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.

翻译：图神经网络利用图的连通结构作为归纳偏置。潜在图推理专注于学习合适的图结构以传播信息并提升模型的下游性能。本文采用双曲与球面模型空间的球极投影，以及黎曼流形的直积，用于潜在图推理。球极投影后的模型空间在实现与非投影版本相当的性能的同时，提供了理论保证，避免了曲率趋近于零时空间发散的问题。我们在同质性与异质性图上进行了实验。