Machine learning discovers invariants of braids and flat braids

Alexei Lisitsa, Mateo Salles, Alexei Vernitski
7/22/2023
math.GTcs.AIcs.LG

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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.

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Cite this paper

@article{lisitsa2023machine,
  title  = {Machine learning discovers invariants of braids and flat braids},
  author = {Alexei Lisitsa and Mateo Salles and Alexei Vernitski},
  year   = {2023},
  eprint = {2307.12185},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2307.12185v1}
}

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