The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective
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 direction-dependent term described by the Busemann function. This yields two main results. First, we prove a radial dichotomy: the sign of a drift coefficient $μ$ determines whether the radius is pushed toward the ideal boundary or back toward the inter...
| Authors | Xingrun Li, Sho Kuno, Yusuke Mukuta et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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