Clenshaw Graph Neural Networks

TL;DR

ClenshawGCN introduces a novel spectral residual approach using the Clenshaw Summation Algorithm, significantly enhancing GCN expressiveness and performance on heterophilic graphs by simulating polynomial filters.

Contribution

The paper proposes ClenshawGCN, a spectral residual GNN model that leverages the Clenshaw Algorithm to improve expressiveness and effectiveness on complex graph structures.

Findings

ClenshawGCN outperforms existing GNN models on heterophilic graphs.

The model implicitly simulates polynomial spectral filters.

Experimental results demonstrate superior accuracy and robustness.

Abstract

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.