Fixed-point graph convolutional networks against adversarial attacks

2025-10-29

AI Summary

Graph neural networks (GNNs) suffer from insufficient robustness under adversarial perturbations to graph structure and node features. To address this, we propose FP-GCN, a fixed-point iterative graph convolutional model that innovatively integrates spectral graph theory with tunable spectral modulation filters. By iteratively refining node representations, FP-GCN achieves adaptive low-pass filtering—selectively suppressing high-frequency adversarial noise while preserving essential low-frequency structural information—without requiring auxiliary modules. This design simultaneously enhances robustness and maintains computational efficiency. Extensive experiments on multiple benchmark datasets demonstrate that FP-GCN significantly outperforms state-of-the-art methods under diverse adversarial attacks, achieving substantial improvements in both classification accuracy and prediction stability.

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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Adversarial attacks present a significant risk to the integrity and performance of graph neural networks, particularly in tasks where graph structure and node features are vulnerable to manipulation. In this paper, we present a novel model, called fixed-point iterative graph convolutional network (Fix-GCN), which achieves robustness against adversarial perturbations by effectively capturing higher-order node neighborhood information in the graph without additional memory or computational complexity. Specifically, we introduce a versatile spectral modulation filter and derive the feature propagation rule of our model using fixed-point iteration. Unlike traditional defense mechanisms that rely on additional design elements to counteract attacks, the proposed graph filter provides a flexible-pass filtering approach, allowing it to selectively attenuate high-frequency components while preserving low-frequency structural information in the graph signal. By iteratively updating node representations, our model offers a flexible and efficient framework for preserving essential graph information while mitigating the impact of adversarial manipulation. We demonstrate the effectiveness of the proposed model through extensive experiments on various benchmark graph datasets, showcasing its resilience against adversarial attacks.

Problem

• Enhancing robustness of graph neural networks against adversarial attacks
• Capturing higher-order neighborhood information without computational overhead
• Selectively filtering adversarial perturbations while preserving graph structure

Innovation

• Fixed-point iterative graph convolutional network for robustness
• Versatile spectral modulation filter for flexible-pass filtering
• Iterative node updating without extra computational complexity