A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks

Hyperbolic neural networks are able to capture the inherent hierarchy of graph datasets, and consequently a powerful choice of GNNs. However, they entangle multiple incongruent (gyro-)vector spaces within a layer, which makes them limited in terms of generalization and scalability. In this work, we propose to use Poincar\'e disk model as our search space, and apply all approximations on the disk (as if the disk is a tangent space derived from the origin), and thus getting rid of all inter-space transformations. Such an approach enables us to propose a hyperbolic normalization layer, and to further simplify the entire hyperbolic model to a Euclidean model cascaded with our hyperbolic normalization layer. We applied our proposed nonlinear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks. We demonstrate that not only does the model leverage the power of Euclidean networks such as interpretability and efficient execution of various model components, but also it outperforms both Euclidean and hyperbolic counterparts in our benchmarks.