Searching for ribbons with machine learning
This work addresses a specific problem in topology for mathematicians, using machine learning to advance understanding of knot theory and the Poincaré conjecture, but it is incremental as it applies existing methods to a new domain.
The researchers tackled the problem of determining when a knot bounds a ribbon disk, a question relevant to disproving the four-dimensional smooth Poincaré conjecture, by applying Bayesian optimization and reinforcement learning, which ruled out many potential counterexamples and successfully detected many ribbon knots up to 70 crossings.
We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincaré conjecture; using our programs, we rule out many potential counterexamples to the conjecture. We also show that the programs are successful in detecting many ribbon knots in the range of up to 70 crossings.