Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines.

翻译：图神经网络（GNNs）近年来在各类图学习任务中展现出显著效果，尤其是基于消息传递机制的方法。然而，其性能常受限于有限的感受野，这一问题在稀疏图中尤为突出。鉴于幂级数具备无穷展开能力，我们提出一种新型图幂滤波器神经网络（GPFN），通过采用幂级数图滤波器扩展感受野来增强节点分类性能。具体而言，我们的GPFN基于收敛幂级数设计了一种构建具有无限感受野图滤波器的新方法，该方法可从频谱域和空间域进行分析。此外，我们从理论上证明了GPFN是一个通用框架，能够整合任意幂级数并捕获长程依赖关系。最后，在三个数据集上的实验结果表明，我们的GPFN相较于当前最优基线方法具有优越性。