  Hyperbolic neural networks can effectively 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 the Poincare 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), 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 our model not only leverages the power of
Euclidean networks such as interpretability and efficient execution of various
model components, but also outperforms both Euclidean and hyperbolic
counterparts on various benchmarks. Our code is made publicly available at
https://github.com/oom-debugger/ijcai23.
