Hyperbolic neural networks have recently gained significant attention due to their promising results on several graph problems including node classification and link prediction. The primary reason for this success is the effectiveness of the hyperbolic space in capturing the inherent hierarchy of graph datasets. However, they are limited in terms of generalization, scalability, and have inferior performance when it comes to non-hierarchical datasets. In this paper, we take a completely orthogonal perspective for modeling hyperbolic networks. We use Poincar\'e disk to model the hyperbolic geometry and also treat it as if the disk itself is a tangent space at origin. This enables us to replace non-scalable M\"obius gyrovector operations with an Euclidean approximation, and thus simplifying the entire hyperbolic model to a Euclidean model cascaded with a hyperbolic normalization function. Our approach does not adhere to M\"obius math, yet it still works in the Riemannian manifold, hence we call it Pseudo-Poincar\'e framework. We applied our non-linear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks and demonstrate significant improvements in performance compared to both Euclidean and hyperbolic counterparts. The primary impact of this work lies in its ability to capture hierarchical features in the Euclidean space, and thus, can replace hyperbolic networks without loss in performance metrics while simultaneously leveraging the power of Euclidean networks such as interpretability and efficient execution of various model components.

翻译：超双曲神经网络最近由于在包括节点分类和链接预测在内的一些图表问题上的可喜结果而获得显著关注。 成功的主要原因是超双曲空间在捕捉图形数据集固有层次结构方面的有效性。 但是,它们在一般化、可缩缩化方面是有限的,并且性能较差。 在本文中, 我们用完全正统的视角模拟超双曲网络。 我们使用Poincar\'e磁盘来模拟超双曲几何测量, 并把它当作磁盘本身是发源的相近空间。 这使我们能够用非可缩动的 M\\\"oblius 旋转轨道操作来取代不可缩动的图形数据集。 因此, 将整个超双曲模型简化为以超双曲线功能升级的 Euclide 模型。 我们的方法不遵循 M\\'obius数学, 但是它仍然在里曼的双流计算中运行, 因此我们把它称为 Psedodo-poindede spal space specreal specal specal real commelation comm commelational netmelation netwocal real liversal real real liversal lab.