In this paper, we aim to find the conditions for input-state stability (ISS) and incremental input-state stability ($\delta$ISS) of Gated Graph Neural Networks (GGNNs). We show that this recurrent version of Graph Neural Networks (GNNs) can be expressed as a dynamical distributed system and, as a consequence, can be analysed using model-based techniques to assess its stability and robustness properties. Then, the stability criteria found can be exploited as constraints during the training process to enforce the internal stability of the neural network. Two distributed control examples, flocking and multi-robot motion control, show that using these conditions increases the performance and robustness of the gated GNNs.

翻译：本文旨在寻找门控图神经网络（GGNNs）的输入-状态稳定性（ISS）与增量输入-状态稳定性（$\delta$ISS）条件。我们证明，图神经网络（GNNs）的这类循环版本可表示为动态分布式系统，进而可利用基于模型的技术分析其稳定性与鲁棒性。所获得的稳定性判据可作为训练过程中的约束条件，以强化神经网络的内部稳定性。通过两个分布式控制实例——集群控制与多机器人运动控制——表明，采用这些条件可提升门控GNN的性能与鲁棒性。