Specialized Mathematical Solving by a Step-By-Step Expression Chain Generation

Math Solving requires both semantic understanding and relation reasoning. Most current approaches treat it as a translation task from natural language to mathematical symbols, generating tokens one by one. However, token-level generation is usually vulnerable when confronted with diverse annotations and complex reasoning. We consider the equation is an ordered combination of multiple sub-expressions, and math reasoning should be performed on the sub-expression level rather than the token level. We treat sub-expression as a minimum generative unit and minimum reasoning node. At each step, candidate sub-expression nodes are generated in parallel, and the whole reasoning chain is deduced by combining multiple nodes in order. Besides, we can obtain multiple valid reasoning chains by sub-expression searching, further improving interpretability and precision. Experiments on multilingual datasets show our method significantly outperforms the baselines. Additionally, our approach is more stable and efficient when faced with the challenges of diverse annotation and complex reasoning with limited resources. Moreover, our approach can be seamlessly integrated with large language models (LLMs), enhancing LLM's mathematical reasoning capabilities at a minimal cost. Experiments show a synergistic collaboration between general-purpose LLM and our specialized model yields superior performance.