Title: Untying Knots with Neural Nets
Abstract: Neural networks can transform 3-dimensional data in a manner reminiscent of an ambient isotopy. With some modifications, a neural network can be trained to manipulate the vertices of a knot while respecting its topological structure. We use the discrete Mo ̈bius energy as a loss function to incentivize a neural network to smooth out curves in a knot, without performing illegal operations. By introducing unconventional neural network layers, we are able to untwist highly tangled polygonal knots until a human can visually recognize whether they are topologically equivalent to the unknot.