Graph neural networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters. Otherwise, GNNs operate as CNNs. Filters are composed of pointwise nonlinearities and stacked in layers. It is shown that GNN architectures exhibit equivariance to permutation and stability to graph deformations. These properties help explain the good performance of GNNs that can be observed empirically. It is also shown that if graphs converge to a limit object, a graphon, GNNs converge to a corresponding limit object, a graphon neural network. This convergence justifies the transferability of GNNs across networks with different numbers of nodes. Concepts are illustrated by the application of GNNs to recommendation systems, decentralized collaborative control, and wireless communication networks.

中文翻译：

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图神经网络：体系结构，稳定性和可转移性

图神经网络（GNN）是图上支持的信号的信息处理体系结构。它们在这里作为卷积神经网络（CNN）的概括表示，其中各个层包含图卷积滤波器组，而不是经典卷积滤波器组。否则，GNN充当CNN。滤波器由逐点非线性组成，并逐层堆叠。结果表明，GNN体系结构对置换具有等方差，对图形变形也具有稳定性。这些特性有助于解释可以凭经验观察到的GNN的良好性能。还表明，如果图收敛到一个极限对象，一个石墨烯，则GNN收敛到一个对应的极限对象，一个石墨烯神经网络。这种融合证明了GNN在具有不同数量节点的网络之间的可传输性。通过将GNN应用于推荐系统，分散式协作控制和无线通信网络来说明概念。