Deep Learning of Topological Equivalence Classes

Abstract:We demonstrate an application of deep learning to the problem of identifying whether two generating vectors correspond to topologically equivalent finite group actions on Riemann surfaces, showing how architectures developed for semantic understanding have use for pure mathematical problems. In doing so we discuss how desired algebraic structure influences model design, and explore which structural properties of topological equivalence classes the model has successfully learnt.

Algebraic Geometry (math.AG); Machine Learning (cs.LG)

arXiv:2610.21981 [math.AG]

(or arXiv:2610.21981v1 [math.AG] for this version)

https://doi.org/10.48550/arXiv.2610.21981 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.