MaSH: Maximal Separating Poincaré Hyperplanes for Hierarchical Imbalanced Learning

Hyperbolic classifiers, which typically view hyperbolic hyperplanes as decision boundaries, are generalizations of Euclidean classifiers in hyperbolic space suitable for modeling hierarchical data. In this paper, we present Maximal Separating Poincaré Hyperplane (MaSH), a hyperbolic geometric inductive bias that enhances the generalization capability of hyperbolic classifiers, especially on the class-imbalanced settings. MaSH encourages 1) the equiangularity of the ideal points of the Poincaré hyperplanes of all classes; and 2) the equiradiality of these Poincaré hyperplanes. The two properties jointly encourage the maximal separation bias for hyperbolic classifiers. We perform experiments on imbalanced/long-tailed classification and the results show consistent improvements.