When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learning

2024-09-21

arXiv.org

AI Summary

To address the insufficient robustness of Graph Neural Networks (GNNs) against adversarial perturbations, this paper proposes the Witness Graph Topology Layer (WGTL), the first method to incorporate witness complexes—drawn from computational topology—into adversarial graph learning for extracting shape features inherently resilient to structural perturbations. WGTL jointly models local and global topological structures and introduces an adaptive robust topological loss. We theoretically establish its topological stability under bounded adversarial budgets. Empirically, WGTL significantly enhances the robustness of five representative GNN architectures and three non-topological defense methods across six benchmark datasets, effectively mitigating diverse graph structure attacks—including edge addition/removal and node injection. Our results validate the efficacy and generality of persistent homology-based topological regularization for improving GNN adversarial robustness.

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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Capitalizing on the intuitive premise that shape characteristics are more robust to perturbations, we bridge adversarial graph learning with the emerging tools from computational topology, namely, persistent homology representations of graphs. We introduce the concept of witness complex to adversarial analysis on graphs, which allows us to focus only on the salient shape characteristics of graphs, yielded by the subset of the most essential nodes (i.e., landmarks), with minimal loss of topological information on the whole graph. The remaining nodes are then used as witnesses, governing which higher-order graph substructures are incorporated into the learning process. Armed with the witness mechanism, we design Witness Graph Topological Layer (WGTL), which systematically integrates both local and global topological graph feature representations, the impact of which is, in turn, automatically controlled by the robust regularized topological loss. Given the attacker's budget, we derive the important stability guarantees of both local and global topology encodings and the associated robust topological loss. We illustrate the versatility and efficiency of WGTL by its integration with five GNNs and three existing non-topological defense mechanisms. Our extensive experiments across six datasets demonstrate that WGTL boosts the robustness of GNNs across a range of perturbations and against a range of adversarial attacks. Our datasets and source codes are available at https://github.com/toggled/WGTL.

Problem

• Enhances robustness in adversarial graph learning
• Integrates topological features with graph neural networks
• Defends against various adversarial attacks effectively

Innovation

• Persistent homology for graph robustness
• Witness complex for adversarial analysis
• WGTL integrates local and global features