Automatic Solving And Text Generation Of Math Word Problems

Artificial intelligence technology represented by deep learning has made remarkable achievements in the fields of computer vision and natural language processing.In recent years,more and more researchers are focusing on a challenging field of automatic reasoning,which requires the model to accurately understand the meaning of the natural language and obtain the correct answer by automatic solving.As the earliest mathematical logic problems that human beings come into contact with,math word problems are often used to teach and test the arithmetic ability of elementary school students,which can be regarded as the ’alchemy stone’ for verifying model reasoning ability.A typical math word problem includes a paragraph of text description and the corresponding solution.According to the presentation form of the solution,math word problems can be divided into arithmetic word problems,equation set problems,and step-bystep solution problems.Previous studies treated the automatic solution task as a one-way translation task of the text description to the corresponding solution,and proposed the encoder-decoder architecture to solve math word problems.However,the single encoder and decoder are insufficient for extracting the textual features of the text description and the generation ability of the model.On the other hand,previous studies ignored to improve the robustness and generalization ability of the model,and construct reasonable text features of the text description from the data perspective.As the inverse problem of the automatic solving task,generating math word problems has not attracted enough attention in current studies.To solve the above issues,this dissertation focuses on the task of automatic solving and text generation of arithmetic word problems and equation set problems,and proposes a general model framework and four augmentation methods.The major contents and contributions of this dissertation are summarized as follows:（1）This dissertation proposes a model framework with multi-encoders and multidecoders for arithmetic word problems solving:The solutions of arithmetic word problems are in the form of arithmetic expressions,with different structures of sequence,tree and tuple.This dissertation proposes a general model framework based on the encoder-decoder architecture.Compared with previous studies that used a single encoder and decoder,our model framework consists of four components:① The text encoder adopts the pre-trained model of Bert extracts text features from the text description;② A graph neural network is used to integrate the numerical comparison information in the text description by the number encoder;③The tree decoder is responsible for generating the tree structure of the arithmetic expression;④The tuple structure of the arithmetic expression is generated by the tuple decoder.Experiments and case studies on both Chinese and English datasets show that our model achieves higher accuracy for solving simple,complex and frequent problems.（2）Four augmentation methods for arithmetic word problems solving are proposed in this dissertation:Different from current studies that still focus on the design of model architecture,this dissertation proposes three data augmentation methods and an auxiliary task for arithmetic word problems solving from the data perspective.The data augmentation methods change the text description and expression to varying degrees through question moving,sentence exchanging and label enhancement.The auxiliary task calculates the similarity of expressions and text descriptions to construct positive and negative samples for each math word problem,which obtains text features with higher discrimination by contrastive learning.These augmentation methods are available for all existing encoder-decoder architectures.Experiments and case studies on the Chinese dataset show that these augmentation methods bring good performance results.（3）This dissertation extends our model framework to equation set problems solving:Equation set problems are the generalization form of arithmetic word problems.Compared with arithmetic word problems,the data scale and data quality of equation set problems are more challenging,which means that this task not only requires the model to deal with more complex problems,but also requires a substantial expansion of datasets.However,this issue has not received enough attention in the current studies.Hence,this dissertation firstly transfers the model framework of arithmetic word problems solving to equation set problems solving,and then provides a label enhancement method for datasets,which makes the data scale expanded 3-4 times.Experiments and case studies on both Chinese and English datasets show that our model is more effective for such complex problems,and the label enhancement method significantly improves the accuracy of different models.（4）Candidate texts are used to improve expression consistency for math word problems generation:The text generation task can be regarded as the inverse problem of the automatic solving task.However,they cannot be directly generated from the expressions since text descriptions with the same expression are quite different.Previous studies provided keywords to hint at the story context of the target,which cannot guarantee that the generated results match the provided expressions.Hence,this dissertation proposes two improvements:①This dissertation proposes a heuristic search method based on expressions and keywords to search candidate texts,which provides prior text descriptions related to provided expressions and keywords;②This dissertation changes the single direction training from expressions to text descriptions,and uses the bidirectional training to improve the quality of the generated texts.Experiments on both Chinese and English datasets show that our model combining expressions,keywords and candidate texts is more competitive in terms of the number of different keywords and the consistency of expressions.In summary,this dissertation focuses on the task of automatic solving and text generation of arithmetic word problems and equation set problems,and proposes a general model framework and four augmentation methods.Experiments and case studies on both Chinese and English datasets show the effectiveness of the proposed methods in solving accuracy and text generation quality.