ResNorm: Tackling Long-tailed Degree Distribution Issue in Graph Neural Networks via Normalization

• URL: http://arxiv.org/abs/2206.08181v2
• Date: Mon, 4 Sep 2023 10:11:12 GMT
• Title: ResNorm: Tackling Long-tailed Degree Distribution Issue in Graph Neural Networks via Normalization
• Authors: Langzhang Liang, Zenglin Xu, Zixing Song, Irwin King, Yuan Qi, Jieping Ye
• Abstract summary: This paper focuses on improving the performance of GNNs via normalization. By studying the long-tailed distribution of node degrees in the graph, we propose a novel normalization method for GNNs. The $scale$ operation of ResNorm reshapes the node-wise standard deviation (NStd) distribution so as to improve the accuracy of tail nodes.
• Score: 80.90206641975375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Neural Networks (GNNs) have attracted much attention due to their ability in learning representations from graph-structured data. Despite the successful applications of GNNs in many domains, the optimization of GNNs is less well studied, and the performance on node classification heavily suffers from the long-tailed node degree distribution. This paper focuses on improving the performance of GNNs via normalization. In detail, by studying the long-tailed distribution of node degrees in the graph, we propose a novel normalization method for GNNs, which is termed ResNorm (\textbf{Res}haping the long-tailed distribution into a normal-like distribution via \textbf{norm}alization). The $scale$ operation of ResNorm reshapes the node-wise standard deviation (NStd) distribution so as to improve the accuracy of tail nodes (\textit{i}.\textit{e}., low-degree nodes). We provide a theoretical interpretation and empirical evidence for understanding the mechanism of the above $scale$. In addition to the long-tailed distribution issue, over-smoothing is also a fundamental issue plaguing the community. To this end, we analyze the behavior of the standard shift and prove that the standard shift serves as a preconditioner on the weight matrix, increasing the risk of over-smoothing. With the over-smoothing issue in mind, we design a $shift$ operation for ResNorm that simulates the degree-specific parameter strategy in a low-cost manner. Extensive experiments have validated the effectiveness of ResNorm on several node classification benchmark datasets.

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