Learning Theorem Rationale for Improving the Mathematical Reasoning Capability of Large Language Models

Large language models (LLMs) have achieved significant progress in mathematical reasoning, especially in elementary math. However, they remain indisposed on tackling complex questions at high-school or college levels, which put forward a more advanced requirement of mastering relevant mathematical theorems. For we humans, whether selecting the appropriate theorems according to the provided question is a crucial factor affecting the quality of the ultimate solutions, yet which has been neglected by previous research in the field of LLM reasoning. In this paper, we propose a novel approach to enhance the LLM's capability of utilizing the mathematical theorems to specific problems, which we refer to as Theorem Rationale (TR). To this end, a new dataset encompassing problem-theorem-solution triples is deliberately established for transferring principles of TR. Furthermore, we develop an evolving strategy to boost hierarchical instructions oriented on the theorems to alleviate difficulty in acquiring the curated data and facilitate the digestion of theorem application from various perspectives. Evaluations on a wide range of public datasets exhibit that the model fine-tuned with our dataset achieves consistent improvements at varying mathematical levels compared to the backbone. And further ablation studies illustrate the effectiveness of our proposed evolutionary strategies on enhancing the model's capability of math problem-solving. Overall, extensive experiments reveal the potential of our proposed method which highlights the significance of aligning the problems with the concrete theorems for LLMs to alleviate hallucination and improve the models' mathematical reasoning capabilities.