Normalization plays an important role in the optimization of deep neural networks. While there are standard normalization methods in computer vision and natural language processing, there is limited understanding of how to effectively normalize neural networks for graph representation learning. In this paper, we propose a principled normalization method, Graph Normalization (GraphNorm), where the key idea is to normalize the feature values across all nodes for each individual graph with a learnable shift. Theoretically, we show that GraphNorm serves as a preconditioner that smooths the distribution of the graph aggregation's spectrum, leading to faster optimization. Such an improvement cannot be well obtained if we use currently popular normalization methods, such as BatchNorm, which normalizes the nodes in a batch rather than in individual graphs, due to heavy batch noises. Moreover, we show that for some highly regular graphs, the mean of the feature values contains graph structural information, and directly subtracting the mean may lead to an expressiveness degradation. The learnable shift in GraphNorm enables the model to learn to avoid such degradation for those cases. Empirically, Graph neural networks (GNNs) with GraphNorm converge much faster compared to GNNs with other normalization methods, e.g., BatchNorm. GraphNorm also improves generalization of GNNs, achieving better performance on graph classification benchmarks.

本文研究了对图神经网络进行归一化的有效方法，将 InstanceNorm 与 BatchNorm 和 LayerNorm 进行比较，证明了 InstanceNorm 对 GNNs 的预处理效果最好。同时，我们也发现 InstanceNorm 的偏移操作可能会导致 GNNs 的表现能力下降，因此引入了可学习的 GraphNorm 对表现力下降的问题进行纠正，实验证明使用 GraphNorm 推出的 GNN 准确率得到了显著提升。

GraphNorm：加速图神经网络训练的原则性方法