论文标题
图形神经网络和图神经网络的可传递性
Graphon Neural Networks and the Transferability of Graph Neural Networks
论文作者
论文摘要
图形神经网络（GNNS）依靠图卷积来从网络数据中提取本地特征。这些图卷积使用在所有节点上共享的系数组合来自相邻节点的信息。由于这些系数是共享的，并且不依赖于图形，因此可以使用相同的系数设想在另一个图上定义GNN。这激发了分析GNN跨图的可传递性。在本文中，我们将Graphon nns作为GNN的极限对象介绍，并证明了GNN输出与其极限Graphon-NN之间的差异。如果图形卷积过滤器在图形光谱域中有限制，则这种结合会随着越来越多的节点而消失。该结果在GNN的可区分性和可转移性之间建立了权衡。
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound vanishes with growing number of nodes if the graph convolutional filters are bandlimited in the graph spectral domain. This result establishes a tradeoff between discriminability and transferability of GNNs.
