Graph neural networks (GNNs), a type of neural network that can learn from graph-structured data and learn the representation of nodes by aggregating their neighbors, have shown excellent performance in downstream tasks.However, it is known that the performance of graph neural networks (GNNs) degrades gradually as the number of layers increases. Based on k-hop subgraph aggregation, which is a new concept, we propose a new perspective to understand the expressive power of GNN.From this perspective, we reveal the potential causes of the performance degradation of the deep traditional GNN - aggregated subgraph overlap, and the fact that the residual-based graph neural networks in fact exploit the aggregation results of 1 to k hop subgraphs to improve the effectiveness.Further, we propose a new sampling-based node-level residual module named SDF, which is shown by theoretical derivation to obtain a superior expressive power compared to previous residual methods by using information from 1 to k hop subgraphs more flexibly. Extensive experiments show that the performance and efficiency of GNN with the SDF module outperform other methods.

翻译：图神经网络（GNNs）是一种能够从图结构数据中学习，并通过聚合邻居信息来学习节点表示的神经网络，在下游任务中表现出色。然而，已知图神经网络的性能会随着层数增加而逐渐退化。基于新概念k跳子图聚合，我们提出了一种理解GNN表达能力的新视角。从这一视角出发，我们揭示了深层传统GNN性能退化的潜在原因——聚合子图重叠，以及基于残差的图神经网络实际上利用了1到k跳子图的聚合结果来提升效果这一事实。进一步地，我们提出了一种新的基于采样的节点级残差模块SDF，理论推导表明，通过更灵活地利用1到k跳子图的信息，该模块相比以往的残差方法获得了更强的表达能力。大量实验表明，带有SDF模块的GNN在性能和效率上均优于其他方法。