让GCN自动学习合适平滑度的节点特征，提升分类效果。
Learning to Control the Smoothness of Graph Convolutional Network Features
- 通过几何分析设计可学习的模块，动态调节特征平滑度。
- 在多个数据集上显著提升GCN分类准确率，尤其在深层网络中优势明显。
- 适合需要优化特征表达的图神经网络研究者和实践者。
Oono and Suzuki（ICLR, 2020）以及Cai and Wang（arXiv:2006.13318）首次揭示了图卷积网络（GCN）特征平滑度与节点分类精度之间的复杂经验相关性。然而，最优的平滑/非平滑特征比例尚不明确，且使用ReLU或leaky ReLU激活函数的深层GCN中，非平滑特征会逐渐消失。本文提出一种新策略，使GCN能够自适应地学习具有目标平滑度的节点特征以增强分类性能。方法包含三步：（1）建立ReLU或leaky ReLU输入与输出间的几何关系；（2）基于此几何洞察，在图卷积层的消息传递过程中引入可学习项，高效调节特征平滑度；（3）研究采用增强消息传递方案的GCN所能达到的平滑与非平滑特征成分比。大量数值实验表明，该增强方案显著提升了GCN及相关模型的节点分类表现。
原文摘要 · Abstract (English)
The pioneering work of Oono and Suzuki [ICLR, 2020] and Cai and Wang [arXiv:2006.13318] initializes the analysis of the smoothness of graph convolutional network (GCN) features. Their results reveal an intricate empirical correlation between node classification accuracy and the ratio of smooth to non-smooth feature components. However, the optimal ratio that favors node classification is unknown, and the non-smooth features of deep GCN with ReLU or leaky ReLU activation function diminish. In this paper, we propose a new strategy to let GCN learn node features with a desired smoothness -- adapting to data and tasks -- to enhance node classification. Our approach has three key steps: (1) We establish a geometric relationship between the input and output of ReLU or leaky ReLU. (2) Building on our geometric insights, we augment the message-passing process of graph convolutional layers (GCLs) with a learnable term to modulate the smoothness of node features with computational efficiency. (3) We investigate the achievable ratio between smooth and non-smooth feature components for GCNs with the augmented message-passing scheme. Our extensive numerical results show that the augmented message-passing schemes significantly improve node classification for GCN and some related models.
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