short-paper

Neural Mathematical Solver with Enhanced Formula Structure

Authors:

Enhong ChenAuthors Info & Claims

SIGIR '20: Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval

Pages 1729 - 1732

https://doi.org/10.1145/3397271.3401227

Published: 25 July 2020 Publication History

Abstract

Automatically answering mathematical problems is a challenging task since it requires not only the ability of linguistic understanding but also mathematical comprehension. Existing studies usually explore solutions on the elementary math word problems that aim to understand the questions described in natural language narratives, which are not capable of solving more general problems containing structural formulas. To this end, in this paper, we propose a novel Neural Mathematical Solver (NMS) with enhanced formula structures. Specifically, we first frame the formulas in a certain problem as a TeX dependency graph to preserve formula-enriched structures. Then, we design a formula graph network (FGN) to capture its mathematical relations. Next, we develop a novel architecture with two GRU models, connecting tokens from both word space and formula space together, to learn the linguistic semantics for the answers. Extensive experiments on a large-scale dataset demonstrate that NMS not only achieves better answer prediction but also visualizes reasonable mathematical representations of problems.

References

[1]

Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2015. Neural machine translation by jointly learning to align and translate. In 3rd International Conference on Learning Representations, ICLR 2015.

[2]

Junyoung Chung, Caglar Gulcehre, Kyunghyun Cho, and Yoshua Bengio. 2014. Empirical evaluation of gated recurrent neural networks on sequence modeling. In NIPS 2014 Workshop on Deep Learning, December 2014.

[3]

Zhenya Huang, Qi Liu, Chengxiang Zhai, Yu Yin, Enhong Chen, Weibo Gao, and Guoping Hu. 2019. Exploring Multi-Objective Exercise Recommendations in Online Education Systems. In Proceedings of the 28th ACM International Conference on Information and Knowledge Management. 1261--1270.

Digital Library

[4]

Zhiheng Huang, Wei Xu, and Kai Yu. 2015. Bidirectional LSTM-CRF models for sequence tagging. arXiv preprint arXiv:1508.01991 (2015).

[5]

Laurens van der Maaten and Geoffrey Hinton. 2008. Visualizing data using t-SNE. Journal of machine learning research, Vol. 9, Nov (2008), 2579--2605.

[6]

Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. 2013. Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems. 3111--3119.

[7]

Subhro Roy and Dan Roth. 2015. Solving General Arithmetic Word Problems. In Proceedings of the 2015 Conference on EMNLP. 1743--1752.

[8]

Adam Santoro, Ryan Faulkner, David Raposo, Jack Rae, Mike Chrzanowski, Theophane Weber, Daan Wierstra, Oriol Vinyals, Razvan Pascanu, and Timothy Lillicrap. 2018. Relational recurrent neural networks. In Advances in neural information processing systems. 7299--7310.

[9]

David Saxton, Edward Grefenstette, Felix Hill, and Pushmeet Kohli. 2019. Analysing mathematical reasoning abilities of neural models. arXiv preprint arXiv:1904.01557 (2019).

[10]

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need. In Advances in neural information processing systems. 5998--6008.

[11]

Hao Wang, Enhong Chen, Qi Liu, Tong Xu, Dongfang Du, Wen Su, and Xiaopeng Zhang. 2018. A United Approach to Learning Sparse Attributed Network Embedding. In 2018 IEEE International Conference on Data Mining (ICDM). IEEE, 557--566.

[12]

Hao Wang, Tong Xu, Qi Liu, Defu Lian, Enhong Chen, Dongfang Du, Han Wu, and Wen Su. 2019. MCNE: An End-to-End Framework for Learning Multiple Conditional Network Representations of Social Network. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 1064--1072.

Digital Library

[13]

Zhipeng Xie and Shichao Sun. 2019. A goal-driven tree-structured neural model for math word problems. In Proceedings of the 28th International Joint Conference on Artificial Intelligence. AAAI Press, 5299--5305.

[14]

Yu Yin, Zhenya Huang, Enhong Chen, Qi Liu, Fuzheng Zhang, Xing Xie, and Guoping Hu. 2018. Transcribing content from structural images with spotlight mechanism. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 2643--2652.

Digital Library

[15]

Dongxiang Zhang, Lei Wang, Luming Zhang, Bing Tian Dai, and Heng Tao Shen. 2019. The gap of semantic parsing: A survey on automatic math word problem solvers. IEEE transactions on pattern analysis and machine intelligence (2019).

Cited By

Xiao TLiu JHuang ZWu JSha JWang SChen ELarson K(2024)Learning to solve geometry problems via simulating human dual-reasoning processProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/725(6559-6568)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/725
Lin XHuang ZZhao HChen ELiu QLian DLi XWang H(2024)Learning Relation-Enhanced Hierarchical Solver for Math Word ProblemsIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2023.327211435:10(13830-13844)Online publication date: Oct-2024
https://doi.org/10.1109/TNNLS.2023.3272114
Li JDeng YMao SQin YJiang Y(2024)Knowledge-Associated Embedding for Memory-Aware Knowledge TracingIEEE Transactions on Computational Social Systems10.1109/TCSS.2023.330690911:3(4016-4028)Online publication date: Jun-2024
https://doi.org/10.1109/TCSS.2023.3306909
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Index Terms

Neural Mathematical Solver with Enhanced Formula Structure
1. Computing methodologies
  1. Artificial intelligence
    1. Natural language processing
      1. Information extraction
  2. Machine learning
    1. Machine learning approaches
      1. Neural networks

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Published In

cover image ACM Conferences

SIGIR '20: Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval

July 2020

2548 pages

ISBN:9781450380164

DOI:10.1145/3397271

General Chairs:
Jimmy Huang
York University, Canada
,
Yi Chang
Jilin University, China
,
Xueqi Cheng
Chinese Academy of Sciences, China
,
Program Chairs:
Jaap Kamps
University of Amsterdam, Netherlands
,
Vanessa Murdock
Amazon, U.S.A.
,
Ji-Rong Wen
Renmin University of China, China
,
Yiqun Liu
Tsinghua University, China

Copyright © 2020 ACM.

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SIGIR: ACM Special Interest Group on Information Retrieval

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 July 2020

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National Natural Science Foundation of China

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SIGIR '20

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SIGIR

SIGIR '20: The 43rd International ACM SIGIR conference on research and development in Information Retrieval

July 25 - 30, 2020

Virtual Event, China

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Overall Acceptance Rate 792 of 3,983 submissions, 20%

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Cited By

Xiao TLiu JHuang ZWu JSha JWang SChen ELarson K(2024)Learning to solve geometry problems via simulating human dual-reasoning processProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/725(6559-6568)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/725
Lin XHuang ZZhao HChen ELiu QLian DLi XWang H(2024)Learning Relation-Enhanced Hierarchical Solver for Math Word ProblemsIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2023.327211435:10(13830-13844)Online publication date: Oct-2024
https://doi.org/10.1109/TNNLS.2023.3272114
Li JDeng YMao SQin YJiang Y(2024)Knowledge-Associated Embedding for Memory-Aware Knowledge TracingIEEE Transactions on Computational Social Systems10.1109/TCSS.2023.330690911:3(4016-4028)Online publication date: Jun-2024
https://doi.org/10.1109/TCSS.2023.3306909
Duan ZGu HKe YZhou D(2024)EBERT: A lightweight expression-enhanced large-scale pre-trained language model for mathematics educationKnowledge-Based Systems10.1016/j.knosys.2024.112118300(112118)Online publication date: Sep-2024
https://doi.org/10.1016/j.knosys.2024.112118
Qin LLiu JHuang ZZhang KLiu QJin BChen EChen HDuh WHuang HKato MMothe JPoblete B(2023)A Mathematical Word Problem Generator with Structure Planning and Knowledge EnhancementProceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval10.1145/3539618.3591937(1750-1754)Online publication date: 19-Jul-2023
https://dl.acm.org/doi/10.1145/3539618.3591937
Huang THu SYang HGeng JLiu SZhang HYang Z(2023)PQSCT: Pseudo-Siamese BERT for Concept Tagging With Both Questions and SolutionsIEEE Transactions on Learning Technologies10.1109/TLT.2023.327570716:5(831-846)Online publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1109/TLT.2023.3275707
Yi HAn XMa J(2023)STSN: A Skim-Then-Scrutinize Network for Understanding Multimodal Educational Questions2023 3rd International Conference on Digital Society and Intelligent Systems (DSInS)10.1109/DSInS60115.2023.10455419(405-409)Online publication date: 10-Nov-2023
https://doi.org/10.1109/DSInS60115.2023.10455419
Xiong JLi CYang MHu XHu BAmigo ECastells PGonzalo JCarterette BCulpepper JKazai G(2022)Expression Syntax Information Bottleneck for Math Word ProblemsProceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval10.1145/3477495.3531824(2166-2171)Online publication date: 6-Jul-2022
https://dl.acm.org/doi/10.1145/3477495.3531824
Zhang YZhou GXie ZHuang J(2022)HGEN: Learning Hierarchical Heterogeneous Graph Encoding for Math Word Problem SolvingIEEE/ACM Transactions on Audio, Speech, and Language Processing10.1109/TASLP.2022.314531430(816-828)Online publication date: 2022
https://doi.org/10.1109/TASLP.2022.3145314
Liu JHuang ZLin XLiu QMa JChen E(2022)A Cognitive Solver with Autonomously Knowledge Learning for Reasoning Mathematical Answers2022 IEEE International Conference on Data Mining (ICDM)10.1109/ICDM54844.2022.00037(269-278)Online publication date: Nov-2022
https://doi.org/10.1109/ICDM54844.2022.00037
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