提出新指标筛选图卷积最优算子，无需试错即可提升模型泛化能力。
Which Graph Shift Operator? A Spectral Answer to an Empirical Question
- 设计几何对齐度量，量化信号与标签空间的结构匹配度。
- 理论证明对齐度越高，模型泛化误差越低，具可证明性。
- 计算高效，训练前就能选出最优图移位算子，适合科研与工程部署。
图神经网络（GNN）在图结构数据学习中占据主导地位，通常分为空间和谱方法。核心是图移位算子（GSO），即用矩阵表示图结构以滤波节点信号。然而，选择最优的固定或可学习 GSO 仍依赖经验。本文提出一种新的对齐增益度量，用于量化输入信号与标签子空间之间的几何失真。关键的是，我们的理论分析表明该对齐度直接关联到泛化界，通过谱代理估计利普希茨常数。这给出了一个原理性强、计算高效的 GSO 选择标准，可在训练前针对任何预测任务进行排序与选取，无需繁琐搜索。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) have established themselves as the leading models for learning on graph-structured data, generally categorized into spatial and spectral approaches. Central to these architectures is the Graph Shift Operator (GSO), a matrix representation of the graph structure used to filter node signals. However, selecting the optimal GSO, whether fixed or learnable, remains largely empirical. In this paper, we introduce a novel alignment gain metric that quantifies the geometric distortion between the input signal and label subspaces. Crucially, our theoretical analysis connects this alignment directly to generalization bounds via a spectral proxy for the Lipschitz constant. This yields a principled, computation-efficient criterion to rank and select the optimal GSO for any prediction task prior to training, eliminating the need for extensive search.
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