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.
翻译:数学推理是一般人工智能的关键能力之一,它要求机器掌握数学逻辑和知识,从而解决问题。然而,现有方法对于在推理过程中所学到和应用的知识来说不透明(因此不易解释),在推理过程中,现有方法不透明(因此不易解释),在本文件中,我们提议了一个应用(LeAp)总体学习框架,以便通过明确的知识学习,以有原则的方式加强现有模型(背脊)。在LeAp,我们在一个新颖的问题-知识表达模式中进行知识学习,由知识编码器从有问题的数据中获取知识,用知识解码器应用知识来应用知识进行表达推理。学数学知识,包括文字关系和文字-操作者关系,形成清晰的知识图表,将知识“学习”和“应用”有机地连接起来。此外,为了解决问题,我们设计了一个以语义强化的模块和一个推理强化模块,将知识应用于提高任何骨干体的问题理解和符号推理能力。我们理论上证明LeAp'自主学习机制的优越性优势。在三个现实世界数据推理学上进行实验,所有能的推理学都显示。