Dissecting vulnerability in information fusion process of Graph Convolutional Networks

Graph Convolutional Networks (GCNs) have demonstrated remarkable success in various graph-based tasks. However, their performance can be severely compromised by perturbations or adversarial attacks on graph structures, and research into understanding the vulnerability of GCNs remains in its infancy. To demystify this issue, this paper reexamines GCNs from a novel perspective, revealing that the recursive neighborhood fusion process in the core mechanism of GCNs is intrinsically linked to graph Laplacian regularization. Through this lens, we identify that the neighborhood fusion process in GCNs suffers from insufficient exploration of the feature space and is driven by an ℓ₂-norm-based graph regularizer, which significantly amplifies their vulnerability to anomalous edges. This insight motivates us to design a more robust objective by introducing a feature fitting term and an ℓ_2,p-norm-based graph regularizer, thereby leading to a GCN with a stabilized fusion process. Consequently, we propose a Stable Fusion-based Graph Convolutional Network (SFGCN) and its enhanced variant SFGCN⁺, which implement a stable neighborhood fusion mechanism that dynamically adjusts edge weights based on their suspiciousness. Extensive experiments under both benign and adversarial settings demonstrate that SFGCN and SFGCN⁺ outperform state-of-the-art methods.