Beyond Node Attention: Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing
This addresses a bottleneck in graph representation learning for tasks like classification, offering a novel method with proven theoretical and empirical gains, though it is domain-specific to graph data.
The paper tackles the problem of conventional Graph Neural Networks lacking fine-grained, feature-wise message passing by proposing MSH-GNN, which uses multi-scale harmonic projections to capture structural patterns, resulting in consistent outperformance of state-of-the-art models on graph and node classification tasks.
Conventional Graph Neural Networks (GNNs) aggregate neighbor embeddings as holistic vectors, lacking the ability to identify fine-grained, direction-specific feature relevance. We propose MSH-GNN (Multi-Scale Harmonic Graph Neural Network), a novel architecture that performs feature-wise adaptive message passing through node-specific harmonic projections. For each node, MSH-GNN dynamically projects neighbor features onto frequency-sensitive directions determined by the target node's own representation. These projections are further modulated using learnable sinusoidal encodings at multiple frequencies, enabling the model to capture both smooth and oscillatory structural patterns across scales. A frequency-aware attention pooling mechanism is introduced to emphasize spectrally and structurally salient nodes during readout. Theoretically, we prove that MSH-GNN approximates shift-invariant kernels and matches the expressive power of the 1-Weisfeiler-Lehman (1-WL) test. Empirically, MSH-GNN consistently outperforms state-of-the-art models on a wide range of graph and node classification tasks. Furthermore, in challenging classification settings involving joint variations in graph topology and spectral frequency, MSH-GNN excels at capturing structural asymmetries and high-frequency modulations, enabling more accurate graph discrimination.