Multi-spectral attention and graph smoothness enhancement for generalized node classification

Existing spectral Graph Neural Networks (GNNs) often rely on fixed polynomial bases or predefined propagation mechanisms, which limits their adaptability to real-world graphs with complex spectral properties and varying levels of homophily. To address this, we propose UniSpecAR, a Unified Spectral Adaptive Representation framework. UniSpecAR introduces a novel Krylov multi-basis filter that dynamically constructs and fuses information from diverse frequency subspaces. Specifically, it generates multiple Krylov bases and parallel diffusion channels, and then employs a channel-level attention mechanism for adaptive fusion of these complementary sources. Furthermore, a spatial-spectral gating mechanism dynamically balances the learned spectral features with local topological structures. To ensure the learned filter is both stable and structurally faithful, we introduce a novel spectral consistency regularizer. This term directly penalizes the filter's complexity and its deviation from the graph's fundamental local topology. Extensive experiments on multiple benchmarks demonstrate that UniSpecAR significantly outperforms state-of-the-art GNNs on both homophilic and heterophilic graphs. The results vali-date that our adaptive multi-basis design and fusion mechanisms lead to enhanced spectral expressiveness and provide valuable interpretability.