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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.

Measuring and Relieving the Over-Smoothing Problem for Graph Neural Networks from the Topological View