Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

翻译：提出一种有效且灵活的图表示矩阵是从多角度（如图傅里叶变换中的滤波）探索的基础性挑战。本文构建了一个新颖且通用的框架，从参数化分解与滤波的角度统一了众多现有图神经网络模型，并展示了该框架如何增强GNN的灵活性，同时缓解现有模型中的平滑性与放大问题。本质上，我们证明了广泛研究的可学习多项式滤波器谱图卷积是此公式的受限变体，而解除这些约束可使模型同时表达所需的分解与滤波。基于这一通用框架，我们开发的模型实现简单，但在多种图学习任务上取得了显著性能提升和计算效率。代码见https://github.com/qslim/PDF。