SRBGCN: Tangent space-Free Lorentz Transformations for Graph Feature Learning

Abdelrahman Mostafa, Wei Peng, Guoying Zhao

Keywords: fully hyperbolic network, Lorentz transformations, boost and rotation, graph convolutional networks, hyperbolic rotations

TL;DR: This work introduces a fully hyperbolic network that uses direct Lorentz transformations to learn the features directly on the manifold.

Abstract: Hyperbolic graph convolutional networks have been successfully applied to represent complex graph data structures. However, optimization on Riemannian manifolds is nontrivial thus most of the existing hyperbolic networks build the network operations on the tangent space of the manifold, which is a Euclidean local approximation. This distorts the learnt features, limits the representation capacity of the network and makes it hard to optimize the network. In this work, we introduce a fully hyperbolic graph convolutional network (GCN), referred to as SRBGCN, which performs neural computations such as feature transformation and aggregation directly on the manifold, using manifold-preserving Lorentz transformations that include spatial rotation (SR) and boost (B) operations. Experiments conducted on static graph datasets for node classification and link prediction tasks validate the performance of the proposed method.

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