When Do Graph Foundation Models Transfer? A Data-Centric Theory
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916060984246272 |
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| author | Zhu, Jiajun Chen, Ying Wang, Peihao He, Yixuan Li, Pan Akella, Aditya Wang, Zhangyang |
| author_facet | Zhu, Jiajun Chen, Ying Wang, Peihao He, Yixuan Li, Pan Akella, Aditya Wang, Zhangyang |
| contents | Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation choices, we ask a data-centric question: which properties of two graph domains determine how much a fixed representation model changes its outputs? Using a graphon-based continuous limit for dense graphs, we show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift into (i) graph-specific finite-sample approximation terms and (ii) an intrinsic, relabeling-invariant domain discrepancy capturing structural mismatch. A key ingredient is positional-encoding (PE) stability: we establish stability guarantees for spectral PEs and highlight contrasting behaviors of eigenvector- versus subspace-based PEs. Experiments on synthetic and real graphs validate the theory and translate the decomposition into guidance for data curation in GFM transfer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29828 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When Do Graph Foundation Models Transfer? A Data-Centric Theory Zhu, Jiajun Chen, Ying Wang, Peihao He, Yixuan Li, Pan Akella, Aditya Wang, Zhangyang Machine Learning Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation choices, we ask a data-centric question: which properties of two graph domains determine how much a fixed representation model changes its outputs? Using a graphon-based continuous limit for dense graphs, we show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift into (i) graph-specific finite-sample approximation terms and (ii) an intrinsic, relabeling-invariant domain discrepancy capturing structural mismatch. A key ingredient is positional-encoding (PE) stability: we establish stability guarantees for spectral PEs and highlight contrasting behaviors of eigenvector- versus subspace-based PEs. Experiments on synthetic and real graphs validate the theory and translate the decomposition into guidance for data curation in GFM transfer. |
| title | When Do Graph Foundation Models Transfer? A Data-Centric Theory |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.29828 |