Variable Typing: Assigning Meaning to Variables in Mathematical Text

Proceedings of NAACL-HLT 2018, pages 303–312 New Orleans, Louisiana, June 1 - 6, 2018. c⃝2018 Association for Computational Linguistics Variable Typing: Assigning Meaning to Variables in Mathematical Text Yiannos A. Stathopoulos♠ Simon Baker♠♣ Marek Rei♠♦ Simone Teufel♠ ♠Computer Laboratory, University of Cambridge, United Kingdom ♣Language Technology Lab, University of Cambridge, United Kingdom ♦The ALTA Institute, University of Cambridge, United Kingdom {yiannos.stathopoulos,simon.baker,marek.rei,simone.teufel}@cl.cam.ac.uk Abstract Information about the meaning of mathemati- cal variables in text is useful in NLP/IR tasks such as symbol disambiguation, topic mod- eling and mathematical information retrieval (MIR). We introduce variable typing, the task of assigning one mathematical type (multi- word technical terms referring to mathemati- cal concepts) to each variable in a sentence of mathematical text. As part of this work, we also introduce a new annotated data set com- posed of 33,524 data points extracted from sci- entific documents published on arXiv. Our in- trinsic evaluation demonstrates that our data set is sufficient to successfully train and eval- uate current classifiers from three different model architectures. The best performing model is evaluated on an extrinsic task: MIR, by producing a typed formula index. Our re- sults show that the best performing MIR mod- els make use of our typed index, compared to a formula index only containing raw symbols, thereby demonstrating the usefulness of vari- able typing. 1 Introduction Scientific documents, such as those from Physics and Computer Science, rely on mathematics to communicate ideas and results. Written mathe- matics, unlike general text, follows strong domain- specific conventions governing how content is pre- sented. According to Ganesalingam (2008), the sense of mathematical text is conveyed through the interaction of two contexts: the textual context (flowing text) and the mathematical (or symbolic) context (mathematical formulae). In this work, we introduce a new task that fo- cuses on one particular interaction: the assignment of meaning to variables by surrounding text in the same sentence1. For example, in the sentence 1Data for the task is available at https://www.cst. cam.ac.uk/˜yas23/ Let P be a parabolic subgroup of GL(n) with Levi decomposition P = MN, where N is the unipotent radical. the variables P and N in the symbolic context are assigned the meaning “parabolic subgroup” and “unipotent radical” by the textual context sur- rounding them respectively. We will refer to the task of assigning one mathematical type to each variable in a sentence as variable typing. We use mathematical types (Stathopoulos and Teufel, 2016) as variable de- notation labels. Types are multi-word phrases drawn from the technical terminology of the math- ematical discourse that label mathematical objects (e.g., “set”), algebraic structures (e.g., “monoid”) and instantiable notions (e.g., “cardinality of a set”). In the sentence presented earlier, the phrases “parabolic subgroup”, “Levi decomposition” and “unipotent radical” are examples of types. Typing variables may be beneficial to other nat- ural language processing (NLP) tasks, such as topic modeling, to group documents that assign meaning to variables consistently (e.g., “E” is “en- ergy” consistently in some branches of Physics). In mathematical information retrieval (MIR), …

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