Knot Recognition via Machine Learning

• William Taylor, Mathematics, University of Delaware

• Deniz Kutluay, Department of Mathematical Sciences, University of Delaware

Traditional methods of distinguishing complex knot diagrams are computationally expensive. Our research explores the effectiveness of machine learning in the recognition of knot diagrams. For our purposes, we developed a Python library for digitally encoding, manipulating and generating knot diagrams. Our library uses planar diagram notation to represent knots in a format well-suited for fast computations. First, we generated a labeled dataset of diagrams of several knot types. We then trained a neural network on this dataset that identifies knot types. Various factors, such as the number of layers in the neural network, the number of nodes in each layer, the size of the training dataset, the number of distinct knot types, and the number of crossings per diagram are investigated for their effects on the prediction accuracy of the model. Preliminary results indicate that neural networks achieve high classification accuracy when trained on datasets with either low crossing numbers or a limited set of knot types. These findings lay the groundwork for future computational study in knot theory and demonstrate the potential of machine learning in the analysis of knot diagrams.