Power up! Robust Graph Convolutional Network against Evasion Attacks based on Graph Powering.
Ming Jin, Heng Chang, Wenwu Zhu, Somayeh Sojoudi · arXiv (Cornell University) · 2019
Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be prone to topological attacks. Despite substantial efforts to search for new architectures, it still remains a challenge to improve performance in both benign and adversarial situations simultaneously. In this paper, we re-examine the fundamental building block of GCN---the Laplacian operator---and highlight some basic flaws in the spatial and domains. As an alternative, we propose an operator based on graph powering, and prove that it enjoys a desirable property of spectral separation. Based on the operator, we propose a robust learning paradigm, where the network is trained on a family of 'smoothed graphs that span a spatial and range for generalizability. We also use the new operator in replacement of the classical Laplacian to construct an architecture with improved robustness, expressivity and interpretability. The enhanced performance and robustness are demonstrated in extensive experiments.