# Machine learning discovers invariants of braids and flat braids

arXiv: https://arxiv.org/abs/2307.12185 · HTML: https://mlsanity.com/paper/2307.12185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 22 Jul 2023.

## Builds on (most cited first, 3 of 3)

- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Untangling Braids with Multi-agent Q-Learning](https://mlsanity.com/paper/2109.14502/) (2021)
- [Detecting unknots via equational reasoning, I: Exploration](https://mlsanity.com/paper/1405.4211/) (2014)

## Abstract (arXiv)

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.