# NNexus Revolutions: NeuralNamed Entity Recognition and Linking for Technical Topics

## Highlights

We propose to adapt contemporary machine learning methods for natural language processing to work with mathematical text.

This constitutes a needed investment in the core infrastructure of mathematical sciences.

## Introduction

There are around 15K articles being added to the Arxiv preprint server *each month*. Can AI be used to help make this technical material easier to access, understand, and apply?

This six month project will use contemporary natural language processing techniques to take the first steps towards building computational models of mathematical language that reflect the richness of mathematical symbolism and the structure of mathematical arguments — as communicated by mathematicians.

Named entity recognition (NER) provides a foundation that can support the creation of knowledge graphs, recommendation services, and enhanced bibliometrics. These services have the potential to significantly improve the mathematical science research landscape. For example, analysis of the graph data could help researchers form coalitions around common themes, and support translation between different disciplinary languages. Recommender systems could help make the talent pipeline more robust, intermediating between the learner’s existing knowledge and a research project or application.

Recent work illustrates the feasibility of this approach. The NaturalProofs project worked with ≈32K theorems, proofs, and definitions, and spotted references between them.^{1} Our project will train a new neural NER system on a much larger corpus (≈10m online records). Because the pretraining strategy we have used preserves mathematical expressions (see “Pretraining Example”), we expect to be able to reliably link symbolic identifiers to their definitions, an entirely novel advance.

Our previous experiments with naive term spotting methods — based on lists of known named entities extracted from online encyclopedias and similar corpora — ran into difficulty with text samples such as these:

“Let G be a group” |
“group the numbers in rows” |

“chain in a graph” |
“chain made of steel” |

“permanent of M” |
“a permanent marker” |

Neural methods for NER offer a key advance, because they can distinguish between different senses of words based on context.^{2}

This project will give evidence that we can effectively bridge the *subsymbolic methods based on neural networks* that underlie contemporary language models with *symbolic methods for mathematical knowledge management*. This opens up a further programme of research in mathematical AI, and will have immediate practical applications.

## Pretraining Example

“Let (𝒳,

d_{∞}) denote the input feature space 𝒳…” →`Let ( calligraphic X , italic d sub ∞ ) denote the input feature space calligraphic X`

…

## Beneficiaries

The direct beneficiaries of this work include STEM researchers and students who will gain a new way to navigate the technical literature. Named entities, assembled in graphs and made traversable with recommendation engines, will help people make use of open source and open access resources such as Arxiv, Wikipedia, and MathOverflow — with the potential for similar applications to resources held by publishers. A secondary benefit will confer to researchers working on mathematical AI. NER has been applied in scientific domains,^{3} but without attention to mathematical notation or syntax. In open symbolic domains like mathematics and programming, the appropriate representations for machine learning and automated reasoning are not a settled issue. Graph representations are a strong candidate.^{4} Broader benefits will confer to society at large as support for formal education, learning on the job, and workplace productivity all improve.

## Research gap addressed

The context-rich nature of mathematical language and reasoning presents unique challenges for artificial intelligence. Classically-derived NLP methods are brittle, and typically only handle strictly conformant texts. Contemporary neural models do not incorporate domain knowledge, at least not without extra work (Note 4). For example, while language models such as GPT-3 have made a splash in the popular press, they do not understand simple word problems.^{5} We currently do not have computer models capable of modelling technical language as used by mathematicians.

## Track record

**Dr Corneli** completed a PhD in 2014 about learning on PlanetMath, one of the first large online encyclopedias. Based at the Open University’s **Knowledge Media Institute**, he worked with members of the German **Knowledge Adaptation and Reasoning for Content** (KWARC) research group to modernise PlanetMath’s software,^{6} including its named entity linking tool NNexus, expanding its scope of application.^{7}^{,}^{8} Corneli then researched computational creativity and social machines at Goldsmiths and the University of Edinburgh. His main thematic focus was mathematical argumentation.^{9}^{,}^{10}^{,}^{11}^{,}^{12} In 2020, he spent six months working on business model development at the startup incubator Entrepreneur First. Corneli has been in close contact with Deyan Ginev at KWARC about the project’s technical groundwork (see “Groundwork”).

**Professor Crook** is Director of the Institute for Ethical AI at Brookes and will help manage the project and explore potential future applications. Crook has a background in both autonomous systems and natural language processing, e.g., with application to conversational agents.^{13}

**Dr Long** is a research software engineer. He specialises in natural language processing using transformer-based tools, with a previous research background in statistical learning. Long has worked as a software developer in Fintech, e-commerce, and business intelligence.

**Mr Batra** is a PhD Candidate at Oxford University and a Researcher at Oxford Brookes. He previously earned an MSc in Computer Science from Oxford University, where he majored in AI. Batra has worked at Snapdeal as a Research Engineer in their Recommendations and Personalization team.

Long and Batra have recently been collaborating on learning-recommender focused tasks with **Learner Shape**, a company working in the training space that “uses AI to recommend individualized learning pathways to bridge skill gaps and get organizations future ready.”^{14} They bring related but distinct skills to the project: both will be employed throughout the project at .5FTE, to enable team work and skill sharing.

## Groundwork

Deyan Ginev prepared a large technical corpus using LaTeX ML and other tools, improving on earlier work with Arxiv data^{15}^{,}^{16} by

*regularising mathematical symbols**significantly expanding the training set*^{17}*developing word-level embeddings.*

Specifically, this data is being used to train a custom ELECTRA-Large model^{18} (estimated total run time: 33 days on one GPU).

## Objectives and Methods

**Objective 1.** *Adapt algorithms for neural named entity recognition over natural language to work with mathematical texts.*

Neural NER methods have been under development for over twenty years.^{19} Among recent systems, **Facebook’s GENRE** system is a strong contender.^{20}^{,}^{21} Various other methods exist that could be quickly applied to adapt our ELECTRA model for NER tasks.^{22}^{,}^{23} However, no existing neural NER system was designed with mathematical symbols in mind, so existing methods are likely to need significant adaptation. One of the key issues here is long-range reference. For example, a human reader would likely accept that “𝒳” appearing anywhere in this document refers to the same input feature space mentioned in above in the “Pretraining Example”, unless informed otherwise, but this may pose challenges for NER. One likely strategy for overcoming these challenges will be to incorporate *relation extraction* methods.^{24}

**Objective 2.** *Evaluate our named entity annotation system by using ground truth sources of ‘significant named entities’ and by eliciting user feedback on a public demonstration deployment.*

We will validate the mathematical NER system using data from textbooks, Wikipedia, PlanetMath, and a recently developed dataset based on ProofWiki (Note 1). We will also use the same methods to identify terms that should in principle be linked, i.e., terms that appear in Wikipedia as “red links”, and assess the quality of these links in a user study.

**Objective 3.** *Co-design a roadmap for further research together with key stakeholders.*

Methods to explore further include adapting (I) ‘fingerprint databases’ to map mathematical documents,^{25} (II) neural relation extraction, and (III) explainable recommendations.^{26}^{,}^{27}

## Research Programme

Challenge: It is hard for researchers to quickly adapt to a new field of research.

**WP1: NER for mathematical text.** We will review existing methods for neural named entity recognition and adapt them for a corpus that is rich with mathematical symbolism. A baseline can be provided by the classical version of NNexus (Note 7); SciBERT and GENRE (Notes 3, 20) provide suggestive directions for implementation work. The resulting NER system will be packaged into a proof-of-concept demonstration of a document recommendation system that can enable a non-expert user to find other relevant texts, and that can add useful cross-references within a given text.

Challenge: Academic papers do not come with an index or links to learning materials.

**WP2: Evaluation.** We will carry out a formal evaluation of the software from WP1 with reference to *precision* and *recall* of index terms in several well-known **Springer GTM** textbooks and (elided) wiki links in the mathematical portion of **Wikipedia**, and the **PlanetMath** encyclopedia (where most existing links were produced by the earlier verison of NNexus). The new NaturalProofs dataset based on **ProofWiki** gives us an additional benchmark for retrieval based evaluation (Note 1). We will also develop a new service that adds links to papers on the Arxiv, and carry out a small-scale evaluation with authors of preprints in various domains of mathematical science. The study will include interviews that will inform the next phase of design.

Challenge: Publishers, universities, and edtech providers will need to rapidly adapt to a changing landscape enriched by AI.

**WP3: Applications.** We will create a roadmap for future work centred on the technical methods listed under Objective 3. We will initially (WP3A) focus on discussions with stakeholders in the UK via the **Oxford International Centre for Publishing** and various contacts in mathematics, supported by developing demos in WP1. As this work matures (WP3B), Corneli will liaise with **Topos Institute** ^{28} to develop related use cases and designs. Futurist Bryan Alexander envisions a scenario in which the rise of open education leads some publishers to become “*essentially data analytics specialists, providing value by helping researchers see links between documents, tracing patterns of discovery, and generating insights about articles and monographs through data mining and AI.*”^{29} We will assess the feasibility and any missing components with publishers.

**Planned outputs**: We will submit to the Conferences on Intelligent Computer Mathematics and Learning Representations (CICM, ICLR). All code and demonstrator services will be released as open source. We will prepare a larger collaborative grant proposal with stakeholders.

## Impact Strategy

In WP3, our developing plan for further work will relate the technical Methods I-III mentioned above to their social context.

*‘Fingerprint databases’ to map mathematical documents.* As discussed in Corneli’s 2014 PhD thesis,^{30} with the rise of the social web, online creativity in mathematics is now widely distributed. The technical aspects of this proposal will give us the key tools we need to create and maintain an up-to-date concept-based index to mathematical communications at large. We plan to collaborate with the Topos Institute to develop this theme, building on Corneli’s prior experience with PlanetMath. This effort will be facilitated by outreach to organisations such as Arxiv and Stack Exchange with demo work based on WP1.

*Neural relation extraction.* Evan Patterson, based at the Topos Institute, previously worked with IBM researchers to develop methods for modelling computer code, piloting this work in the field of data science.^{31}^{,}^{32} Patterson’s system decomposes programs using a database of known programmatic patterns. Neural relation extraction could help to identify such composable patterns in mathematical language. Corneli will seek funding to support a current MSc thesis student to develop this work in a PhD.

*Explainable recommendations.* Bibliometrics is a well-established area of research, typically focusing on citation graphs. However, books usually contain additional metadata: the *index* and *table of contents*, which convey a sense of the document’s structure. Generalising this, we will be able to create something akin to a citation network, but for named entities. Such structures could allow users or client programs to reject or accept certain meanings. This suggests a new way to think about context that goes beyond the contemporary affordances of language models, which predict the next word in a sequence. This would inform the development of learning support tools, which would also benefit from our team’s experience working with Learner Shape.

## National Importance

The project presages future technologies that translate high-level descriptions of proofs and algorithms into custom learning pathways — or even directly runnable code.

Reviewers will be familiar with the fact that investments in mathematical sciences have an exceptionally high return-on-investment.^{33} This project constitutes a needed investment in the infrastructure of mathematical sciences itself, promising outsized leverage. The immediate economic relevance of this project is that computational models of technical subjects can provide students and researchers with a map of technical domains — showing not only how topics relate to each other, but also allowing users to keep track of skills that they themselves have mastered. Skills certification is key to closing the well-documented “skills gap”. Success with these endeavours would motivate similar experiments in software engineering.

By making transforming everyday mathematical language into computational structures the project has the potential to open new paths towards automated discovery, alongside AI tutoring and other forms of software assistance. Corneli’s prior work on argumentation (see Notes 10-12) may provide useful scaffolding for new methods of AI reasoning.

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