Beyond Homophily: Spectrum-Based Graph Pre-Training and Cluster-Augmented Prompt Tuning

Abstract

Graph pre-training and prompt tuning provide an effective route to label-efficient node classification by learning transferable backbones and adapting them with lightweight prompts. However, existing pre-train-and-prompt pipelines often generalize poorly across graphs with diverse homophily due to two fundamental limitations: (i) spectral bias, where learned representations overemphasize a single frequency band, and (ii) prompt misalignment, where spatial-domain prompts cannot explicitly modulate critical spectral components and may even disrupt frequency-aware backbones. In this paper, we propose SCA-GPPT, a spectrum-aware framework that unifies Spectrum-based Graph Pre-training and Cluster-Augmented Prompt Tuning. First, we present a systematic spectral analysis of graph prompting, revealing the inherent limitations of spatial-domain prompts in capturing attenuated high-frequency signals. Second, we explicitly learn complementary low- and high-frequency spectral filters via parameterized Chebyshev polynomials and employ band-aware contrastive learning to model diverse spectral patterns during pre-training. For downstream adaptation, we freeze the pre-trained backbone and introduce cluster-augmented prompts that directly adapt Chebyshev coefficients while enforcing global structural consistency, enabling stable few-shot transfer across varying homophily regimes. Extensive experiments on real-world benchmarks demonstrate that SCA-GPPT consistently outperforms strong baselines under both transductive and inductive settings. Our code is available at https://anonymous.4open.science/r/SCA-GPPT-17B2.