# Discovery and Recognition of Formula Concepts using Machine Learning

arXiv: https://arxiv.org/abs/2303.01994 · HTML: https://mlsanity.com/paper/2303.01994/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 61 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Distributed Representations of Sentences and Documents](https://mlsanity.com/paper/1405.4053/) (2014)
- [Introducing MathQA -- A Math-Aware Question Answering System](https://mlsanity.com/paper/1907.01642/) (2019)
- [Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context](https://mlsanity.com/paper/1804.04956/) (2018)
- [A Survey on Retrieval of Mathematical Knowledge](https://mlsanity.com/paper/1505.06646/) (2015)
- [Discovering Mathematical Objects of Interest -- A Study of Mathematical Notations](https://mlsanity.com/paper/2002.02712/) (2020)
- [Fast Linking of Mathematical Wikidata Entities in Wikipedia Articles Using Annotation Recommendation](https://mlsanity.com/paper/2104.05111/) (2021)
- [Mining Mathematical Documents for Question Answering via Unsupervised Formula Labeling](https://mlsanity.com/paper/2211.06664/) (2022)
- [Classification and Clustering of arXiv Documents, Sections, and Abstracts, Comparing Encodings of Natural and Mathematical Language](https://mlsanity.com/paper/2005.11021/) (2020)
- [AutoMSC: Automatic Assignment of Mathematics Subject Classification Labels](https://mlsanity.com/paper/2005.12099/) (2020)
- [ARQMath Lab: An Incubator for Semantic Formula Search in zbMATH Open?](https://mlsanity.com/paper/2012.02413/) (2020)
- [Digital Repository of Mathematical Formulae](https://mlsanity.com/paper/1404.6519/) (2014)
- [Collaborative and AI-aided Exam Question Generation using Wikidata in Education](https://mlsanity.com/paper/2211.08361/) (2022)

## Built on by (most cited first, 1 of 1)

- [Using General Large Language Models to Classify Mathematical Documents](https://mlsanity.com/paper/2406.10274/) (2024)

## Abstract (arXiv)

Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In science, technology, engineering, and mathematics, researchers often employ mathematical concepts through formula notation to refer to prior knowledge. Our long-term goal is to generalize citation-based IR methods and apply this generalized method to both classical references and mathematical concepts. In this paper, we suggest how mathematical formulas could be cited and define a Formula Concept Retrieval task with two subtasks: Formula Concept Discovery (FCD) and Formula Concept Recognition (FCR). While FCD aims at the definition and exploration of a 'Formula Concept' that names bundled equivalent representations of a formula, FCR is designed to match a given formula to a prior assigned unique mathematical concept identifier. We present machine learning-based approaches to address the FCD and FCR tasks. We then evaluate these approaches on a standardized test collection (NTCIR arXiv dataset). Our FCD approach yields a precision of 68% for retrieving equivalent representations of frequent formulas and a recall of 72% for extracting the formula name from the surrounding text. FCD and FCR enable the citation of formulas within mathematical documents and facilitate semantic search and question answering as well as document similarity assessments for plagiarism detection or recommender systems.