Margin in Abstract Spaces

ArXi:2603.07221v1 Announce Type: new Margin-based learning, exemplified by linear and kernel methods, is one of the few classical settings where generalization guarantees are independent of the number of parameters. This makes it a central in modern highly over-parameterized learning. We ask what minimal mathematical structure underlies this phenomenon. We begin with a simple margin-based problem in arbitrary metric spaces: concepts are defined by a center point and classify points according to whether their distance lies below $r$ or above $R.