Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibrium

TL;DR

The paper reframes graph adversarial resilience as a dynamic-system problem and hypothesizes that every graph regime harbors an asymptotically-stable equilibrium point ($ASEP$) representing a critical resilience state. It introduces a generalized framework linking linear and nonlinear perturbations to a condensed one-dimensional map via HMF, derives conditions for the existence and stability of ASEP (including Theorems 5–6), and uses Laplace-transform-based reasoning to justify resilience trajectories. The authors implement EquiliRes, an adjacency-matrix optimization approach guided by the ASEP trajectory, and show that resilience can be boosted by restructuring graph topology while achieving favorable rank and singular-value behavior with modest overhead. Across five real-world datasets and three representative GAAs, EquiliRes improves robustness compared to state-of-the-art defenses and can also serve as a booster for existing methods. This work provides a provable, lightweight route to intrinsic graph robustness by locating and steering toward a critical resilience state through topology design.

Abstract

Adversarial attacks to graph analytics are gaining increased attention. To date, two lines of countermeasures have been proposed to resist various graph adversarial attacks from the perspectives of either graph per se or graph neural networks. Nevertheless, a fundamental question lies in whether there exists an intrinsic adversarial resilience state within a graph regime and how to find out such a critical state if exists. This paper contributes to tackle the above research questions from three unique perspectives: i) we regard the process of adversarial learning on graph as a complex multi-object dynamic system, and model the behavior of adversarial attack; ii) we propose a generalized theoretical framework to show the existence of critical adversarial resilience state; and iii) we develop a condensed one-dimensional function to capture the dynamic variation of graph regime under perturbations, and pinpoint the critical state through solving the equilibrium point of dynamic system. Multi-facet experiments are conducted to show our proposed approach can significantly outperform the state-of-the-art defense methods under five commonly-used real-world datasets and three representative attacks.

Figures (12)

• Figure 1: Three balls' motion states and equilibrium points.
• Figure 2: Adversarial effect with Polblogs.
• Figure 3: Adversarial effect with Cora_ML.
• Figure 4: Adversarial effect with Cora.
• Figure 5: Adversarial effect with Citeseer.

Theorems & Definitions (12)

• Remark 2.1
• Definition 2.3
• Remark 2.4
• Remark 2.5
• Theorem 2.6
• Remark 3.1
• Theorem 3.2
• Theorem 3.3
• Remark 3.4
• Theorem A.1