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When Do Graph Foundation Models Transfer? A Data-Centric Theory

arXiv 2605.29828 ↗First posted 28 May 2026cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 21 of its 28 references that are in the map. First posted on arXiv 28 May 2026.

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21 of 28 references.

References · 21

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9 more
  1. 2019Gromov-Wasserstein Learning for Graph Matching and Node Embeddingcited by 126
  2. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 118
  3. 2024Position: Graph Foundation Models are Already Herecited by 86
  4. 2024GFT: Graph Foundation Model with Transferable Tree Vocabularycited by 85
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  7. 2024AnyGraph: Graph Foundation Model in the Wildcited by 53
  8. 2023On the Stability of Expressive Positional Encodings for Graphscited by 33
  9. 2024Generalization Bounds for Message Passing Networks on Mixture of Graphonscited by 17

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