USBD: Universal Structural Basis Distillation for Source-Free Graph Domain Adaptation

Abstract: SF-GDA is pivotal for privacy-preserving knowledge transfer across graph datasets. Although recent works incorporate structural information, they implicitly condition adaptation on the smoothness priors of sourcetrained GNNs, thereby limiting their generalization to structurally distinct targets. This dependency becomes a critical bottleneck under significant topological shifts, where the source model misinterprets distinct topological patterns unseen in the source domain as noise, rendering pseudo-label-based adaptation unreliable. To overcome this limitation, we propose the Universal Structural Basis Distillation, a framework that shifts the paradigm from adapting a biased model to learning a universal structural basis for SF-GDA. Instead of adapting a biased source model to a specific target, our core idea is to construct a structure-agnostic basis that proactively covers the full spectrum of potential topological patterns. Specifically, USBD employs a bi-level optimization framework to distill the source dataset into a compact structural basis. By enforcing the prototypes to span the full Dirichlet energy spectrum, the learned basis explicitly captures diverse topological motifs, ranging from low-frequency clusters to high-frequency chains, beyond those present in the source. This ensures that the learned basis creates a comprehensive structural covering capable of handling targets with disparate structures. For inference, we introduce a spectral-aware ensemble mechanism that dynamically activates the optimal prototype combination based on the spectral fingerprint of the target graph. Extensive experiments on benchmarks demonstrate that USBD significantly outperforms state-of-the-art methods, particularly in scenarios with severe structural shifts, while achieving superior computational efficiency by decoupling the adaptation cost from the target data scale.