Learning Graph Foundation Models on Riemannian Graph-of-Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917479800897536 |
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| author | Liu, Haokun Ding, Zezhong Xie, Xike |
| author_facet | Liu, Haokun Ding, Zezhong Xie, Xike |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09993 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning Graph Foundation Models on Riemannian Graph-of-Graphs Liu, Haokun Ding, Zezhong Xie, Xike Machine Learning 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. |
| title | Learning Graph Foundation Models on Riemannian Graph-of-Graphs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.09993 |