Preliminary Exploration of Formula Embedding for Mathematical Information Retrieval: can mathematical formulae be embedded like a natural language?

Gao, Liangcai; Jiang, Zhuoren; Yin, Yue; Yuan, Ke; Yan, Zuoyu; Tang, Zhi

doi:10.48550/arxiv.1707.05154

Cited by 7 publications

(21 citation statements)

References 5 publications

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“…More recently, data-driven approaches which incorporate classic word embeddings (Gao et al, 2017;Mansouri et al, 2019), GNN (Song and Chen, 2021) or transformer models Reusch et al, 2021a,b) have also been proposed for the MIR domain. By observing token co-occurrence during training, these models can easily discover synonyms, equivalent mathematically transformed formulas, or high-level semantic similarities, making them a good enhancement for structure search approaches.…”

Section: Data-driven Methodsmentioning

confidence: 99%

Evaluating Token-Level and Passage-Level Dense Retrieval Models for Math Information Retrieval

Wang¹,

Yang²,

Lin³

2022

Preprint

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With the recent success of dense retrieval methods based on bi-encoders, a number of studies have applied this approach to various interesting downstream retrieval tasks with good efficiency and in-domain effectiveness. Recently, we have also seen the presence of dense retrieval models in Math Information Retrieval (MIR) tasks, but the most effective systems remain "classic" retrieval methods that consider rich structure features. In this work, we try to combine the best of both worlds: a well-defined structure search method for effective formula search and biencoder dense retrieval models to capture contextual similarities in mathematical documents. Specifically, we have evaluated two representative bi-encoder models (ColBERT and DPR) for token-level and passage-level dense retrieval on recent MIR tasks. To our best knowledge, this is the first time a DPR model has been evaluated in the MIR domain. Our result shows that bi-encoder models are complementary to existing structure search methods, and we are able to advance the state of the art on a recent MIR dataset. We have made our model checkpoints and source code publicly available for the reproduction of our results. 1

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Section: Data-driven Methodsmentioning

confidence: 99%

Evaluating Token-Level and Passage-Level Dense Retrieval Models for Math Information Retrieval

Wang¹,

Yang²,

Lin³

2022

Preprint

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“…Recent work (Roy, Upadhyay, and Roth 2016;Zanibbi et al 2016;) focused mainly on the structural features of math equations, and utilized tree structures to represent equations for mathematical information retrieval and mathematical word problem solving. Other work Krstovski and Blei 2018;Yasunaga and Lafferty 2019) instead focused mainly on the semantic features of equations. They processed an equation as a sequence of symbols in order to learn its representation.…”

Section: Related Work Mathematical Equation Representationmentioning

confidence: 99%

“…We view headline generation as a special type of summarizaton, with the constraint that only a short sequence of words is generated and that it preserves the essential meaning of a math question document. Recently, headline generation methods with end-to-end frameworks (Tan, Wan, and Xiao 2017b;Narayan, Cohen, and Lapata 2018;Zhang et al 2018;Gavrilov, Kalaidin, and Malykh 2019) achieved significant success. Math headline generation is similar to existing headline generation tasks, but still differs in several aspects.…”

Section: Summarization and Headline Generationmentioning

confidence: 99%

Automatic Generation of Headlines for Online Math Questions

Yuan¹,

He²,

Jiang³

et al. 2019

Preprint

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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 multihead 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 humanwritten 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.

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“…is extracted from the English Wikipedia page about Van der Waerden's theorem 4 . Without further explanation, the symbols W , k, and ε might have several possible meanings.…”

Section: Introductionmentioning

confidence: 99%

“…Word embedding techniques has received significant attention over the last years in the Natural Language Processing (NLP) community, especially after the publication of word2vec [18]. Recently, more and more projects try to adapt this knowledge for solving Mathematical Information Retrieval (MIR) tasks [4,12,36,34]. While all of these projects follow similar approaches and obtain promising results, all of them fail to understand mathematical expressions because of the same fundamental issues.…”

Section: Introductionmentioning

confidence: 99%

Why Machines Cannot Learn Mathematics, Yet

Greiner-Petter¹,

Ruas²,

Schubotz³

et al. 2019

Preprint

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Nowadays, Machine Learning (ML) is seen as the universal solution to improve the effectiveness of information retrieval (IR) methods. However, while mathematics is a precise and accurate science, it is usually expressed by less accurate and imprecise descriptions, contributing to the relative dearth of machine learning applications for IR in this domain. Generally, mathematical documents communicate their knowledge with an ambiguous, context-dependent, and non-formal language. Given recent advances in ML, it seems canonical to apply ML techniques to represent and retrieve mathematics semantically. In this work, we apply popular text embedding techniques to the arXiv collection of STEM documents and explore how these are unable to properly understand mathematics from that corpus. In addition, we also investigate the missing aspects that would allow mathematics to be learned by computers.

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Preliminary Exploration of Formula Embedding for Mathematical Information Retrieval: can mathematical formulae be embedded like a natural language?

Cited by 7 publications

References 5 publications

Evaluating Token-Level and Passage-Level Dense Retrieval Models for Math Information Retrieval

Evaluating Token-Level and Passage-Level Dense Retrieval Models for Math Information Retrieval

Automatic Generation of Headlines for Online Math Questions

Why Machines Cannot Learn Mathematics, Yet

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