AI-guided discovery of new topological invariants

We have recently demonstrated that Neural Networks (NN) can learn to identify and classify complex knotted curves up to 10 crossings with high accuracy (Sleiman 2024). Even more strikingly, NNs can be trained to distinguish so-called “mutant” knots, such as Conway and Kinoshita-Terasaka knots, that share many topological invariants. This impressive feat is achieved when NNs are trained using a “segment-to-segment” writhe (StS writhe), a quantity that measures the level of entanglement between segments along the knotted molecule or polymer. Our results suggest that understanding how NNs classify knots could potentially guide mathematicians in formulating new topological invariants in knot theory. 

Bio
https://www.ph.ed.ac.uk/people/davide-michieletto