Projections of Model Spaces for Latent Graph Inference

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. Differential geometry has been widely used in physics; for instance, it has laid the mathematical foundations of the theory of general relativity as well as the gauge theory of quantum fields (Isham, 1989). Moreover, recent work within the machine learning community has started leveraging ideas which stem from differential geometry and topology to improve the performance of learning algorithms (Hensel et al., 2021; Chamberlain et al., 2021; Barbero et al., 2022a;b).