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.

翻译：图神经网络（GNNs）已成为解决各类图任务的关键组成部分。尽管取得了显著成功，GNNs 仍易受到对抗攻击形式的输入扰动影响。本文提出一种创新方法，通过收缩动力系统的视角来增强 GNNs 对抗对抗扰动的能力。我们的方法引入了基于具有收缩性质的微分方程的图神经层，并证明其能提升 GNNs 的鲁棒性。所提方法的一个显著特点是同时学习节点特征与邻接矩阵的演化，从而从本质上增强了模型对输入特征扰动和图结构连接扰动的鲁棒性。我们从数学上推导了这一新颖架构的理论基础，并提供了理论分析以阐释其预期行为。通过在多个真实世界基准测试上的实验，我们证明了该方法的有效性，其性能达到或超越了现有方法。