The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective

Excerpt

arXiv:2610.07131v1 Announce Type: new Abstract: We study the implicit bias of Riemannian gradient flow for hyperbolic multiclass classification with fixed class prototypes in hyperbolic space $\mathbb{H}^n$. Our framework accommodates general permutation invariant relative margin (PERM) losses, a class that includes cross entropy and other standard multiclass losses. Our analysis is based on a decomposition: at large radius, the distance to each prototype splits into a radial term and a directio