Math word problem (MWP) solving is an important task in question answering which requires human-like reasoning ability. Analogical reasoning has long been used in mathematical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver's generalization ability across different kinds of MWPs. The key idea, named analogy identification, is to associate the analogical MWP pairs in a latent space, i.e., encoding an MWP close to another analogical MWP, while moving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between the representations of MWPs and their true solutions. The evaluation results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the-art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs.
翻译:数学问题解答是一项重要的任务,需要人性化推理能力。 数学教育长期以来一直使用模拟推理法,因为它使学生能够应用数学情况的共同关系结构解决新问题。 在本文中,我们提议利用模拟MWP来建立一个新的MWP求解器,通过利用模拟MWP来提高解决者在不同种类的MWP中的一般化能力。 关键的想法,称为类比识别,是将模拟MWP配对结合到一个隐蔽空间,即将一个MWP与另一个模拟的MWP相连接,同时摆脱非模拟的MWP。此外,在MWP解答器中融入了一种解决办法歧视者,以加强MWP代表及其真正解决办法之间的联系。评价结果证实,我们提议的模拟学习战略促进了MWP-BERT在Mat23k上对状态-艺术模型Generate2Rank的性能,而其参数则要少5倍。 我们还发现,我们的模型在解决困难的MWPMWP的简单学习方面,具有更强的普及能力。