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

arXiv: https://arxiv.org/abs/2206.05373 · HTML: https://mlsanity.com/paper/2206.05373/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 7 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 2 of 2)

- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Untangling Braids with Multi-agent Q-Learning](https://mlsanity.com/paper/2109.14502/) (2021)

## Built on by (most cited first, 2 of 2)

- [Geometric deep learning approach to knot theory](https://mlsanity.com/paper/2305.16808/) (2023)
- [Learning the Word Problem: Geodesic Lengths and Cryptographic Applications](https://mlsanity.com/paper/2607.26241/) (2026)

## Abstract (arXiv)

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.