Graphon Neural Networks and the Transferability of Graph Neural Networks
Graphon Neural Networks and the Transferability of Graph Neural Networks
复制标题
DOI：
--
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Luana Ruiz;Luiz F. O. Chamon;Alejandro Ribeiro
中科院分区：
文献类型：
--
作者：
Luana Ruiz;Luiz F. O. Chamon;Alejandro Ribeiro
图神经网络（gnn）依靠图卷积从网络数据中提取局部特征。这些图卷积使用所有节点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，不依赖于图，因此可以设想使用相同的系数在另一个图上定义GNN。这促使我们分析gnn在图间的可转移性。本文引入graphon nn作为GNN的极限对象，并证明了GNN的输出与其极限graphon nn之差的一个界。如果图卷积滤波器在图谱域中是带宽限制的，那么这个边界会随着节点数量的增加而消失。这一结果建立了gnn的可辨别性和可转移性之间的权衡。
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.