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.

Graph neural network (GNN) models play a pivotal role in numerous tasks involving graph-related data analysis. Despite their efficacy, similar to other deep learning models, GNNs are susceptible to adversarial attacks. Even minor perturbations in graph data can induce substantial alterations in model predictions. While existing research has explored various adversarial defense techniques for GNNs, the challenge of defending against adversarial attacks on real-world scale graph data remains largely unresolved. On one hand, methods reliant on graph purification and preprocessing tend to excessively emphasize local graph information, leading to sub-optimal defensive outcomes. On the other hand, approaches rooted in graph structure learning entail significant time overheads, rendering them impractical for large-scale graphs. In this paper, we propose a new defense method named Talos, which enhances the global, rather than local, homophily of graphs as a defense. Experiments show that the proposed approach notably outperforms state-of-the-art defense approaches, while imposing little computational overhead.