Hyperbolic manifolds for visual representation learning allow for effective
learning of semantic class hierarchies by naturally embedding tree-like
structures with low distortion within a low-dimensional representation space.
The highly separable semantic class hierarchies produced by hyperbolic learning
have shown to be powerful in low-shot tasks, however, their application in
self-supervised learning is yet to be explored fully. In this work, we explore
the use of hyperbolic representation space for self-supervised representation
learning for prototype-based clustering approaches. First, we extend the Masked
Siamese Networks to operate on the Poincar\'e ball model of hyperbolic space,
secondly, we place prototypes on the ideal boundary of the Poincar\'e ball.
Unlike previous methods we project to the hyperbolic space at the output of the
encoder network and utilise a hyperbolic projection head to ensure that the
representations used for downstream tasks remain hyperbolic. Empirically we
demonstrate the ability of these methods to perform comparatively to Euclidean
methods in lower dimensions for linear evaluation tasks, whilst showing
improvements in extreme few-shot learning tasks.

本文研究使用超几何流形来进行自监督学习中的原型聚类。作者扩展了遮蔽孪生网络以操作包含理想边界的超几何空间，并利用超几何投影来确保下游任务的表示保持超几何性。实验证明这种方法在极少样本学习任务中具有改进，并在低维线性评估任务中与欧几里得方法相当。