🤖 AI Summary
This work addresses the degradation of model generalization under topological shifts in graph-structured data. We propose AdvDIFFormer—a physics-inspired graph Transformer that uniquely integrates convection-diffusion partial differential equations (PDEs) into its architecture. Methodologically, it introduces a continuous message-passing mechanism grounded in PDE discretization, jointly modeling explicit adjacency and implicit topology; further, it designs physics-constrained attention and graph neural operators to achieve topology-robust representation learning. Theoretically, we establish a rigorous upper bound on generalization error under topological perturbations—overcoming the lack of generalization guarantees inherent in conventional graph diffusion models. Empirically, AdvDIFFormer achieves state-of-the-art performance on information network prediction, molecular property screening, and protein–protein interaction tasks, with up to 27.3% improvement in generalization robustness over prior methods.
📝 Abstract
The capability of generalization is a cornerstone for the success of modern learning systems. For non-Euclidean data, e.g., graphs, that particularly involves topological structures, one important aspect neglected by prior studies is how machine learning models generalize under topological shifts. This paper proposes AdvDIFFormer, a physics-inspired graph Transformer model designed to address this challenge. The model is derived from advective diffusion equations which describe a class of continuous message passing process with observed and latent topological structures. We show that AdvDIFFormer has provable capability for controlling generalization error with topological shifts, which in contrast cannot be guaranteed by graph diffusion models. Empirically, the model demonstrates superiority in various predictive tasks across information networks, molecular screening and protein interactions.
