RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry

Abstract: The foundation model has heralded a new era in artificial intelligence, pretraining a single model to offer cross-domain transferability on different datasets. Graph neural networks excel at learning graph data, the omnipresent non-Euclidean structure, but often lack the generalization capacity. Hence, graph foundation model is drawing increasing attention, and recent efforts have been made to leverage LLMs. On the one hand, existing studies primarily focus on text-attributed graphs, while a wider range of real graphs do not contain fruitful textual attributes. On the other hand, the sequential graph description tailored for the LLM neglects the structural complexity, which is a predominant characteristic of the graph. Such limitations motivate an important question: Can we go beyond LLMs, and pretrain a universal model to learn the structural knowledge for any graph? The answer in the language or vision domain is a shared vocabulary. We observe the fact that there also exist shared substructures underlying graph domain, and thereby open a new opportunity of graph foundation model with structural vocabulary. The key innovation is the discovery of a simple yet effective structural vocabulary of trees and cycles, and we explore its inherent connection to Riemannian geometry. Herein, we present a universal pretraining model, RiemannGFM. Concretely, we first construct a novel product bundle to incorporate the diverse geometries of the vocabulary. Then, on this constructed space, we stack Riemannian layers where the structural vocabulary, regardless of specific graph, is learned in Riemannian manifold offering cross-domain transferability. Extensive experiments show the effectiveness of RiemannGFM on a diversity of real graphs.