Machine learning discovers invariants of braids and flat braids
This work addresses a problem in mathematical knot theory by providing new invariants for braids, which is incremental as it builds on existing classification methods but introduces a novel machine learning-driven approach to generate and prove mathematical results.
The researchers tackled the problem of classifying braids and flat braids as trivial or non-trivial using machine learning, specifically neural networks, and discovered new invariants, including a complete invariant for flat braids, by interpreting the network structures as mathematical conjectures and proving them as theorems.
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.