MathAlign: Linking Formula Identifiers to their Contextual Natural Language Descriptions

Proceedings of the 12th Conference on Language Resources and Evaluation (LREC 2020), pages 2204–2212 Marseille, 11–16 May 2020 c⃝ European Language Resources Association (ELRA), licensed under CC-BY-NC 2204 MathAlign: Linking Formula Identifiers to their Contextual Natural Language Descriptions Maria Alexeeva∗, Rebecca Sharp†, Marco A. Valenzuela-Esc´arcega†, Jennifer Kadowaki+, Adarsh Pyarelal‡, and Clayton Morrison‡ Dept. of Linguistics∗, Dept. of Computer Science†, Dept. of Astronomy+, School of Information‡ University of Arizona, Tucson, AZ {alexeeva, bsharp, marcov, jkadowaki, adarsh, claytonm}@email.arizona.edu Abstract Extending machine reading approaches to extract mathematical concepts and their descriptions is useful for a variety of tasks, ranging from mathematical information retrieval to increasing accessibility of scientific documents for the visually impaired. This entails segmenting mathematical formulae into identifiers and linking them to their natural language descriptions. We propose a rule-based approach for this task, which extracts LATEX representations of formula identifiers and links them to their in-text descriptions, given only the original PDF and the location of the formula of interest. We also present a novel evaluation dataset for this task, as well as the tool used to create it. The data and the source code are open source and are available at https://osf.io/bdxmr/ and https://github.com/ml4ai/automates, respectively. Keywords: machine reading, relation extraction, math information retrieval, corpus creation, tool creation 1. Introduction Automatic reading of scientific literature has received atten- tion due to the proliferation of publications, as well as the importance of their content. A crucial aspect of understand- ing scientific publications is understanding the mathemat- ical formulae expressed in those publications, since they provide an explicit, concise representation of the key rela- tions between the relevant concepts (Schubotz et al., 2018). Extending machine reading to extract relations from math- ematical formulae requires reading the formulae into inter- nal representations, segmenting them into their component terms, and linking the terms to their textual descriptions. The proposed work stands to impact many different tasks that rely on understanding scientific content, including math information retrieval (Schubotz et al., 2016; Kris- tianto et al., 2017), scientific keyphrase and relation extrac- tion (Sterckx et al., 2016; Augenstein and Søgaard, 2017; Marsi and ¨Ozt¨urk, 2015), mathematical formula format conversion (Schubotz et al., 2018), and even accessibility efforts to make written content available to the visually im- paired (Pontelli et al., 2009; Alajarmeh and Pontelli, 2015). Beyond these tasks, there have also been recent efforts to apply machine reading to automatically analyze, ground, and compare executable models (Pyarelal et al., 2019). For this task, formulae found in papers describing these models can illuminate important semantics of how model variables interact with each other. Specifically, given a formula such as the one shown in Fig- ure 1 (Details of the annotation tool interface depicted in Figure 1 will be described below in Section 5.3.), there are several mathematical identifiers including simple iden- tifiers (i.e., xi), compound identifiers (θij(xi, xj)) and even subscripts (i). Each of these identifiers is referred to in the text, where the author expresses what they represent. Our goal is to find these identifiers in …

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