Graph neural networks (GNNs) often struggle to learn discriminative node representations for heterophilic graphs, where connected nodes tend to have dissimilar labels and feature similarity provides weak structural cues. We propose frequency-guided graph structure learning (FgGSL), an end-to-end graph inference framework that jointly learns homophilic and heterophilic graph structures along with a spectral encoder. FgGSL employs a learnable, symmetric, feature-driven masking function to infer said complementary graphs, which are processed using pre-designed low- and high-pass graph filter banks. A label-based structural loss explicitly promotes the recovery of homophilic and heterophilic edges, enabling task-driven graph structure learning. We derive stability bounds for the structural loss and establish robustness guarantees for the filter banks under graph perturbations. Experiments on six heterophilic benchmarks demonstrate that FgGSL consistently outperforms state-of-the-art GNNs and graph rewiring methods, highlighting the benefits of combining frequency information with supervised topology inference.

翻译：图神经网络（GNNs）在处理异配图时，往往难以学习到具有区分度的节点表示，因为在这种图中相连的节点通常具有不同的标签，且特征相似性提供的结构线索较弱。我们提出了频率引导的图结构学习（FgGSL），一种端到端的图推断框架，能够联合学习同配与异配的图结构以及一个谱编码器。FgGSL采用一个可学习的、对称的、特征驱动的掩蔽函数来推断上述互补图，这些图通过预设计的低通与高通图滤波器组进行处理。一个基于标签的结构损失显式地促进同配边与异配边的恢复，从而实现任务驱动的图结构学习。我们推导了该结构损失的稳定性界，并建立了滤波器组在图扰动下的鲁棒性保证。在六个异配基准数据集上的实验表明，FgGSL在性能上持续优于最先进的GNNs和图重连方法，凸显了将频率信息与监督式拓扑推断相结合的优势。