A math word problem is a narrative with a specific topic that provides clues to the correct equation with numerical quantities and variables therein. In this paper, we focus on the task of generating math word problems. Previous works are mainly template-based with pre-defined rules. We propose a novel neural network model to generate math word problems from the given equations and topics. First, we design a fusion mechanism to incorporate the information of both equations and topics. Second, an entity-enforced loss is introduced to ensure the relevance between the generated math problem and the equation. Automatic evaluation results show that the proposed model significantly outperforms the baseline models. In human evaluations, the math word problems generated by our model are rated as being more relevant (in terms of solvability of the given equations and relevance to topics) and natural (i.e., grammaticality, fluency) than the baseline models.

To solve math word problems, previous statistical approaches attempt at learning a direct mapping from a problem description to its corresponding equation system. However, such mappings do not include the information of a few higher-order operations that cannot be explicitly represented in equations but are required to solve the problem. The gap between natural language and equations makes it difficult for a learned model to generalize from limited data. In this work we present an intermediate meaning representation scheme that tries to reduce this gap. We use a sequence-to-sequence model with a novel attention regularization term to generate the intermediate forms, then execute them to obtain the final answers. Since the intermediate forms are latent, we propose an iterative labeling framework for learning by leveraging supervision signals from both equations and answers. Our experiments show using intermediate forms outperforms directly predicting equations.

Sequence-to-sequence model has been applied to solve math word problems. The model takes math problem descriptions as input and generates equations as output. The advantage of sequence-to-sequence model requires no feature engineering and can generate equations that do not exist in training data. However, our experimental analysis reveals that this model suffers from two shortcomings: (1) generate spurious numbers; (2) generate numbers at wrong positions. In this paper, we propose incorporating copy and alignment mechanism to the sequence-to-sequence model (namely CASS) to address these shortcomings. To train our model, we apply reinforcement learning to directly optimize the solution accuracy. It overcomes the “train-test discrepancy” issue of maximum likelihood estimation, which uses the surrogate objective of maximizing equation likelihood during training while the evaluation metric is solution accuracy (non-differentiable) at test time. Furthermore, to explore the effectiveness of our neural model, we use our model output as a feature and incorporate it into the feature-based model. Experimental results show that (1) The copy and alignment mechanism is effective to address the two issues; (2) Reinforcement learning leads to better performance than maximum likelihood on this task; (3) Our neural model is complementary to the feature-based model and their combination significantly outperforms the state-of-the-art results.

This paper presents a novel template-based method to solve math word problems. This method learns the mappings between math concept phrases in math word problems and their math expressions from training data. For each equation template, we automatically construct a rich template sketch by aggregating information from various problems with the same template. Our approach is implemented in a two-stage system. It first retrieves a few relevant equation system templates and aligns numbers in math word problems to those templates for candidate equation generation. It then does a fine-grained inference to obtain the final answer. Experiment results show that our method achieves an accuracy of 28.4% on the linear Dolphin18K benchmark, which is 10% (54% relative) higher than previous state-of-the-art systems while achieving an accuracy increase of 12% (59% relative) on the TS6 benchmark subset.