More Domains, No Gains? FLO: Fast–Slow Reciprocal Learning for Multi-Domain Graph Pre-training

Inspired by the great success of foundation models in the development of artificial general intelligence, Graph Foundation Models (GFMs) have recently attracted significant attention and have the potential to advance graph intelligence. Exhibiting such intelligence requires effectively learning knowledge from large-scale, multi-domain graph data during pre-training. Increasing domain diversity during pre-training is expected to yield richer and more generalizable knowledge. Most existing methods pursue this goal by designing domain alignment strategies that help a single graph model learn from multiple domains. However, we observe that existing methods struggle to benefit from increasing domain diversity. Through empirical and theoretical analysis, we reveal two key limitations. Firstly, pre-training in most GFMs is confined to a single message-passing paradigm. Since propagation flattens relations among neighboring nodes, the graph model can hardly perceive the knowledge beyond propagation, namely the attribute-predictable component of these relations. Secondly, domain alignment strategies often rely on randomly initialized parameters that are jointly updated with the graph model using immediate loss feedback, leaving early knowledge acquisition vulnerable to cross-domain interference. To address these issues, we propose FLO, a Fast–sLow reciprOcal approach for multi-domain graph pre-training. Specifically, a propagation-free attribute branch predicts the graph model’s relations without message passing and returns these predictions to refine the model. We further stabilize knowledge acquisition by pairing a fast process that adapts to the current domain with a slow process that integrates knowledge across domains. On 12 datasets, FLO benefits from increasing domain diversity and achieves the best average performance in cross-domain and cross-task transfer.