Graph Neural Networks (GNNs) have achieved promising performance on a wide range of graph-based tasks. Despite their success, one severe limitation of GNNs is the over-smoothing issue (indistinguishable representations of nodes in different classes). In this work, we present a systematic and quantitative study on the over-smoothing issue of GNNs. First, we introduce two quantitative metrics, MAD and MADGap, to measure the smoothness and over-smoothness of the graph nodes representations, respectively. Then, we verify that smoothing is the nature of GNNs and the critical factor leading to over-smoothness is the low information-to-noise ratio of the message received by the nodes, which is partially determined by the graph topology. Finally, we propose two methods to alleviate the over-smoothing issue from the topological view: (1) MADReg which adds a MADGap-based regularizer to the training objective;(2) AdaGraph which optimizes the graph topology based on the model predictions. Extensive experiments on 7 widely-used graph datasets with 10 typical GNN models show that the two proposed methods are effective for relieving the over-smoothing issue, thus improving the performance of various GNN models.

本文研究了图神经网络的过度平滑问题，并提出了两个定量度量指标MAD和MADGap。通过量化实验和分析，我们发现过度平滑是GNNs的基本性质，且由于节点接收到的噪声信息比例较高，是导致过度平滑的主要因素。最后我们提出了两种针对拓扑结构的方法：MADReg和AdaGraph，证明了这两种方法在7个广泛使用的图形数据集上都有效降低了过度平滑问题，并改善了各种GNN模型的性能。

从拓扑视角度量和缓解图神经网络的过度平滑问题