  We introduce Hyperbolic Prototype Learning, a type of supervised learning,
where class labels are represented by ideal points (points at infinity) in
hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann
loss', a new loss function based on the Busemann function of hyperbolic
geometry. We discuss several theoretical features of this setup. In particular,
Hyperbolic Prototype Learning becomes equivalent to logistic regression in the
one-dimensional case.
