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

Source-Free Graph Domain Adaptation (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 source-trained 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 (USBD), 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.