Geometric deep learning approach to knot theory

TL;DR

This paper proposes a geometric deep learning method that transforms knot data into graphs and employs graph neural networks to predict knot invariants, showing strong generalization.

Contribution

Introduces a novel functor-based approach converting knots to graphs for deep learning, advancing knot invariant prediction techniques.

Findings

High accuracy in predicting knot invariants

Strong generalization across different knot types

Effective use of graph neural networks for topological data

Abstract

In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this approach. This approach demonstrates high generalization capabilities.