让图神经网络按频率选择性传递特征，提升结构分析能力
Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing
- 按节点特征子空间分解消息，实现特征级选择性传播
- 多尺度谐波调制捕捉平滑与振荡结构模式，性能优于主流方法
- 适合需联合分析图结构与频率特性的任务，如化学分子建模
多数图神经网络将节点嵌入视为整体特征向量，隐含假设各特征维度重要性一致，限制了对信息组件的选择性传递，尤其在图结构具有明显频率特性时。本文提出MSH-GNN（多尺度谐波图神经网络），一种频率感知的消息传递框架，实现特征级自适应传播。每个节点将其接收消息投影到由自身表示决定的特征子空间，从而选择性提取与频率相关的内容。可学习的多尺度谐波调制机制使模型能捕捉平滑与振荡的结构模式。引入频率感知注意力池化机制进行图级别读出。我们证明MSH-GNN可解释为核化消息函数的可学习傅里叶特征近似，并具备与1-魏斯费勒-莱曼（1-WL）测试相当的表达能力。在节点级与图级基准测试中，该模型持续优于现有最先进方法，尤其在联合结构-频率分析任务中表现突出。
原文摘要 · Abstract (English)
Most Graph Neural Networks (GNNs) propagate messages by treating node embeddings as holistic feature vectors, implicitly assuming uniform relevance across feature dimensions. This limits their ability to selectively transmit informative components, especially when graph structures exhibit distinct frequency characteristics. We propose MSH-GNN (Multi-Scale Harmonic Graph Neural Network), a frequency-aware message passing framework that performs feature-wise adaptive propagation. Each node projects incoming messages onto node-conditioned feature subspaces derived from its own representation, enabling selective extraction of frequency-relevant components. Learnable multi-scale harmonic modulations further allow the model to capture both smooth and oscillatory structural patterns. A frequency-aware attention pooling mechanism is introduced for graph-level readout. We show that MSH-GNN admits an interpretation as a learnable Fourier-feature approximation of kernelized message functions and matches the expressive power of the 1-Weisfeiler-Lehman (1-WL) test. Extensive experiments on node- and graph-level benchmarks demonstrate consistent improvements over state-of-the-art methods, particularly in joint structure-frequency analysis tasks.
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