Graph Neural Networks~(GNNs) have emerged as a powerful category of learning architecture for handling graph-structured data. However, existing GNNs typically ignore crucial structural characteristics in node-induced subgraphs, which thus limits their expressiveness for various downstream tasks. In this paper, we strive to strengthen the representative capabilities of GNNs by devising a dedicated plug-and-play normalization scheme, termed as~\emph{\textbf{SU}bgraph-s\textbf{PE}cific Facto\textbf{R} Embedded Normalization}~(SuperNorm), that explicitly considers the intra-connection information within each node-induced subgraph. To this end, we embed the subgraph-specific factor at the beginning and the end of the standard BatchNorm, as well as incorporate graph instance-specific statistics for improved distinguishable capabilities. In the meantime, we provide theoretical analysis to support that, with the elaborated SuperNorm, an arbitrary GNN is at least as powerful as the 1-WL test in distinguishing non-isomorphism graphs. Furthermore, the proposed SuperNorm scheme is also demonstrated to alleviate the over-smoothing phenomenon. Experimental results related to predictions of graph, node, and link properties on the eight popular datasets demonstrate the effectiveness of the proposed method. The code is available at \url{https://github.com/chenchkx/SuperNorm}.

翻译：图神经网络（GNNs）已成为处理图结构数据的一类强大学习架构。然而，现有GNN通常忽略节点诱导子图中的关键结构特征，从而限制了其在各类下游任务中的表达能力。本文旨在通过设计一种专用即插即用归一化方案来增强GNN的代表能力，该方案称为子图特定因子嵌入归一化（SuperNorm），显式考虑每个节点诱导子图内部的连接信息。为此，我们在标准批量归一化的起始和结束位置嵌入子图特定因子，并融入图实例特定统计量以提升区分能力。同时，我们提供理论分析证明：采用精心设计的SuperNorm，任意GNN在区分非同构图方面至少具有与1-WL测试同等的表达能力。此外，所提出的SuperNorm方案还可缓解过平滑现象。在八个流行数据集上关于图、节点和链接属性预测的实验结果验证了所提方法的有效性。代码可访问\url{https://github.com/chenchkx/SuperNorm}获取。