A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks

TL;DR

This paper introduces a unification framework that simplifies hyperbolic and Euclidean graph neural networks by using the Poincare disk model, leading to improved performance and scalability on graph datasets.

Contribution

The authors propose a hyperbolic normalization layer and a unified model that reduces hyperbolic GNNs to Euclidean models with normalization, enhancing scalability and interpretability.

Findings

The unified model outperforms existing Euclidean and hyperbolic GNNs on benchmarks.

The approach simplifies hyperbolic models without sacrificing performance.

The method improves scalability and interpretability of graph neural networks.

Abstract

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.