Narrowing the Gap between Combinatorial and Hyperbolic Knot Invariants via Deep Learning

TL;DR

This paper introduces a deep learning approach to uncover empirical relationships between combinatorial and hyperbolic knot invariants, bridging a gap in mathematical understanding through neural networks.

Contribution

It applies neural networks and linear regression to knot data, revealing new empirical connections between different types of knot invariants.

Findings

Empirical relationships between knot invariants are discovered.

Deep learning effectively models complex mathematical relationships.

The approach offers a new tool for mathematical discovery in knot theory.

Abstract

We present a statistical approach for the discovery of relationships between mathematical entities that is based on linear regression and deep learning with fully connected artificial neural networks. The strategy is applied to computational knot data and empirical connections between combinatorial and hyperbolic knot invariants are revealed.