When Do Graph Foundation Models Transfer? A Data-Centric Theory
Jiajun Zhu, Ying Chen, Peihao Wang, Yixuan He, Pan Li, Aditya Akella, Zhangyang “Atlas” Wang
Abstract
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.
BibTeX
@inproceedings{
zhu2026when,
title={When Do Graph Foundation Models Transfer? A Data-Centric Theory},
author={Jiajun Zhu and Ying Chen and Peihao Wang and Yixuan He and Pan Li and Aditya Akella and Zhangyang Wang},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=Dp0YWzPAGM}
}