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Generalize across Homophily and Heterophily: Hybrid Spectral Graph Pre-Training and Prompt Tuning
Haitong Luo, Suhang Wang, Weiyao Zhang, Ruiqi Meng, Xuying Meng, Yujun Zhang
https://arxiv.org/abs/2508.11328

Generalize across Homophily and Heterophily: Hybrid Spectral Graph Pre-Training and Prompt Tuning
Graph ``pre-training and prompt-tuning'' aligns downstream tasks with pre-trained objectives to enable efficient knowledge transfer under limited supervision. However, existing methods rely on homophily-based low-frequency knowledge, failing to handle diverse spectral distributions in real-world graphs with varying homophily. Our theoretical analysis reveals a spectral specificity principle: optimal knowledge transfer requires alignment between pre-trained spectral filters and the intrinsic spe…