Rectangular knot diagrams classification with deep learning

Abstract

In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of 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 the given finite families 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.

An application of neural networks to a problem in knot theory and group theory (untangling braids)

“…Recent studies [1,3] report that they use elements of deep learning to untangle braids (or knots), but do not provide details. Here we present all details of our implementation.…”