Designing spectral convolutional networks is a formidable task in graph learning. In traditional spectral graph neural networks (GNNs), polynomial-based methods are commonly used to design filters via the Laplacian matrix. In practical applications, however, these polynomial methods encounter inherent limitations, which primarily arise from the the low-order truncation of polynomial filters and the lack of overall modeling of the graph spectrum. This leads to poor performance of existing spectral approaches on real-world graph data, especially when the spectrum is highly concentrated or contains many numerically identical values, as they tend to apply the exact same modulation to signals with the same frequencies. To overcome these issues, in this paper, we propose Graph State Space Network (GrassNet), a novel graph neural network with theoretical support that provides a simple yet effective scheme for designing and learning arbitrary graph spectral filters. In particular, our GrassNet introduces structured state space models (SSMs) to model the correlations of graph signals at different frequencies and derives a unique rectification for each frequency in the graph spectrum. To the best of our knowledge, our work is the first to employ SSMs for the design of GNN spectral filters, and it theoretically offers greater expressive power compared with polynomial filters. Extensive experiments on nine public benchmarks reveal that GrassNet achieves superior performance in real-world graph modeling tasks.

本研究针对传统谱图神经网络在处理实际图数据时的不足，提出了一种新的图神经网络GrassNet，通过引入结构化状态空间模型来处理信号在不同频率下的相关性，具有更强的表达能力。实验结果表明，GrassNet在九个公开基准数据集上的表现优于现有谱图方滤波器。

GrassNet：状态空间模型与图神经网络的结合