Graph Convolutional Networks (GCNs), which use a message-passing paradigm with stacked convolution layers, are foundational methods for learning graph representations. Recent GCN models use various residual connection techniques to alleviate the model degradation problem such as over-smoothing and gradient vanishing. Existing residual connection techniques, however, fail to make extensive use of underlying graph structure as in the graph spectral domain, which is critical for obtaining satisfactory results on heterophilic graphs. In this paper, we introduce ClenshawGCN, a GNN model that employs the Clenshaw Summation Algorithm to enhance the expressiveness of the GCN model. ClenshawGCN equips the standard GCN model with two straightforward residual modules: the adaptive initial residual connection and the negative second-order residual connection. We show that by adding these two residual modules, ClenshawGCN implicitly simulates a polynomial filter under the Chebyshev basis, giving it at least as much expressive power as polynomial spectral GNNs. In addition, we conduct comprehensive experiments to demonstrate the superiority of our model over spatial and spectral GNN models.

本文介绍 ClenshawGCN 模型，采用 Clenshaw 求和算法增强 GCN 模型的表现力，通过两种残差模块来模拟多项式滤波器，从而提高了在异构图上的学习表现，实验结果表明，我们的模型优于空间和谱 GNN 模型。

Clenshaw图神经网络