TY - JOUR

T1 - Rectangular knot diagrams classification with deep learning

AU - Kauffman, L. H.

AU - Russkikh, N. E.

AU - Taimanov, I. A.

N1 - Publisher Copyright: © 2022 World Scientific Publishing Company.

PY - 2022/10/1

Y1 - 2022/10/1

N2 - 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.

AB - 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.

KW - Dynnikov moves

KW - knot

KW - machine learning

KW - neural networks

KW - rectangular diagrams

KW - unknotting problem

UR - http://www.scopus.com/inward/record.url?scp=85141254542&partnerID=8YFLogxK

U2 - 10.1142/S0218216522500675

DO - 10.1142/S0218216522500675

M3 - Article

AN - SCOPUS:85141254542

VL - 31

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 11

M1 - 2250067

ER -