A Theory of Hyperbolic Prototype Learning
This work proposes a novel theoretical framework for hyperbolic prototype learning, which is incremental as it builds on existing hyperbolic geometry concepts.
The paper tackles the problem of supervised learning by representing class labels as ideal points in hyperbolic space and minimizing a new penalized Busemann loss, showing equivalence to logistic regression in the one-dimensional case.
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.