Machine learning discovers invariants of braids and flat braids

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.

An application of neural networks to a problem in knot theory and group theory

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.

Untangling Braids with Multi-agent Q-Learning

We use reinforcement learning to tackle the problem of untangling braids. We experiment with braids with 2 and 3 strands. Two competing players learn to tangle and untangle a braid. We interface the braid untangling problem with the OpenAI Gym environment, a widely used way of connecting agents to reinforcement learning problems. The results provide evidence that the more we train the system, the better the untangling player gets at untangling braids. At the same time, our tangling player produces good examples of tangled braids.