Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibrium
Xinxin Fan, Wenxiong Chen, Mengfan Li, Wenqi Wei, Ling Liu
TL;DR
This paper investigates the existence of an intrinsic adversarial resilience state in graphs, modeling adversarial attacks as a dynamic system, and proposes a theoretical framework and method to identify this critical state, improving defense strategies.
Contribution
It introduces a novel dynamic equilibrium framework to identify the critical adversarial resilience state in graphs, advancing understanding and defense against adversarial attacks.
Findings
The proposed method outperforms existing defenses on multiple datasets.
Theoretical proof of the existence of a critical resilience state.
Effective identification of the equilibrium point under attack scenarios.
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…
Peer Reviews
Decision·Submitted to ICLR 2026
1. The paper introduces a complex multi-object dynamic system perspective to study adversarial robustness of graph neural networks. 2. The paper obtains an asymptotically stable equilibrium point.
1. The intrinsic adversarial-resilience state exists only under bounded, smooth perturbations and the paper’s modelling assumptions, which can be a significant limitation for general graph structures. 2. The use of the analogy in Fig. 1 is helpful to understand the motivation of the method. However, using the analogy to guide the method design somehow oversimplifies the problem space, e.g., the node/edge states in a graph may have the correlations or dependencies that cannot be captured by the
* The paper presents an interesting theoretical perspective that connects adversarial graph learning with complex dynamic systems. * The equilibrium-based framework offers a potentially generalizable and interpretable way to reason about adversarial robustness. * Experimental results indicate consistent performance gains across different attacks and datasets, suggesting the practical potential of the proposed approach.
* Insufficient baselines: The comparison is incomplete. Key recent robust GNN methods, such as RUNG [1], are missing from the evaluation. Including these would make the empirical validation more convincing. [1] Hou, Z., Feng, R., Derr, T., & Liu, X. (2023). Robust Graph Neural Networks via Unbiased Aggregation * Weak experimental completeness: The experiments are not comprehensive. For instance, in Table 2 (GOttack), only one baseline (GCN-SVD) is reported, which is far from sufficient for a f
1.The paper’s approach is highly original, combining concepts from dynamical systems and graph adversarial learning in a novel way. This cross-disciplinary perspective could potentially open up new research directions. 2.The paper tackles a bold, high-level idea with the potential to transform the way we think about graph adversarial defense. The theoretical framework, if fully validated, could offer a profound contribution.
1.The connection between the theoretical framework (Lyapunov stability and Laplace transforms) and the concrete implementation based on degree centrality is not adequately justified. This “leap of faith” leaves a critical gap in understanding why such a simplification is both valid and effective for adversarial defense in graphs. 2.The empirical comparison is insufficient, primarily involving older and simpler baselines like GCN and GCN-SVD. To demonstrate the true effectiveness of the method,
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Taxonomy
TopicsAdversarial Robustness in Machine Learning · Supply Chain Resilience and Risk Management · Terrorism, Counterterrorism, and Political Violence