Projections of Model Spaces for Latent Graph Inference
This work addresses graph structure learning for machine learning applications, but it is incremental as it builds on existing latent graph inference methods with minor theoretical improvements.
The paper tackles the problem of latent graph inference for Graph Neural Networks by using stereographic projections of hyperbolic and spherical model spaces, achieving comparable performance to non-projected methods while providing theoretical guarantees to avoid divergence when curvature tends to zero.
Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias. Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model. In this work we employ stereographic projections of the hyperbolic and spherical model spaces, as well as products of Riemannian manifolds, for the purpose of latent graph inference. Stereographically projected model spaces achieve comparable performance to their non-projected counterparts, while providing theoretical guarantees that avoid divergence of the spaces when the curvature tends to zero. We perform experiments on both homophilic and heterophilic graphs.