Learning Graph Foundation Models on Riemannian Graph-of-Graphs

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov-Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.

Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference. However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabilities of GFMs. Specifically, the introduced Hyperbolic Knowledge Indexing module retains the tree-like hierarchies of the external knowledge base by modeling them within hyperbolic space. The Multi-granularity Retrieval module then provides GFMs with the global semantic anchors and local semantic nuances through coarse-grained and fine-grained knowledge retrieval, respectively. Finally, the Dual-path Fusion module achieves effective knowledge integration for graph tasks at both the feature and structural levels. Experiments on multiple graph benchmarks demonstrate significant improvements in the zero-shot setting, highlighting the generalization of our method for robust GFMs inference.

Graph foundation models (GFMs) aim to learn transferable representations across severely heterogeneous graph domains. However, severe domain shifts in topology, graph scale, and feature semantics impede the construction of a unified, domain-agnostic representation space. To address this, we propose SCGFM-ART, a structure-centric GFM framework that aligns arbitrary graphs onto a shared relational atlas via Amortized Relational Transport (ART). The relational atlas serves as a universal coordinate system defined by a finite set of relational landmarks (bases), while ART directly predicts reusable, end-to-end graph-to-base transport plans, bypassing costly runtime Gromov-Wasserstein optimizations. Under this formulation, SCGFM-ART decomposes a graph into a unified representation: globally via its relational response coordinates relative to the atlas, and locally via its node-to-role structural correspondences. These correspondences project disparate node attributes into a canonical role space, resolving structural and semantic heterogeneity within a singular alignment interface. Rigorously modeling graphs and atlas bases as finite measured relational spaces, we establish coordinate fidelity bounds, prove stability under predicted transport plans, and derive an amortized coverage bound that guarantees our learning objective tightly surrogates ideal relational coverage. Benchmarked across 14 cross-domain graph- and node-level classification tasks, SCGFM-ART achieves state-of-the-art transferability, securing superior average ranks of 2.29 and 1.14, respectively. Topological perturbation analyses demonstrate that node-role transport retains fine-grained structural nuances beyond global coordinates. On real-world benchmarks, the amortized formulation yields 44.2 to 85.1 times faster frozen target-domain inference by avoiding iterative alignment at test time.