Sequence to General Tree: Knowledge-Guided Geometry Word Problem Solving

With the recent advancements in deep learning, neural solvers have gained promising results in solving math word problems. However, these SOTA solvers only generate binary expression trees that contain basic arithmetic operators and do not explicitly use the math formulas. As a result, the expression trees they produce are lengthy and uninterpretable because they need to use multiple operators and constants to represent one single formula. In this paper, we propose sequence-to-general tree (S2G) that learns to generate interpretable and executable operation trees where the nodes can be formulas with an arbitrary number of arguments. With nodes now allowed to be formulas, S2G can learn to incorporate mathematical domain knowledge into problem-solving, making the results more interpretable. Experiments show that S2G can achieve a better performance against strong baselines on problems that require domain knowledge.1

[1]  Daisuke Kawahara,et al.  Tree-structured Decoding for Solving Math Word Problems , 2019, EMNLP.

[2]  Graham Neubig,et al.  A Syntactic Neural Model for General-Purpose Code Generation , 2017, ACL.

[3]  Dongxiang Zhang,et al.  Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions , 2019, ACL.

[4]  Yoshua Bengio,et al.  Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation , 2014, EMNLP.

[5]  Luke S. Zettlemoyer,et al.  Learning to Automatically Solve Algebra Word Problems , 2014, ACL.

[6]  Oren Etzioni,et al.  Learning to Solve Arithmetic Word Problems with Verb Categorization , 2014, EMNLP.

[7]  Jinlan Fu,et al.  A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving , 2020, EMNLP.

[8]  Jing Liu,et al.  Neural Math Word Problem Solver with Reinforcement Learning , 2018, COLING.

[9]  Chitta Baral,et al.  Learning To Use Formulas To Solve Simple Arithmetic Problems , 2016, ACL.

[10]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[11]  Keh-Yih Su,et al.  A Meaning-based English Math Word Problem Solver with Understanding, Reasoning and Explanation , 2016, COLING.

[12]  Neeraj Varshney,et al.  Towards Question Format Independent Numerical Reasoning: A Set of Prerequisite Tasks , 2020, ArXiv.

[13]  Oren Etzioni,et al.  Parsing Algebraic Word Problems into Equations , 2015, TACL.

[14]  Keh-Yih Su,et al.  A Meaning-Based Statistical English Math Word Problem Solver , 2018, NAACL.

[15]  Heng Tao Shen,et al.  The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Dan Klein,et al.  Abstract Syntax Networks for Code Generation and Semantic Parsing , 2017, ACL.

[17]  Shuming Shi,et al.  Automatically Solving Number Word Problems by Semantic Parsing and Reasoning , 2015, EMNLP.

[18]  Yan Wang,et al.  Graph-to-Tree Learning for Solving Math Word Problems , 2020, ACL.

[19]  Daniel G. Bobrow,et al.  Natural Language Input for a Computer Problem Solving System , 1964 .

[20]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[21]  Alexander M. Rush,et al.  Sequence-to-Sequence Learning as Beam-Search Optimization , 2016, EMNLP.

[22]  Quoc V. Le,et al.  Sequence to Sequence Learning with Neural Networks , 2014, NIPS.

[23]  Dan Roth,et al.  Mapping to Declarative Knowledge for Word Problem Solving , 2017, TACL.

[24]  Hang Li,et al.  “ Tony ” DNN Embedding for “ Tony ” Selective Read for “ Tony ” ( a ) Attention-based Encoder-Decoder ( RNNSearch ) ( c ) State Update s 4 SourceVocabulary Softmax Prob , 2016 .

[25]  Shuming Shi,et al.  Deep Neural Solver for Math Word Problems , 2017, EMNLP.

[26]  Mihai Surdeanu,et al.  The Stanford CoreNLP Natural Language Processing Toolkit , 2014, ACL.

[27]  Shuming Shi,et al.  Learning Fine-Grained Expressions to Solve Math Word Problems , 2017, EMNLP.

[28]  Pietro Liò,et al.  Graph Attention Networks , 2017, ICLR.

[29]  Mirella Lapata,et al.  Language to Logical Form with Neural Attention , 2016, ACL.

[30]  Zhipeng Xie,et al.  A Goal-Driven Tree-Structured Neural Model for Math Word Problems , 2019, IJCAI.

[31]  Yoshua Bengio,et al.  Neural Machine Translation by Jointly Learning to Align and Translate , 2014, ICLR.

[32]  Fengyuan Xu,et al.  Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem , 2020, FINDINGS.