This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to noisy, incomplete, or perturbed graph signals, making them fragile in such conditions. Our newly proposed framelet convolution addresses these limitations by decomposing graph data into low-pass and high-pass spectra through a finely-tuned multiscale approach. Our approach directly designs filtering functions within the spectral domain, allowing for precise control over the spectral components. The proposed design excels in filtering out unwanted spectral information and significantly reduces the adverse effects of noisy graph signals. Our approach not only enhances the robustness of GNNs but also preserves crucial graph features and structures. Through extensive experiments on diverse, real-world graph datasets, we demonstrate that our framelet convolution achieves superior performance in node classification tasks. It exhibits remarkable resilience to noisy data and adversarial attacks, highlighting its potential as a robust solution for real-world graph applications. This advancement opens new avenues for more adaptive and reliable spectral GNN architectures.

翻译：本文旨在为谱图神经网络（GNNs）提供一种新颖的多尺度框架小波卷积设计。尽管当前的谱方法在各种图学习任务中表现出色，但它们通常缺乏适应噪声、不完整或受扰动的图信号的灵活性，使其在此类条件下表现脆弱。我们新提出的框架小波卷积通过精细调整的多尺度方法将图数据分解为低通和高通谱，从而解决了这些局限性。我们的方法直接在谱域内设计滤波函数，允许对谱分量进行精确控制。所提出的设计在滤除不需要的谱信息方面表现出色，并显著降低了噪声图信号的不利影响。我们的方法不仅增强了GNN的鲁棒性，还保留了关键的图特征和结构。通过对多样化的真实世界图数据集进行大量实验，我们证明了我们的框架小波卷积在节点分类任务中实现了卓越的性能。它对噪声数据和对抗性攻击表现出显著的韧性，突显了其作为现实世界图应用鲁棒解决方案的潜力。这一进展为更具适应性和可靠性的谱GNN架构开辟了新途径。