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Rethinking Spectral Graph Neural Networks With Spatially Adaptive Filtering
IEEE Transactions on Neural Networks and Learning Systems
|March 17, 2026
Summary
Spectral graph neural networks (GNNs) are better understood through their spatial domain connections. This study reveals how spectral filtering adapts graphs for better spatial aggregation, improving nonlocal dependencies and graph heterophily.
Area of Science:
- Graph Neural Networks
- Machine Learning
- Network Science
Background:
- Spectral graph neural networks (GNNs) are theoretically grounded but lack spatial interpretability.
- Existing GNNs struggle with capturing long-range dependencies and graph heterophily due to polynomial approximations.
Purpose of the Study:
- Investigate the spatial-domain interpretability of spectral GNNs.
- Unveil the connection between spectral filtering and spatial aggregation.
- Propose a novel framework to address limitations in GNNs.
Main Methods:
- Analyzed the theoretical link between spectral filtering and spatial aggregation.
- Developed a spatially adaptive filtering (SAF) framework.
- Conducted extensive experiments on 13 node classification benchmarks.
Main Results:
- Spectral filtering implicitly creates an adapted graph for spatial aggregation.
- The adapted graph exhibits nonlocality and signed edge weights for label consistency.
- The SAF framework effectively models node similarity and dissimilarity globally.
Conclusions:
- Spectral GNNs have an interpretable spatial role beyond fixed-order polynomials.
- The SAF framework significantly improves GNN performance on node classification tasks.
- The findings offer new perspectives on designing spectral graph filters.
