Tangent-CFT: An embedding model for mathematical formulas

Behrooz Mansouri, Shaurya Rohatgi, Douglas W. Oard, Jian Wu, C. Lee Giles, Richard Zanibbi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

When searching for mathematical content, accurate measures of formula similarity can help with tasks such as document ranking, query recommendation, and result set clustering. While there have been many attempts at embedding words and graphs, formula embedding is in its early stages. We introduce a new formula embedding model that we use with two hierarchical representations, (1) Symbol Layout Trees (SLTs) for appearance, and (2) Operator Trees (OPTs) for mathematical content. Following the approach of graph embeddings such as DeepWalk, we generate tuples representing paths between pairs of symbols depth-first, embed tuples using the fastText n-gram embedding model, and then represent an SLT or OPT by its average tuple embedding vector. We then combine SLT and OPT embeddings, leading to state-of-the-art results for the NTCIR-12 formula retrieval task. Our fine-grained holistic vector representations allow us to retrieve many more partially similar formulas than methods using structural matching in trees. Combining our embedding model with structural matching in the Approach0 formula search engine produces state-of-the-art results for both fully and partially relevant results on the NTCIR-12 benchmark. Source code for our system is publicly available.

Original languageEnglish (US)
Title of host publicationICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval
PublisherAssociation for Computing Machinery, Inc
Pages11-18
Number of pages8
ISBN (Electronic)9781450368810
DOIs
Publication statusPublished - Sep 23 2019
Event9th ACM SIGIR International Conference on the Theory of Information Retrieval, ICTIR 2019 - Santa Clara, United States
Duration: Oct 2 2019Oct 5 2019

Publication series

NameICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval

Conference

Conference9th ACM SIGIR International Conference on the Theory of Information Retrieval, ICTIR 2019
CountryUnited States
CitySanta Clara
Period10/2/1910/5/19

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All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Information Systems

Cite this

Mansouri, B., Rohatgi, S., Oard, D. W., Wu, J., Giles, C. L., & Zanibbi, R. (2019). Tangent-CFT: An embedding model for mathematical formulas. In ICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval (pp. 11-18). (ICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval). Association for Computing Machinery, Inc. https://doi.org/10.1145/3341981.3344235