Towards Downstream Tuning-Free Graph Foundation Models with Manifold-based Structural Adaptation

Graph foundation models (GFMs) demonstrate strong potential in cross-domain graph learning by pre-training on multiple source domains and adapting to unseen target domains. Many existing GFMs are generally prompt-based and address graph domain gaps through downstream tuning of additional prompt embeddings, and therefore focus primarily on representation-level adaptation under a Euclidean geometric assumption. However, real-world graphs often share transferable structural patterns across domains, such as tree-like and cyclic substructures, that are naturally non-Euclidean and thus cannot be sufficiently exploited by existing Euclidean-based prompt-centric GFMs. To address this issue, this paper presents GFManifold, a graph structure-centric framework that adopts hyperbolic and spherical Riemannian manifold branches with learnable curvatures to learn manifold-induced structural relations across source domains for efficient parameter tuning-free GFM adaptation. During pre-training, GFManifold learns cross-domain graph structural patterns through domain alignment and geodesic link prediction across diverse source-domain graphs. During downstream adaptation, GFManifold exploits manifold-induced geodesic relations to adapt the target graph structure for downstream tasks, enabling efficient target-domain parameter tuning-free adaptation and avoiding downstream gradient-based parameter updates in most existing GFMs. Extensive experiments on 14 benchmarks showcase its effectiveness and efficiency on cross-domain graph adaptation tasks. Code is available upon acceptance.