Graph neural networks (GNNs), a type of neural network that can learn from graph-structured data and learn the representation of nodes through aggregating neighborhood information, have shown superior performance in various downstream tasks. However, it is known that the performance of GNNs degrades gradually as the number of layers increases. In this paper, we evaluate the expressive power of GNNs from the perspective of subgraph aggregation. We reveal the potential cause of performance degradation for traditional deep GNNs, i.e., aggregated subgraph overlap, and we theoretically illustrate the fact that previous residual-based GNNs exploit the aggregation results of 1 to $k$ hop subgraphs to improve the effectiveness. Further, we find that the utilization of different subgraphs by previous models is often inflexible. Based on this, we propose a sampling-based node-level residual module (SNR) that can achieve a more flexible utilization of different hops of subgraph aggregation by introducing node-level parameters sampled from a learnable distribution. Extensive experiments show that the performance of GNNs with our proposed SNR module outperform a comprehensive set of baselines.

翻译：图神经网络（GNNs）是一类能够从图结构数据中学习，并通过聚合邻域信息来学习节点表示的神经网络，已在各种下游任务中展现出优越性能。然而，众所周知，GNNs的性能随着层数增加而逐渐退化。在本文中，我们从子图聚合的角度评估了GNNs的表达能力。我们揭示了传统深度GNNs性能退化的潜在原因，即聚合子图重叠，并从理论上阐明，先前的基于残差的GNNs通过利用1到k跳子图的聚合结果来提升有效性。进一步地，我们发现先前模型对不同子图的利用往往缺乏灵活性。基于此，我们提出一种基于采样的节点级残差模块（SNR），通过引入从可学习分布中采样的节点级参数，实现对不同跳数子图聚合的更灵活利用。大量实验表明，搭载我们提出的SNR模块的GNNs性能全面超越了各类基线模型。