揭示图模型迁移效果好坏的关键数据因素，提出可解释的迁移分析框架
When Do Graph Foundation Models Transfer? A Data-Centric Theory
- 基于图论极限建模，将跨域输出变化分解为采样误差与结构差异
- 发现位置编码稳定性是决定迁移性能的核心因素，谱编码有不同行为表现
- 理论指导真实图数据清洗，提升图基础模型迁移效率
图基础模型（GFMs）旨在跨多种图领域复用同一骨干网络，但其迁移效果常不均衡，甚至出现负迁移。现有工作多通过架构或适配策略改进，本文从数据角度出发：哪些图域属性决定了固定表示模型在跨域时输出的变化程度？基于稠密图的图论连续极限，我们证明：对于集合型与消息传递型标记化方式，任意满足Lipschitz条件的骨干网络，其跨域输出偏移可被显式分解为（i）图特异性有限样本近似项，和（ii）一个与重标号无关的内在域间差异项，反映结构不匹配。关键发现是位置编码（PE）的稳定性：我们建立了谱位置编码的稳定性保证，并揭示特征向量型与子空间型编码的对比行为。在合成与真实图上的实验验证了理论，且该分解可转化为数据整理的实际指导。
原文摘要 · Abstract (English)
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.
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