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

TL;DR

This paper demonstrates the successful application of neural networks combined with reinforcement learning to efficiently untangle braids up to length 20 and width 4, advancing computational methods in knot and group theory.

Contribution

It introduces a novel neural network approach utilizing reinforcement learning to solve braid untangling problems, achieving minimal move solutions.

Findings

Successfully untangled braids up to length 20 and width 4

Neural networks can learn effective strategies for braid untangling

Reinforcement learning optimizes move sequences for minimal untangling steps

Abstract

We report on our success on solving the problem of untangling braids up to length 20 and width 4. We use feed-forward neural networks in the framework of reinforcement learning to train the agent to choose Reidemeister moves to untangle braids in the minimal number of moves.