Lyapunov Stable Graph Neural Flow

2026-03-12

AI Summary

Graph neural networks are vulnerable to adversarial perturbations in both graph topology and node features, exhibiting insufficient robustness. To address this limitation, this work proposes a graph neural flow framework grounded in control theory, incorporating integer- and fractional-order Lyapunov stability constraints. By introducing a learnable adaptive Lyapunov function together with a novel projection mechanism, the method maps network dynamics into a provably stable region of the state space, thereby achieving theoretically guaranteed robustness. The proposed approach is orthogonally compatible with existing defense strategies and demonstrates significant performance gains over both baseline models and current state-of-the-art methods across multiple benchmark datasets and diverse attack scenarios.

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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Graph Neural Networks (GNNs) are highly vulnerable to adversarial perturbations in both topology and features, making the learning of robust representations a critical challenge. In this work, we bridge GNNs with control theory to introduce a novel defense framework grounded in integer- and fractional-order Lyapunov stability. Unlike conventional strategies that rely on resource-heavy adversarial training or data purification, our approach fundamentally constrains the underlying feature-update dynamics of the GNN. We propose an adaptive, learnable Lyapunov function paired with a novel projection mechanism that maps the network's state into a stable space, thereby offering theoretically provable stability guarantees. Notably, this mechanism is orthogonal to existing defenses, allowing for seamless integration with techniques like adversarial training to achieve cumulative robustness. Extensive experiments demonstrate that our Lyapunov-stable graph neural flows substantially outperform base neural flows and state-of-the-art baselines across standard benchmarks and various adversarial attack scenarios.

Problem

• Graph Neural Networks
• adversarial perturbations
• robust representations
• Lyapunov stability

Innovation

• Lyapunov stability
• Graph Neural Networks
• adversarial robustness
• neural flows
• control theory