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Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Paper · 2018 · Moritz Schubotz, Andre Greiner-Petter, Philipp Scharpf et al.

Summary

Mathematical notation is highly ambiguous. The same symbol can mean different things in different documents: E might be energy or expected value, and [a, b] might be an interval or a commutator. Presentation formats such as LaTeX record only layout, while computer algebra systems need explicit semantics, so converting between them is error-prone. The authors make three contributions. First, they release MathMLben, an open benchmark containing:

  • formulae drawn from NTCIR tasks and the DLMF;
  • a manually curated MathML gold standard covering both presentation and content, with formula components linked to Wikidata;
  • annotation-support tools;
  • tree-based evaluation metrics.

Second, they systematically evaluate common LaTeX-to-MathML converters. Many tools cannot produce content MathML at all, and those that can often yield mathematically wrong trees even for simple input. LaTeXML performs best but is slow. Third, they enrich LaTeXML conversion with textual context. A mathematical language processing (MLP) pipeline extracts identifier-definiens pairs from the surrounding text, and rule-based tree refinements are then applied. In a small pilot, these refinements fully repaired several content trees. The work matters as a reusable resource for format conversion and math information retrieval.

Key points

  • MathMLben benchmark: a gold standard with presentation and content MathML. Identifiers, operators and other entities are linked to Wikidata, so the data can also support formula concept discovery.
  • Converter evaluation:
    • The authors evaluated state-of-the-art LaTeX-to-MathML and CAS import tools with an automated, rerunnable framework.
    • LaTeXML had the lowest error rate and was the most extensible, but it was also slow.
  • Context-aware method:
    • The MLP software was extended beyond Wikipedia to parse XHTML (NTCIR, DLMF) and to identify general symbols, not only identifiers.
    • It was combined with semantic macros and a custom LaTeXML style sheet. The style sheet handles superscripts versus powers, subscripts as parameters, and function application versus multiplication.
  • Pilot result: out of 10 test functions, MLP ranked "function" as the top definiens in 4 cases. In those 4 cases, the content-tree distance to the gold standard dropped to zero.
  • Limitations and future work:
    • The rule-based selection has a long tail of special cases, and automatic learning of notation did not succeed.
    • Planned work covers automated notation detection and "notational name spaces".

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University of KonstanzKonstanz · Germany19 works · 274 citations🔬National Institute of Standards and TechnologyGaithersburg · United States5 works · 492 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksComputer Vision and Pattern Recognition · 3,621 worksMathematics · 233 worksComputational Theory and Mathematics · 496 worksModeling and Simulation · 12 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,948 works

Cite

Cite as Moritz Schubotz, Andre Greiner-Petter, Philipp Scharpf, Norman Meuschke, Howard Cohl and Bela Gipp. 2018. Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context. arXiv:1804.04956 (Proceedings of the ACM/IEEE-CS Joint Conference on Digital Libraries (JCDL), Jun. 2018, Fort Worth, USA).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.1145/3197026.3197058 · arXiv 1804.04956

@misc{schubotz2018improving,
  title = {{Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context}},
  author = {Moritz Schubotz, Andre Greiner-Petter, Philipp Scharpf, Norman Meuschke, Howard Cohl and Bela Gipp},
  year = {2018},
  doi = {10.1145/3197026.3197058},
  eprint = {1804.04956},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1145/3197026.3197058}
}

References

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