论文标题
双曲原型学习理论
A Theory of Hyperbolic Prototype Learning
论文作者
论文摘要
我们介绍了双曲线原型学习，这是一种监督学习，其中类标签由双曲线空间中的理想点（无穷大）表示。学习是通过最大程度地减少“惩罚的Busemann损失”来实现的，这是一种基于双曲线几何形状的Busemann函数的新损失函数。我们讨论此设置的几个理论特征。特别是，双曲线原型学习在一维情况下等效于逻辑回归。
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.
