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Large Language Models (LLMs) have showcased impressive reasoningcapabilities, particularly when guided by specifically designed prompts incomplex reasoning tasks such as math word problems. These models typicallysolve tasks using a chain-of-thought approach, which not only bolsters theirreasoning abilities but also provides valuable insights into theirproblem-solving process. However, there is still significant room for enhancingthe reasoning abilities of LLMs. Some studies suggest that the integration ofan LLM output verifier can boost reasoning accuracy without necessitatingadditional model training. In this paper, we follow these studies and introducea novel graph-based method to further augment the reasoning capabilities ofLLMs. We posit that multiple solutions to a reasoning task, generated by anLLM, can be represented as a reasoning graph due to the logical connectionsbetween intermediate steps from different reasoning paths. Therefore, wepropose the Reasoning Graph Verifier (RGV) to analyze and verify the solutionsgenerated by LLMs. By evaluating these graphs, models can yield more accurateand reliable results.Our experimental results show that our graph-basedverification method not only significantly enhances the reasoning abilities ofLLMs but also outperforms existing verifier methods in terms of improving thesemodels' reasoning performance.

Enhancing Reasoning Capabilities of Large Language Models: A Graph-Based Verification Approach