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）已成为处理各类图任务的核心组件。尽管取得了显著成功，GNNs仍易受对抗性攻击形式的输入扰动影响。本文通过收缩动态系统的视角，提出了一种增强GNNs对抗扰动鲁棒性的创新方法。该方法基于具有收缩性质的微分方程构建图神经层，理论分析表明这些层能提升GNNs的鲁棒性。所提方法的独特之处在于同时学习节点特征与邻接矩阵的演化，从而在固有层面增强模型对输入特征和图连通性扰动的鲁棒性。我们数学推导了新架构的理论基础，并提供理论洞见以阐释其预期行为。通过多项真实世界基准测试，我们验证了该方法的有效性，其性能与现有方法相当或更优。