Abstract: In this paper, we discuss applications of neural networks to recognizing knots and, in particular, to the unknotting problem. One of the motivations for this study is to understand how neural networks work on the example of a problem for which rigorous mathematical algorithms for its solution are known. We represent knots by rectangular Dynnikov diagrams and apply neural networks to distinguish a given diagram’s class from a finite family of topological types. The data presented to the program is generated by applying Dynnikov moves to initial samples. The significance of using these diagrams and moves is that in this context the problem of determining whether a diagram is unknotted is a finite search of a bounded combinatorial space. In this way, this paper provides a foundation for further work where the neural network itself will learn to use the Dynnikov moves for knot recognition. Source code of the programs is available at https://github.com/nerusskikh/deepknots.

Cite: Kauffman L.H. , Russkikh N.E. , Taimanov I.A.
Rectangular knot diagrams classification with deep learning
Journal of Knot Theory and its Ramifications. 2022. V.31. N11. 2250067 . DOI: 10.1142/s0218216522500675 WOS Scopus РИНЦ OpenAlex

Identifiers:

Web of science:	WOS:000874057700001
Scopus:	2-s2.0-85141254542
Elibrary:	59007273
OpenAlex:	W4287604207

Citing:

DB	Citing
Web of science	2
Scopus	3
OpenAlex	3

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