SMART：基于属性语法的代数故事问题情境模型
SMART: A Situation Model for Algebra Story Problems via Attributed Grammar
摘要：
解决代数故事问题仍然是人工智能中一项具有挑战性的任务，它需要对现实世界的情况有详细的了解和强大的数学推理能力。以前的数学应用题神经求解器直接将问题文本转换为方程，缺乏对情况的明确解释，并且通常无法处理更复杂的情况。为了解决神经求解器的这种限制，我们引入了\emph{situation model}的概念，它起源于心理学研究，以表示人类在解决问题时的心理状态，并提出了\emph{SMART}，它采用归因语法作为代数故事问题的情景模型的表示。具体来说，我们首先训练一个信息抽取模块，从问题文本中抽取节点、属性和关系，然后根据预定义的属性语法生成解析图。提出了一种迭代学习策略，进一步提高了SMART的性能。为了严格研究这个任务，我们精心策划了一个名为\emph{ASP6.6k}的新数据集。在ASP 6.6k上的实验结果表明，该模型在保持更好的可解释性的同时，大大优于所有以前的神经求解器。为了测试这些模型的泛化能力，我们还设计了一个分布外（OOD）评估，其中的问题比训练集中的问题更复杂。我们的模型在OOD评估中超过了最先进的模型17%，证明了其优越的泛化能力。
英文摘要：
Solving algebra story problems remains a challenging task in artificial intelligence, which requires a detailed understanding of real-world situations and a strong mathematical reasoning capability. Previous neural solvers of math word problems directly translate problem texts into equations, lacking an explicit interpretation of the situations, and often fail to handle more sophisticated situations. To address such limits of neural solvers, we introduce the concept of a \emph{situation model}, which originates from psychology studies to represent the mental states of humans in problem-solving, and propose \emph{SMART}, which adopts attributed grammar as the representation of situation models for algebra story problems. Specifically, we first train an information extraction module to extract nodes, attributes, and relations from problem texts and then generate a parse graph based on a pre-defined attributed grammar. An iterative learning strategy is also proposed to improve the performance of SMART further. To rigorously study this task, we carefully curate a new dataset named \emph{ASP6.6k}. Experimental results on ASP6.6k show that the proposed model outperforms all previous neural solvers by a large margin while preserving much better interpretability. To test these models' generalization capability, we also design an out-of-distribution (OOD) evaluation, in which problems are more complex than those in the training set. Our model exceeds state-of-the-art models by 17\% in the OOD evaluation, demonstrating its superior generalization ability.
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