Learning by Applying: A General Framework for Mathematical Reasoning via Enhancing Explicit Knowledge Learning

Mathematical reasoning is one of the crucial abilities general artificial intelligence, which requires machines to master mathematical logic and knowledge from solving problems. However, existing approaches are not transparent (thus interpretable) in terms what has been learned applied process. In this paper, we propose a Learning by Applying (LeAp) framework enhance models (backbones) principled way explicit learning. LeAp, perform learning novel problem-knowledge-expression paradigm, with Knowledge Encoder acquire problem data Decoder apply for expression reasoning. The knowledge, including word-word relations word-operator relations, forms an graph, bridges “learning” “applying” organically. Moreover, solving, design semantics-enhanced module reasoning-enhanced that improve comprehension symbol any backbone, respectively. We theoretically prove superiority LeAp's autonomous mechanism. Experiments on three real-world datasets show LeAp improves all backbones' performances, learns accurate achieves more interpretable