Training AI to Recognize Realizable Gauss Diagrams: The Same Instances Confound AI and Human Mathematicians

Khan, Abdullah, Lisitsa, Alexei and Vernitski, Alexei (2022) Training AI to Recognize Realizable Gauss Diagrams: The Same Instances Confound AI and Human Mathematicians. In: 14th International Conference on Agents and Artificial Intelligence, 2022-2-3 - 2022-2-5.

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Official URL: http://dx.doi.org/10.5220/0010992700003116

Abstract

Recent research in computational topology found sets of counterexamples demonstrating that several recent mathematical articles purporting to describe a mathematical concept of realizable Gauss diagrams contain a mistake. In this study we propose several ways of encoding Gauss diagrams as binary matrices, and train several classical ML models to recognise whether a Gauss diagram is realizable or unrealizable. We test their accuracy in general, on the one hand, and on the counterexamples, on the other hand. Intriguingly, accuracy is good in general and surprisingly bad on the counterexamples. Thus, although human mathematicians and AI perceive Gauss diagrams completely differently, they tend to make the same mistake when describing realizable Gauss diagrams.

Item Type:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	Computational Topology, Gauss Diagrams, Realizable Diagrams, Machine Learning
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	26 Sep 2023 14:32
Last Modified:	30 Jan 2024 19:33
DOI:	10.5220/0010992700003116
Open Access URL:	https://www.scitepress.org/Link.aspx?doi=10.5220/0...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3173084