Learning the Topological Invariance of Knots

Explore a 56-minute mathematics lecture from the CMSA Mathematics and Machine Learning Closing Workshop where Northeastern University's James Halverson delves into applying machine learning techniques to solve fundamental knot theory problems. Discover how transformers and convolutional neural networks can be trained to differentiate between topologically distinct knots without prior knowledge of topological invariants. Learn about the fascinating results showing how equivalent knots cluster within neural network embedding spaces and how trained decoders effectively map from embedding space back to knot space. Gain insights into new approaches addressing the Jones unknot conjecture, as this presentation bridges the gap between classical mathematical topology and modern machine learning techniques.