Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems. We study the generalization error of MPNNs in graph classification and regression. We assume that graphs of different classes are sampled from different random graph models. We show that, when training a MPNN on a dataset sampled from such a distribution, the generalization gap increases in the complexity of the MPNN, and decreases, not only with respect to the number of training samples, but also with the average number of nodes in the graphs. This shows how a MPNN with high complexity can generalize from a small dataset of graphs, as long as the graphs are large. The generalization bound is derived from a uniform convergence result, that shows that any MPNN, applied on a graph, approximates the MPNN applied on the geometric model that the graph discretizes.
翻译:电文传递神经网络(MPNN)自被引入为图表结构化数据的进化神经网络(MPNN)以来,其受欢迎程度急剧上升,目前被视为解决大量图表重点问题的最先进的工具。我们研究了图解分类和回归中MPNNNs的通用错误。我们假设不同类别的图表是从不同的随机图表模型中抽样的。我们显示,在对MPNNN进行关于从这种分布中抽样的数据集的培训时,MPNN的复杂程度将增加,不仅在培训样本的数量方面,而且在图形中平均节点的数量方面,也减少了。这表明,只要图形是大,一个高度复杂的MPNNN如何从小的图表数据集中进行概括。一般化的界限来自一个统一的组合结果,即显示任何MPNNN在图表上应用的任何组合,都接近了在图形分解的几何模型上应用的MPNN。