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Previous neural solvers of math word problems (MWPs) are learned with fullsupervision and fail to generate diverse solutions. In this paper, we addressthis issue by introducing a \textit{weakly-supervised} paradigm for learningMWPs. Our method only requires the annotations of the final answers and cangenerate various solutions for a single problem. To boost weakly-supervisedlearning, we propose a novel \textit{learning-by-fixing} (LBF) framework, whichcorrects 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 theleaf nodes and infers the most probable fix that can be executed to get thedesired answer. To generate more diverse solutions, \textit{treeregularization} is applied to guide the efficient shrinkage and exploration ofthe solution space, and a \textit{memory buffer} is designed to track and savethe discovered various fixes for each problem. Experimental results on theMath23K dataset show the proposed LBF framework significantly outperformsreinforcement learning baselines in weakly-supervised learning. Furthermore, itachieves comparable top-1 and much better top-3/5 answer accuracies thanfully-supervised methods, demonstrating its strength in producing diversesolutions.

Learning by Fixing: Solving Math Word Problems with Weak Supervision