LaTeXML and the Math-rich Scholarly Web

Symposium at Perimeter Institute for Theoretical Physics

Theory and AI Symposium

ar5iv

arXiv

LaTeXML

https://creativecommons.org/licenses/by/4.0/

An invited talk for the "Theory and AI Symposium". A tour of leveraging LaTeXML for AI research in arXiv and beyond.

2025-04-08

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## <span style="color:#7113a0;">LaTeXML</span> and the Math-rich Scholarly Web

<span style="font-size:24px;">Deyan Ginev</span>
.remark-venue[Theory + AI Symposium<br>Perimeter Institute for Theoretical Physics<br>April 8, 2025]

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## An idea in 2006

*Why 2006?* W3C Math group is re-chartered for work on MathML 3.

<br>

Several one-on-one conversations between:
* Michael Kohlhase, KWARC group in Germany
* Bruce Miller, NIST
* Robert Miner, Design Science

<br>

Common needs:
- "It would be great to modernize arXiv for viewing in a browser."
- "It would be great to have enough MathML for Math Search."
- "It would be great to solve LaTeX conversion to XHTML."

<br>

Aside: Deyan joins in 2007, age 19 and is turning 38 later this year.

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## LaTeXML

<img class="titlepage-sammy" src="https://math.nist.gov/~BMiller/LaTeXML/x9.png">
https://dlmf.nist.gov/LaTeXML

* "free, public domain software, which converts LaTeX documents<br> to XML, HTML, EPUB, JATS and TEI" ([wiki](https://en.wikipedia.org/wiki/LaTeXML))

* Developed for, and actively maintained by
 - NIST Digital Library of Mathematical Functions
 - [dlmf.nist.gov](https://dlmf.nist.gov/)

* version **0.8.8**, a production-ready Perl<sup>†</sup> application
  * new version coming up shortly - and tested against arXiv
* implements a variant of the TeX typesetting engine
  * and a small part of the CTAN package ecosystem
* over 500 supported LaTeX packages
  * with another >50 experimental

<br>
<span style="font-size:13px;position:absolute;bottom:12px;left:108px;"><sup>†</sup>ongoing Rust rewrite at 26% test coverage</span>

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## A taste of LaTeXML's ecosystem (1/2)
Platforms:
  * NIST: Digital Library of Mathematical Functions (DLMF)
  * arXiv.org [HTML Papers](https://info.arxiv.org/about/accessible_HTML.html) and the [ar5iv Lab](ar5iv.labs.arxiv.org)
  * [PlanetMath](https://en.wikipedia.org/wiki/PlanetMath), [Authorea](https://en.wikipedia.org/wiki/Authorea), [Enabla](https://enabla.com/en/), [MELBA journal](https://www.melba-journal.org/blog/015-html-version-available.html), ...

<br>
Manuscripts, lectures, documentation pages:
  * APEX Calculus: Late Transcendentals ([textbook](https://arts-sciences.und.edu/academics/math/calc-1-texts.html))
  * Artificial Intelligence: Foundations of Computational Agents ([textbook]((https://artint.info/3e/html/ArtInt3e.html))
  * European Space Agency, GAIA Data ([documentation](https://gea.esac.esa.int/archive/documentation/GDR3/))
  * forall x: Calgary ([textbook](https://forallx.openlogicproject.org/))
  * Neuronal Dynamics ([textbook](https://neuronaldynamics.epfl.ch/online/index.html))
  * PHAS0067: Advanced Physical Cosmology ([lecture notes](https://phas0067.pontzen.uk/))
  * Rich Screen Reader Experiences for Accessible Data Visualization ([article](https://vis.csail.mit.edu/pubs/rich-screen-reader-vis-experiences/))

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## A taste of LaTeXML's ecosystem (2/2)
Research:
  * Search: [ARQMath](https://www.cs.rit.edu/~dprl/ARQMath/2021/) and NTCIR Math Task
  * Data: [ar5iv-04.2024](https://sigmathling.kwarc.info/resources/ar5iv-dataset-2024/), [arXMLiv](https://sigmathling.kwarc.info/resources/arxmliv-dataset-2020/)
  * OCR: Nougat model, work by Meta AI, [arXiv:2308.13418](https://arxiv.org/abs/2308.13418)
  * Classification: Scientific statements, work by NIST [arXiv:2308.13418](https://arxiv.org/abs/1908.10993)

<br>

Contributors and tools:
  * [BookML](https://vlmantova.github.io/bookml/) extension
  * [GROBID](https://grobid.readthedocs.io/en/latest/Principles/) component to emit TEI from LaTeX 
  * ResearchGate contributed JATS output

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## TLDR: What is ar5iv?

An official preview site for arXiv.org as HTML5 (with MathML)<br>

2.4 million e-print documents; updated monthly<br><br>
HTML for 97% of all LaTeX sources in arXiv, 74% error-free<br><br>
available at [ar5iv.labs.arxiv.org](https://ar5iv.labs.arxiv.org)

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## LaTeX is all you need for AI ? (1/3)
- The Unreasonable Effectiveness of Recurrent Neural Networks ([2015](https://karpathy.github.io/2015/05/21/rnn-effectiveness/))
- Galactica: A Large Language Model for Science ([arXiv:2211.09085](https://arxiv.org/abs/2211.09085))
- Formalizing the proof of PFR in Lean4 using Blueprint: a short tour ([Terence Tao, 2023](https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr-in-lean4-using-blueprint-a-short-tour/))
- NotebookLM ([June 2024](https://notebooklm.google/))
  - "Ah the bra. It's written as langle f phi and it's a bit of a different beast." ([audio](https://notebooklm.google.com/notebook/007fba0f-fc26-4ebc-9e6b-326bb4da88ec/audio))

<br>

How well could a model generalize to the long tail of math syntax?
  - Pretraining data gets sparse at the research frontier.

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## LaTeX is all you need for AI/web/search/a11y? (2/3)

_As seen on arXiv.org_

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## LaTeX is all you need for AI/web/search/a11y? (3/3)

_As seen on arXiv.org_

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## The LaTeX Social Contract

- arXiv authors write for their human readers
- If the PDF can be read, the job is done
- authors do **not** write to please markup developers
  - we all inevitably take shortcuts
  - the exception proves the rule
- So far, adoption favors messy systems

<br>

Instead, mapping into a minimal, standard, markup target improves:
 - AI: pretrain on better signal-to-noise ratio
 - search: index on better signal-to-noise ratio
 - web: render a narrative tree (DOM) quickly and reliably. Native benefits.
 - accessibility: able to speak the visual layout from the DOM, without fragility.
   - MathML 4 allows additional enhancements.

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# MathML Today

https://developer.mozilla.org/en-US/docs/Web/MathML#browser_compatibility

Coming soon: Advanced accessibility with MathML 4 Intent