Contractive Systems Improve Graph Neural Networks Against Adversarial
  Attacks
Moshe Eliasof Davide Murari Ferdia Sherry Carola-Bibiane Schönlieb
Graph Neural Networks (GNNs) have established themselves as a key component
in addressing diverse graph-based tasks. Despite their notable successes, GNNs
remain susceptible to input perturbations in the form of adversarial attacks.
This paper introduces an innovative approach to fortify GNNs against
adversarial perturbations through the lens of contractive dynamical systems.
Our method introduces graph neural layers based on differential equations with
contractive properties, which, as we show, improve the robustness of GNNs. A
distinctive feature of the proposed approach is the simultaneous learned
evolution of both the node features and the adjacency matrix, yielding an
intrinsic enhancement of model robustness to perturbations in the input
features and the connectivity of the graph. We mathematically derive the
underpinnings of our novel architecture and provide theoretical insights to
reason about its expected behavior. We demonstrate the efficacy of our method
through numerous real-world benchmarks, reading on par or improved performance
compared to existing methods.