Machine learning discovers invariants of braids and flat braids

TL;DR

This paper employs machine learning, specifically neural networks, to classify braids and flat braids, leading to the discovery of new invariants and the proof of related conjectures, advancing mathematical understanding in braid theory.

Contribution

It introduces a novel approach combining machine learning with mathematical conjecture formulation and proof to discover invariants of braids and flat braids.

Findings

Neural networks effectively classify braid triviality.

Mathematically interpretable invariants are derived from ML structures.

A complete invariant for flat braids is established.

Abstract

We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we are able to interpret their structure as mathematical conjectures and then prove these conjectures as theorems. As a result, we find new convenient invariants of braids, including a complete invariant of flat braids.