A Bottom-Up DAG Structure Extraction Model for Math Word Problems

Research on automatically solving mathematical word problems (MWP) has a long history. Most recent works adopt the Seq2Seq approach to predict the result equations as a sequence of quantities and operators. Although result equations can be written as a sequence, it is essentially a structure. More precisely, it is a Direct Acyclic Graph (DAG) whose leaf nodes are the quantities, and internal and root nodes are arithmetic or comparison operators. In this paper, we propose a novel Seq2DAG approach to extract the equation set directly as a DAG structure. It extracts the structure in a bottom-up fashion by aggregating quantities and sub-expressions layer by layer iteratively. The advantages of our approach are threefold: it is intrinsically suitable to solve multivariate problems, it always outputs valid structure, and its computation satisfies commutative law for +,× and =. Experimental results on DRAW1K and Math23K datasets demonstrate that our model outperforms state-of-the-art deep learning methods. We also conduct detailed analysis on the results to show the strengths and limitations of our approach.

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

[2]  Hongwei Li,et al.  Nested relation extraction with iterative neural network , 2019, Frontiers of Computer Science.

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

[4]  Dan Roth,et al.  Solving General Arithmetic Word Problems , 2016, EMNLP.

[5]  Ping Luo,et al.  Nested relation extraction with iterative neural network , 2021, Frontiers Comput. Sci..

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

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

[8]  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.

[9]  Dan Roth,et al.  Unit Dependency Graph and Its Application to Arithmetic Word Problem Solving , 2016, AAAI.

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

[11]  Wei-Ying Ma,et al.  How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation , 2016, ACL.

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

[13]  Anirban Mukherjee,et al.  A review of methods for automatic understanding of natural language mathematical problems , 2008, Artificial Intelligence Review.

[14]  Eugene Charniak,et al.  Computer Solution of Calculus Word Problems , 1969, IJCAI.

[15]  Ming-Wei Chang,et al.  Annotating Derivations: A New Evaluation Strategy and Dataset for Algebra Word Problems , 2016, EACL.

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

[17]  Lukasz Kaiser,et al.  Attention is All you Need , 2017, NIPS.

[18]  Ming-Wei Chang,et al.  Learning from Explicit and Implicit Supervision Jointly For Algebra Word Problems , 2016, EMNLP.

[19]  John Cocke,et al.  Programming languages and their compilers: Preliminary notes , 1969 .

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

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

[22]  Ping Luo,et al.  Towards Automatic Numerical Cross-Checking: Extracting Formulas from Text , 2018, WWW.

[23]  Yefim Bakman,et al.  Robust Understanding of Word Problems with Extraneous Information , 2007, math/0701393.

[24]  Makoto Miwa,et al.  End-to-End Relation Extraction using LSTMs on Sequences and Tree Structures , 2016, ACL.

[25]  Ming-Wei Chang,et al.  BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding , 2019, NAACL.

[26]  Dan Roth,et al.  Equation Parsing : Mapping Sentences to Grounded Equations , 2016, EMNLP.

[27]  Christopher D. Manning,et al.  Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks , 2015, ACL.

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

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

[30]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.