String Theory Journal Club

Knots are embedded circles in a R^3 and are considered equivalent if related by ambient isotopy. We propose to use techniques from generative AI and contrastive learning to automate the process of learning knot invariance. We set up a neural network with a contrastive loss that clusters different representations from the same knot equivalence class in the embedding dimension. We also use transformers to map different representations from the same knot equivalence class to a single (arbitrary) representative of their class. We explain how to use the generative model to study the Jones unknotting conjecture and how we examine which invariants are learned by the trained model. Note: this talk will be online.