑关联，可表示为推理图。因此，我们提出了推理图验证器，用于分析和验证大型语言模型生成的解。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大型语言模型的推理能力，而且在提升这些模型的推理性能方面优于现有验证器方法。