Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem

The celebrated Seq2Seq technique and its numerous variants achieve excellent performance on many tasks such as neural machine translation, semantic parsing, and math word problem solving. However, these models either only consider input objects as sequences while ignoring the important structural information for encoding, or they simply treat output objects as sequence outputs instead of structural objects for decoding. In this paper, we present a novel Graph-to-Tree Neural Networks, namely Graph2Tree consisting of a graph encoder and a hierarchical tree decoder, that encodes an augmented graph-structured input and decodes a tree-structured output. In particular, we investigated our model for solving two problems, neural semantic parsing and math word problem. Our extensive experiments demonstrate that our Graph2Tree model outperforms or matches the performance of other state-of-the-art models on these tasks.

[1]  Mo Yu,et al.  Exploiting Rich Syntactic Information for Semantic Parsing with Graph-to-Sequence Model , 2018, EMNLP.

[2]  Thomas Hofmann,et al.  Gaussian process classification for segmenting and annotating sequences , 2004, ICML.

[3]  Heng Tao Shen,et al.  Template-Based Math Word Problem Solvers with Recursive Neural Networks , 2019, AAAI.

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

[5]  Tommi S. Jaakkola,et al.  Tree-structured decoding with doubly-recurrent neural networks , 2016, ICLR.

[6]  Thomas Hofmann,et al.  Predicting structured objects with support vector machines , 2009, Commun. ACM.

[7]  Hannaneh Hajishirzi,et al.  Data-Driven Methods for Solving Algebra Word Problems , 2018, ArXiv.

[8]  Wei Lu,et al.  Dependency-based Hybrid Trees for Semantic Parsing , 2018, EMNLP.

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

[10]  Christopher D. Manning,et al.  Effective Approaches to Attention-based Neural Machine Translation , 2015, EMNLP.

[11]  Xiaojie Guo,et al.  Deep Graph Translation , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Xianpei Han,et al.  Sequence-to-Action: End-to-End Semantic Graph Generation for Semantic Parsing , 2018, ACL.

[13]  Wei Lu,et al.  Text2Math: End-to-end Parsing Text into Math Expressions , 2019, EMNLP.

[14]  Wang Ling,et al.  Latent Predictor Networks for Code Generation , 2016, ACL.

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

[16]  Yue Zhang,et al.  A Graph-to-Sequence Model for AMR-to-Text Generation , 2018, ACL.

[17]  Khalil Sima'an,et al.  Graph Convolutional Encoders for Syntax-aware Neural Machine Translation , 2017, EMNLP.

[18]  Dawn Xiaodong Song,et al.  Tree-to-tree Neural Networks for Program Translation , 2018, NeurIPS.

[19]  Danqi Chen,et al.  of the Association for Computational Linguistics: , 2001 .

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

[21]  Yejin Choi,et al.  MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms , 2019, NAACL.

[22]  Wang Ling,et al.  Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems , 2017, ACL.

[23]  Geoffrey E. Hinton,et al.  Speech recognition with deep recurrent neural networks , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

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

[25]  Samuel S. Schoenholz,et al.  Neural Message Passing for Quantum Chemistry , 2017, ICML.

[26]  Anoop Sarkar,et al.  Top-down Tree Structured Decoding with Syntactic Connections for Neural Machine Translation and Parsing , 2018, EMNLP.

[27]  Gholamreza Haffari,et al.  Graph-to-Sequence Learning using Gated Graph Neural Networks , 2018, ACL.

[28]  Jure Leskovec,et al.  Inductive Representation Learning on Large Graphs , 2017, NIPS.

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

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

[31]  Mirella Lapata,et al.  Coarse-to-Fine Decoding for Neural Semantic Parsing , 2018, ACL.

[32]  Thomas Hofmann,et al.  Large Margin Methods for Structured and Interdependent Output Variables , 2005, J. Mach. Learn. Res..

[33]  Richard S. Zemel,et al.  Gated Graph Sequence Neural Networks , 2015, ICLR.

[34]  Mark Steedman,et al.  Transforming Dependency Structures to Logical Forms for Semantic Parsing , 2016, TACL.

[35]  Alexander I. Rudnicky,et al.  Expanding the Scope of the ATIS Task: The ATIS-3 Corpus , 1994, HLT.

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

[37]  Hannaneh Hajishirzi,et al.  MAWPS: A Math Word Problem Repository , 2016, NAACL.

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

[39]  Qun Liu,et al.  Deep Neural Machine Translation with Linear Associative Unit , 2017, ACL.

[40]  Mohammed J. Zaki,et al.  Reinforcement Learning Based Graph-to-Sequence Model for Natural Question Generation , 2019, ICLR.

[41]  Jian Li,et al.  Multi-Head Attention with Disagreement Regularization , 2018, EMNLP.

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

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

[44]  Luke S. Zettlemoyer,et al.  Learning to Map Sentences to Logical Form: Structured Classification with Probabilistic Categorial Grammars , 2005, UAI.

[45]  Giorgio Satta,et al.  AMR Parsing With Cache Transition Systems , 2018, AAAI.

[46]  Mohammed J. Zaki,et al.  GraphFlow: Exploiting Conversation Flow with Graph Neural Networks for Conversational Machine Comprehension , 2019, IJCAI.

[47]  Percy Liang,et al.  Data Recombination for Neural Semantic Parsing , 2016, ACL.

[48]  Heng Tao Shen,et al.  MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning , 2018, AAAI.

[49]  Yansong Feng,et al.  Graph2Seq: Graph to Sequence Learning with Attention-based Neural Networks , 2018, ArXiv.

[50]  Vadim Sheinin,et al.  SQL-to-Text Generation with Graph-to-Sequence Model , 2018, EMNLP.

[51]  Jeffrey Pennington,et al.  GloVe: Global Vectors for Word Representation , 2014, EMNLP.

[52]  Yan Wang,et al.  Translating a Math Word Problem to a Expression Tree , 2018, EMNLP.

[53]  Graham Neubig,et al.  Learning to Represent Edits , 2018, ICLR.

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

[55]  Jianfeng Gao,et al.  Natural- to formal-language generation using Tensor Product Representations , 2019, ArXiv.

[56]  Graham Neubig,et al.  StructVAE: Tree-structured Latent Variable Models for Semi-supervised Semantic Parsing , 2018, ACL.