Learning Graph Foundation Models on Riemannian Graph-of-Graphs

2026-05-11

AI Summary

This work addresses the limited receptive fields of existing graph foundation models, which rely on fixed-hop subgraph sampling and struggle to accommodate the diverse structural scales required by downstream tasks. To overcome this limitation, we propose Riemannian Graph-of-Graphs Foundation Model (R-GFM), which treats structural scale as a first-class modeling primitive. R-GFM constructs a hierarchical graph-of-graphs (GoG) architecture through multi-scale subgraphs and learns geometrically adaptive graph representations on a Riemannian manifold, thereby unifying multi-scale structural information within a single framework. Theoretical analysis demonstrates that our approach reduces structural domain generalization error. Extensive experiments show that R-GFM achieves state-of-the-art performance across multiple benchmark datasets, with relative improvements of up to 49% on downstream tasks.

Abstract

Graph foundation models (GFMs), pretrained on massive graph data, have transformed graph machine learning by supporting general-purpose reasoning across diverse graph tasks and domains. Existing GFMs pretrained with fixed-hop subgraph sampling impose a fixed receptive field, causing scale mismatch on diverse tasks, which often require heterogeneous and unknown structural contexts beyond a fixed sampling scale. We propose R-GFM, a Riemannian Graph-of-Graphs (GoG) based foundation model, that treats structural scale as a first-class citizen in modeling. R-GFM constructs a multi-scale GoG over-sampled subgraphs at different hop distances and learns geometry-adaptive representations from Riemannian manifolds. Theoretical analysis shows that R-GFM reduces structural domain generalization error compared to fixed-scale GFMs. Experiments on various datasets demonstrate that R-GFM achieves state-of-the-art performance, with up to a 49% relative improvement on downstream tasks. Our code is available at https://github.com/USTC-DataDarknessLab/R-GFM.

Problem

• graph foundation models
• scale mismatch
• structural context
• subgraph sampling
• receptive field

Innovation

• Riemannian manifold
• Graph-of-Graphs
• multi-scale representation
• graph foundation model
• structural scale