What Does the Gradient Tell When Attacking the Graph Structure

TL;DR

This paper investigates how gradient-based attacks on GNNs tend to increase inter-class edges, introduces a novel surrogate model with multi-level propagation to preserve node dissimilarity, and proposes an attack loss balancing effectiveness and imperceptibility.

Contribution

The paper provides a theoretical explanation for attack patterns on GNNs, proposes a new surrogate model with multi-level propagation, and introduces an attack loss that balances effectiveness and imperceptibility.

Findings

Gradient-based attackers tend to add inter-class edges.

The proposed surrogate model improves dissimilarity preservation.

The new attack loss enhances imperceptibility with acceptable effectiveness.

Abstract

Recent research has revealed that Graph Neural Networks (GNNs) are susceptible to adversarial attacks targeting the graph structure. A malicious attacker can manipulate a limited number of edges, given the training labels, to impair the victim model's performance. Previous empirical studies indicate that gradient-based attackers tend to add edges rather than remove them. In this paper, we present a theoretical demonstration revealing that attackers tend to increase inter-class edges due to the message passing mechanism of GNNs, which explains some previous empirical observations. By connecting dissimilar nodes, attackers can more effectively corrupt node features, making such attacks more advantageous. However, we demonstrate that the inherent smoothness of GNN's message passing tends to blur node dissimilarity in the feature space, leading to the loss of crucial information during the forward process. To address this issue, we propose a novel surrogate model with multi-level propagation that preserves the node dissimilarity information. This model parallelizes the propagation of unaggregated raw features and multi-hop aggregated features, while introducing batch normalization to enhance the dissimilarity in node representations and counteract the smoothness resulting from topological aggregation. Our experiments show significant improvement with our approach.Furthermore, both theoretical and experimental evidence suggest that adding inter-class edges constitutes an easily observable attack pattern. We propose an innovative attack loss that balances attack effectiveness and imperceptibility, sacrificing some attack effectiveness to attain greater imperceptibility. We also provide experiments to validate the compromise performance achieved through this attack loss.