2019
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Towards Generating Math Word Problems from Equations and Topics
Qingyu Zhou

Danqing Huang
Proceedings of the 12th International Conference on Natural Language Generation
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 templatebased with predefined 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 entityenforced 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.
2018
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Neural Math Word Problem Solver with Reinforcement Learning
Danqing Huang

Jing Liu

ChinYew Lin

Jian Yin
Proceedings of the 27th International Conference on Computational Linguistics
Sequencetosequence 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 sequencetosequence 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 sequencetosequence model (namely CASS) to address these shortcomings. To train our model, we apply reinforcement learning to directly optimize the solution accuracy. It overcomes the “traintest discrepancy” issue of maximum likelihood estimation, which uses the surrogate objective of maximizing equation likelihood during training while the evaluation metric is solution accuracy (nondifferentiable) 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 featurebased 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 featurebased model and their combination significantly outperforms the stateoftheart results.
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Using Intermediate Representations to Solve Math Word Problems
Danqing Huang

JinGe Yao

ChinYew Lin

Qingyu Zhou

Jian Yin
Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
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 higherorder 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 sequencetosequence 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.
2017
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Learning FineGrained Expressions to Solve Math Word Problems
Danqing Huang

Shuming Shi

ChinYew Lin

Jian Yin
Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing
This paper presents a novel templatebased 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 twostage 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 finegrained 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 stateoftheart systems while achieving an accuracy increase of 12% (59% relative) on the TS6 benchmark subset.
2016
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How well do Computers Solve Math Word Problems? LargeScale Dataset Construction and Evaluation
Danqing Huang

Shuming Shi

ChinYew Lin

Jian Yin

WeiYing Ma
Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)