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接结构作为归纳偏置。潜在图推断侧重于学习合适的图结构以扩散信息并提升模型的下游性能。本文采用双曲模型空间与球面模型空间的立体投影，以及黎曼流形的乘积，用于潜在图推断。立体投影后的模型空间在性能上与非投影模型空间相当，同时提供了理论保障，避免了空间在曲率趋近于零时的发散问题。我们在同质性和异质性图上进行了实验。