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

TL;DR

This paper introduces the LeAp framework that explicitly learns and applies mathematical knowledge to improve reasoning in AI models, making the process more transparent and interpretable.

Contribution

The paper proposes a novel knowledge learning and applying framework with a problem-knowledge-expression paradigm, enhancing existing models' reasoning capabilities.

Findings

LeAp improves performance of various backbones on real-world datasets.

LeAp learns accurate, explicit mathematical knowledge.

The framework results in more interpretable reasoning processes.

Abstract

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