Enhancing Graph Classification Robustness with Singular Pooling

2025-10-26

AI Summary

Graph Neural Networks (GNNs) exhibit insufficient adversarial robustness in graph classification, and existing defenses predominantly target message passing while neglecting the critical vulnerability introduced by pooling operations. This work presents the first theoretical analysis of standard pooling mechanisms—sum, mean, and max—demonstrating their susceptibility to adversarial perturbations across diverse attack settings and graph structures, leading to distorted graph-level representations. To address this, we propose Robust Singular Pooling (RS-Pool), a model-agnostic pooling method that constructs graph-level representations from the dominant singular vectors of the node embedding matrix, efficiently computed via power iteration. Theoretical analysis establishes RS-Pool’s robustness guarantees under bounded perturbations. Extensive experiments show that RS-Pool significantly improves robustness against multiple state-of-the-art adversarial attacks while maintaining clean accuracy comparable to baselines on several real-world benchmark datasets. Moreover, RS-Pool is architecture-agnostic and seamlessly integrates with various GNN backbones.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Natural Language Processing: Safety and Robustness

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) have achieved strong performance across a range of graph representation learning tasks, yet their adversarial robustness in graph classification remains underexplored compared to node classification. While most existing defenses focus on the message-passing component, this work investigates the overlooked role of pooling operations in shaping robustness. We present a theoretical analysis of standard flat pooling methods (sum, average and max), deriving upper bounds on their adversarial risk and identifying their vulnerabilities under different attack scenarios and graph structures. Motivated by these insights, we propose extit{Robust Singular Pooling (RS-Pool)}, a novel pooling strategy that leverages the dominant singular vector of the node embedding matrix to construct a robust graph-level representation. We theoretically investigate the robustness of RS-Pool and interpret the resulting bound leading to improved understanding of our proposed pooling operator. While our analysis centers on Graph Convolutional Networks (GCNs), RS-Pool is model-agnostic and can be implemented efficiently via power iteration. Empirical results on real-world benchmarks show that RS-Pool provides better robustness than the considered pooling methods when subject to state-of-the-art adversarial attacks while maintaining competitive clean accuracy. Our code is publicly available at:href{https://github.com/king/rs-pool}{https://github.com/king/rs-pool}.

Problem

• Investigating pooling operations' role in graph classification robustness
• Analyzing vulnerabilities of standard pooling methods under adversarial attacks
• Proposing robust singular pooling to enhance adversarial defense capabilities

Innovation

• Proposes Robust Singular Pooling for robust graph representation
• Leverages dominant singular vector of node embedding matrix
• Model-agnostic pooling method with efficient power iteration implementation