通过修复学习：解决数学应用题与弱监督
Learning by Fixing: Solving Math Word Problems with Weak Supervision
摘要：
以前的数学应用题（MWP）神经解决器是在完全监督下学习的，无法生成多样化的解决方案。在本文中，我们解决这个问题，通过引入一个\textit{weakly-supervised}范式学习MWPs。我们的方法只需要最终答案的注释，可以为单个问题生成各种解决方案。为了增强弱监督学习，我们提出了一种新的\textit{learning-by-fixing}（LBF）框架，它通过符号推理纠正了神经网络的误解。具体地，对于由神经网络生成的不正确的解决方案树，\textit{fixing}机制将错误从根结点传播到叶节点，并推断可以被执行以获得期望的答案的最可能的修复。为了生成更多样化的解决方案，应用\textit{tree regularization}来指导解决方案空间的有效收缩和探索，并且设计\textit{memory buffer}来跟踪和保存针对每个问题发现的各种修复。在Math23 K数据集上的实验结果表明，该LBF框架在弱监督学习中的性能明显优于强化学习基线。此外，它实现了与完全监督方法相比相当的前1和更好的前3/5答案准确度，证明了其在产生不同解决方案方面的实力。
英文摘要：
Previous neural solvers of math word problems (MWPs) are learned with full supervision and fail to generate diverse solutions. In this paper, we address this issue by introducing a \textit{weakly-supervised} paradigm for learning MWPs. Our method only requires the annotations of the final answers and can generate various solutions for a single problem. To boost weakly-supervised learning, we propose a novel \textit{learning-by-fixing} (LBF) framework, which corrects the misperceptions of the neural network via symbolic reasoning. Specifically, for an incorrect solution tree generated by the neural network, the \textit{fixing} mechanism propagates the error from the root node to the leaf nodes and infers the most probable fix that can be executed to get the desired answer. To generate more diverse solutions, \textit{tree regularization} is applied to guide the efficient shrinkage and exploration of the solution space, and a \textit{memory buffer} is designed to track and save the discovered various fixes for each problem. Experimental results on the Math23K dataset show the proposed LBF framework significantly outperforms reinforcement learning baselines in weakly-supervised learning. Furthermore, it achieves comparable top-1 and much better top-3/5 answer accuracies than fully-supervised methods, demonstrating its strength in producing diverse solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
