Solving math word problem (MWP) with AI techniques has recently made great progress with the success of deep neural networks (DNN), but it is far from being solved. We argue that the ability of learning by analogy is essential for an MWP solver to better understand same problems which may typically be formulated in diverse ways. However most existing works exploit the shortcut learning to train MWP solvers simply based on samples with a single question. In lack of diverse questions, these methods merely learn shallow heuristics. In this paper, we make a first attempt to solve MWPs by generating diverse yet consistent questions/equations. Given a typical MWP including the scenario description, question, and equation (i.e., answer), we first generate multiple consistent equations via a group of heuristic rules. We then feed them to a question generator together with the scenario to obtain the corresponding diverse questions, forming a new MWP with a variety of questions and equations. Finally we engage a data filter to remove those unreasonable MWPs, keeping the high-quality augmented ones. To evaluate the ability of learning by analogy for an MWP solver, we generate a new MWP dataset (called DiverseMath23K) with diverse questions by extending the current benchmark Math23K. Extensive experimental results demonstrate that our proposed method can generate high-quality diverse questions with corresponding equations, further leading to performance improvement on Diverse-Math23K. The code and dataset is available at: https://github.com/zhouzihao501/DiverseMWP

翻译：利用人工智能技术解决数学应用题（MWP）近年来随着深度神经网络（DNN）的成功取得了显著进展，但仍远未得到完全解决。我们认为，类比学习能力对于MWP求解器更好地理解可能以多种形式表述的同类问题至关重要。然而，现有研究大多利用捷径学习，仅基于单一问题的样本训练MWP求解器。由于缺乏多样化的题目，这些方法仅能学习浅层启发式规则。本文首次尝试通过生成多样化且一致的问题/方程来解决MWP。针对包含场景描述、问题和方程（即答案）的典型MWP，我们首先通过一组启发式规则生成多个一致的方程，然后将这些方程与场景一同输入问题生成器，以获取相应的多样化问题，从而形成包含多种问题与方程的新MWP。最后，我们使用数据过滤器剔除不合理的MWP，保留高质量增强样本。为评估MWP求解器的类比学习能力，我们基于现有基准数据集Math23K，生成了包含多样化问题的新MWP数据集（称为DiverseMath23K）。大量实验结果表明，所提方法能够生成与对应方程相匹配的高质量多样化问题，从而进一步提升Diverse-Math23K上的性能表现。代码和数据集详见：https://github.com/zhouzihao501/DiverseMWP