Graph Neural Networks (GNNs) have gained significant popularity for learning representations of graph-structured data due to their expressive power and scalability. However, despite their success in domains such as social network analysis, recommendation systems, and bioinformatics, GNNs often face challenges related to stability, generalization, and robustness to noise and adversarial attacks. Regularization techniques have shown promise in addressing these challenges by controlling model complexity and improving robustness. Building on recent advancements in contractive GNN architectures, this paper presents a novel method for inducing contractive behavior in any GNN through SVD regularization. By deriving a sufficient condition for contractiveness in the update step and applying constraints on network parameters, we demonstrate the impact of SVD regularization on the Lipschitz constant of GNNs. Our findings highlight the role of SVD regularization in enhancing the stability and generalization of GNNs, contributing to the development of more robust graph-based learning algorithms dynamics.

翻译：图神经网络（GNNs）凭借其强大的表达能力和可扩展性，在图表征学习领域获得了广泛关注。尽管在社交网络分析、推荐系统和生物信息学等领域取得了成功，GNNs仍常面临稳定性不足、泛化能力有限以及对噪声和对抗攻击鲁棒性较弱等挑战。正则化技术通过控制模型复杂度与提升鲁棒性，为应对这些挑战提供了可行路径。基于近期收缩式GNN架构的研究进展，本文提出一种通过奇异值分解（SVD）正则化诱导任意GNN产生收缩行为的新方法。通过推导网络更新步骤中收缩性的充分条件，并对网络参数施加约束，我们论证了SVD正则化对GNN利普希茨常数的调控作用。研究结果揭示了SVD正则化在增强GNN稳定性与泛化能力方面的关键机制，为发展更鲁棒的图学习算法动态提供了理论支撑。