Broad graph convolutional network: a novel graph convolutional network paradigm without hidden layer

Abstract

Abstract Graph convolutional networks (GCNs) have shown promising performance in real-world applications involving graph-structured data. To enhance the model’s ability to integrate information from neighbor nodes, GCNs typically expand the receptive field by stacking more layers, which can lead to the problem of over-smoothing. To address this limitation, high-order graph convolutional networks (HGCNs) such as Mixhop have been proposed. These high-order models, however, introduce the risk of overfitting due to the increased number of parameters required for designing different order convolutions, which in turn can degrade classification performance. To overcome these issues, we first provide a theoretical analysis of the bottlenecks in conventional GCNs and establish that an effective graph convolutional model should integrate multi-hop neighborhood information in a unified manner. Inspired by this, we propose a novel broad graph convolutional network (BGCN) paradigm, which completely eliminates hidden layers and instead expands the receptive field through network width. We introduce four specific BGCN architectures and provide a detailed analysis of their computational complexity and parameter efficiency. A number of experiments on citation networks demonstrate that the proposed methods achieve state-of-the-art performance in terms of both classification accuracy and stability. In particular, our BGCN with simple attention mechanism ( $$\text {BGCN}_{\text {SA}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>BGCN</mml:mtext> <mml:mtext>SA</mml:mtext> </mml:msub> </mml:math> ) achieves top performance on the Citeseer, Cora, and Pubmed datasets, with accuracies of 73.3%, 83.5%, and 81.1%, respectively. The main advantage of this work lies in offering a robust, efficient, and scalable alternative for graph representation learning, effectively circumventing the inherent limitations of over-smoothing and overfitting in existing deep and high-order GCN models.