Lyapunov Stable Graph Neural Flow
This addresses the critical challenge of robust representation learning in GNNs for applications like network security and social analysis, offering a novel theoretical approach that is incremental but orthogonal to prior methods.
The paper tackles the vulnerability of Graph Neural Networks (GNNs) to adversarial perturbations by introducing a defense framework based on Lyapunov stability from control theory, which constrains feature-update dynamics and integrates with existing defenses to achieve cumulative robustness, outperforming state-of-the-art baselines in experiments.
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.