Automatic Generation of Headlines for Online Math Questions

Mathematical equations are an important part of dissemination and communication of scientific information. Students, however, often feel challenged in reading and understanding math content and equations. With the development of the Web, students are posting their math questions online. Nevertheless, constructing a concise math headline that gives a good description of the posted detailed math question is nontrivial. In this study, we explore a novel summarization task denoted as geNerating A concise Math hEadline from a detailed math question (NAME). Compared to conventional summarization tasks, this task has two extra and essential constraints: 1) Detailed math questions consist of text and math equations which require a unified framework to jointly model textual and mathematical information; 2) Unlike text, math equations contain semantic and structural features, and both of them should be captured together. To address these issues, we propose MathSum, a novel summarization model which utilizes a pointer mechanism combined with a multi-head attention mechanism for mathematical representation augmentation. The pointer mechanism can either copy textual tokens or math tokens from source questions in order to generate math headlines. The multi-head attention mechanism is designed to enrich the representation of math equations by modeling and integrating both its semantic and structural features. For evaluation, we collect and make available two sets of real-world detailed math questions along with human-written math headlines, namely EXEQ-300k and OFEQ-10k. Experimental results demonstrate that our model (MathSum) significantly outperforms state-of-the-art models for both the EXEQ-300k and OFEQ-10k datasets.

[1]  Alon Lavie,et al.  Meteor Universal: Language Specific Translation Evaluation for Any Target Language , 2014, WMT@ACL.

[2]  Katsumi Tanaka,et al.  Learning to Generate Coherent Summary with Discriminative Hidden Semi-Markov Model , 2014, COLING.

[3]  Jian Qin,et al.  An interactive metadata model for structural, descriptive, and referential representation of scholarly output , 2014, J. Assoc. Inf. Sci. Technol..

[4]  Zhi Tang,et al.  Formula Ranking within an Article , 2018, JCDL.

[5]  Yoram Singer,et al.  Adaptive Subgradient Methods for Online Learning and Stochastic Optimization , 2011, J. Mach. Learn. Res..

[6]  Xiaojun Wan,et al.  From Neural Sentence Summarization to Headline Generation: A Coarse-to-Fine Approach , 2017, IJCAI.

[7]  Bipin Indurkhya,et al.  Pattern Generation Strategies for Improving Recognition of Handwritten Mathematical Expressions , 2019, Pattern Recognit. Lett..

[8]  Mirella Lapata,et al.  Don’t Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization , 2018, EMNLP.

[9]  Michihiro Yasunaga,et al.  TopicEq: A Joint Topic and Mathematical Equation Model for Scientific Texts , 2019, AAAI.

[10]  Wei Zhang,et al.  An Improved Approach Based on CNN-RNNs for Mathematical Expression Recognition , 2019, Proceedings of the 2019 4th International Conference on Multimedia Systems and Signal Processing - ICMSSP 2019.

[11]  Frank Wm. Tompa,et al.  Multi-Stage Math Formula Search: Using Appearance-Based Similarity Metrics at Scale , 2016, SIGIR.

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

[13]  Alexander M. Rush,et al.  Image-to-Markup Generation with Coarse-to-Fine Attention , 2016, ICML.

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

[15]  Christopher D. Manning,et al.  Get To The Point: Summarization with Pointer-Generator Networks , 2017, ACL.

[16]  Chin-Yew Lin,et al.  ROUGE: A Package for Automatic Evaluation of Summaries , 2004, ACL 2004.

[17]  Xiaojun Wan,et al.  Abstractive Document Summarization with a Graph-Based Attentional Neural Model , 2017, ACL.

[18]  Zheng Gao,et al.  Mathematics Content Understanding for Cyberlearning via Formula Evolution Map , 2018, CIKM.

[19]  David M. Blei,et al.  Equation Embeddings , 2018, ArXiv.

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

[22]  Valentin Malykh,et al.  Self-Attentive Model for Headline Generation , 2019, ECIR.

[23]  Yuehan Wang,et al.  A mathematical information retrieval system based on RankBoost , 2016, 2016 IEEE/ACM Joint Conference on Digital Libraries (JCDL).

[24]  Volker Markl,et al.  Semantification of Identifiers in Mathematics for Better Math Information Retrieval , 2016, SIGIR.

[25]  Yue Yin,et al.  Preliminary Exploration of Formula Embedding for Mathematical Information Retrieval: can mathematical formulae be embedded like a natural language? , 2017, ArXiv.

[26]  Salim Roukos,et al.  Bleu: a Method for Automatic Evaluation of Machine Translation , 2002, ACL.

[27]  Rada Mihalcea,et al.  TextRank: Bringing Order into Text , 2004, EMNLP.

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

[29]  Jun Xu,et al.  Question Headline Generation for News Articles , 2018, CIKM.

[30]  Fei Yin,et al.  Image-to-Markup Generation via Paired Adversarial Learning , 2018, ECML/PKDD.

[31]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.