Math word problem (MWP) solving aims to understand the descriptive math problem and calculate the result, for which previous efforts are mostly devoted to upgrade different technical modules. This paper brings a different perspective of \textit{reexamination process} during training by introducing a pseudo-dual task to enhance the MWP solving. We propose a pseudo-dual (PseDual) learning scheme to model such process, which is model-agnostic thus can be adapted to any existing MWP solvers. The pseudo-dual task is specifically defined as filling the numbers in the expression back into the original word problem with numbers masked. To facilitate the effective joint learning of the two tasks, we further design a scheduled fusion strategy for the number infilling task, which smoothly switches the input from the ground-truth math expressions to the predicted ones. Our pseudo-dual learning scheme has been tested and proven effective when being equipped in several representative MWP solvers through empirical studies. \textit{The codes and trained models are available at:} \url{https://github.com/steven640pixel/PsedualMWP}. \end{abstract}

翻译：数学应用题解答旨在理解描述性的数学问题并计算结果，先前的研究主要致力于升级不同技术模块。本文通过引入一种伪对偶任务来增强数学应用题解答，提出了训练过程中"重新审视过程"的新视角。我们设计了一种伪对偶学习方案来建模这一过程，该方案与模型无关，因此可适配于任何现有数学应用题解答器。伪对偶任务具体定义为：将表达式中的数字回填至原应用题中被掩码的数字位置。为促进两个任务的有效联合学习，我们进一步设计了针对数字填充任务的调度融合策略，该策略能平滑地将输入从真实数学表达式切换至预测表达式。通过实验研究，我们的伪对偶学习方案在多个代表性数学应用题解答器上进行了测试，并证明其有效性。代码与训练模型已公开于：\url{https://github.com/steven640pixel/PsedualMWP}。