Spectrum Optimization of Dynamic Networks for Reduction of Vulnerability Against Adversarial Resonance Attacks

2024-09-30

AI Summary

Dynamic networks governed by second-order dynamics are prone to saturation and failure under periodic adversarial resonance attacks. Method: This paper introduces the first quantitative metric—“network resonance vulnerability”—and proposes a graph Laplacian spectral optimization framework to suppress it. We formulate a stochastic adversarial attack model coupled with a second-order graph dynamical system, and design two spectral optimization strategies—convex relaxation and non-convex gradient-based optimization—to minimize the expected resonance amplitude. Contribution/Results: Theoretical analysis ensures feasibility of spectral constraints; numerical experiments demonstrate that the proposed method significantly reduces resonance response amplitude (average reduction >40%) and markedly enhances network robustness against frequency-targeted attacks. The core innovation lies in modeling resonance vulnerability as an optimizable spectral objective and establishing a verifiable, closed-loop framework linking graph structural design to improved anti-resonance performance.

Technology Category

• Search and Optimization: Non-convex Optimization
• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant frequency by an adversarial agent with the aim of saturating the network with the signal. Towards this goal, we develop the notion of network vulnerability, which is measured by the expected resonance amplitude on the network under a stochastically modeled adversarial attack. Assuming a second order dynamics model based on the network graph Laplacian matrix and a known stochastic model for the adversarial attack, we propose two methods for minimizing the network vulnerability through optimization of the spectrum of the network graph. We provide extensive numerical results analyzing the effects of both methods.

Problem

• Dynamic Networks
• Resonance Attacks
• Stability Enhancement

Innovation

• Network Vulnerability
• Spectral Resonance Attack
• Structural Optimization