Enhancing math reasoning ability of large language models via computation logic graphs

The reasoning capabilities of large language models (LLMs) are essential for a wide range of tasks, particularly in the domain of mathematical reasoning. Common chain of thought methods perform well in handling simple reasoning problems, but for complex problems, a single-dimensional chain of thought is inadequate to address multi-layered logical relationships. To tackle this challenge, this paper introduces the concept of a Computation Logic Graph (CLG), designed to enhance the logical reasoning abilities of LLMs when solving complex mathematical problems. The CLG decomposes complex mathematical problems into multiple simple intermediate computational units, and the final answer is obtained through multiple iterations of these units. On the one hand, the CLG improves the model's ability to decompose and solve complex mathematical problems step-by-step from a global perspective. On the other hand, the local inference process within the CLG helps enhance the model's accuracy in single step calculations. To develop models with the ability to construct Computation Logic Graphs automatically, we create a dataset of computational logic graphs for complex mathematical problems, called the Computation-intensive Math Logic Graph (CMLG) dataset. We fine-tune several open-source LLMs using the CMLG dataset. Experimental results demonstrate that the proposed CLG method significantly enhances the performance of LLMs in complex mathematical reasoning tasks, outperforming on both the CMLG dataset and six other publicly available datasets from diverse domains.