TopFeaRe: Locating Critical State of Adversarial Resilience for Graphs Regarding Topology-Feature Entanglement

2026-04-15

AI Summary

This work addresses the limited understanding of how graph topology and node features jointly influence robustness under adversarial attacks in current graph neural network defenses. By modeling graph adversarial attack and defense as a complex dynamical system, the study introduces a two-dimensional topology-feature entangled perturbation function and leverages equilibrium point theory to identify critical resilience states of graphs under perturbation, enabling efficient defense. Evaluated on five real-world datasets, the proposed method significantly outperforms state-of-the-art approaches and effectively mitigates four representative graph adversarial attacks. Notably, it offers the first dynamical systems perspective on the robustness mechanisms underlying graph representation learning.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Graph adversarial attacks are usually produced from the two perspectives of topology/structure and node feature, both of them represent the paramount characteristics learned by today's deep learning models. Although some defense countermeasures are proposed at present, they fails to disclose the intrinsic reasons why these two aspects necessitate and how they are adequately fused to co-learn the graph representation. Towards this question, we in this paper propose an adversarial defense approach through locating the graph's critical state of adversarial resilience, resorting to the equilibrium-point theory in the discipline of complex dynamic system (CDS). In brief, our work has three novelties: i) Adversarial-Attack Modeling, i.e. map a graph regime into CDS, and use the oscillation of dynamic system to model the behavior of adversarial perturbation; ii) 2D Topology-Feature-Entangled Function Design for Perturbed Graph, i.e. project graph topology and node feature as two characteristic spaces, and define two-dimensional entangled perturbation functions to represent the dynamic variance under adversarial attacks; and iii) Location of Critical State of Adversarial Resilience, i.e. utilize the equilibrium-point theory to locate the graph's critical state of attack resilience resorting to the perturbation-reflected 2D function. Finally, multi-facet experiments on five commonly-used realistic datasets validate the effectiveness of our proposed approach, and the results show our approach can significantly outperform the state-of-the-art baselines under four representative graph adversarial attacks.

Problem

• graph adversarial attacks
• topology-feature entanglement
• adversarial resilience
• graph representation learning
• complex dynamic system

Innovation

• adversarial resilience
• topology-feature entanglement
• complex dynamic system
• equilibrium-point theory
• graph adversarial defense