DeloopSGNN: Revisiting Spectral GNNs Through the Lens of Spatial Aggregation

Abstract Graph Neural Networks (GNNs) have been studied from two primary perspectives: spectral, which employs global graph signal filtering and is theoretically more expressive, and spatial, which builds on local neighborhood aggregation and generalizes well across diverse graph structures. While spectral GNNs are expected to perform better in theory, they often underperform in practice compared to spatial models. To better understand this gap, we introduce a novel theoretical framework for converting spectral GNNs into the spatial domain, allowing for more intuitive analysis. This transformation reveals that signal looping and repeated high-order aggregation are major causes of over-smoothing in spectral GNNs. By addressing these issues in the spatial domain and converting the model back to the spectral domain, we propose DeloopSGNN, a spectral GNN with improved expressive capacity. Experiments on benchmark datasets show that DeloopSGNN achieves consistently strong performance in terms of accuracy and adversarial robustness, demonstrating that spectral GNNs can benefit significantly from careful architectural design grounded in our proposed framework.