Events

MaD Seminar: Kernel Learning on Manifolds

Speaker: Boris Hanin

Location: 60 Fifth Avenue, Room 7th floor open space

Date: Thursday, October 23, 2025

This talk concerns ongoing joint work with Mengxuan Yang on minimum norm interpolation with n samples in the RKHS of a kernel K. Unlike most prior work in this space our kernels will be defined on any close d-dimensional Riemannian manifold, and we require only that the kernels are trace class and elliptic. With these assumptions we get nearly sharp risk bounds with high probability over the data. Like prior work on round spheres our results essentially say that the number of samples n, the dimension of the manifold, and some details of the kernel determine a natural spectral cutoff lambda(n,d,K) and that minimal norm interpolation essentially learns exactly the projection of the data generating process onto the eigenfunctions of the Laplacian with frequency at most lambda(n,d,K). Joint work with Mengxuan Yang.

Bio: Boris an Associate Professor at Princeton ORFE (and Associated Faculty at Princeton PACM) working on deep learning, probability, and spectral asymptotics. Prior to Princeton, Boris was an Assistant Professor in Mathematics at Texas A&M, an NSF Postdoc at MIT Math, and a PhD student in Math at Northwestern, where he was supervised by Steve Zelditch.

He also works part time at Mithril (formerly Foundry), an incredible AI/computing startup that seeks to orchestrate the world’s computers, where Boris leads the Mithril Institute.