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Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective
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Shows that GNN outputs can flexibly recover frequency components absent from the input, so non-linear layers (not just the filter) shape spectral behavior, and introduces a spectral benchmark (Normalized AUAC on binned Laplacian eigenvectors) evaluating 14 GNNs on six citation/coauthor/Amazon datasets.
Problem
Whether the spectral behavior of GNNs is dominated by the neighborhood-aggregation filter, and how to measure and benchmark GNNs' ability to capture and output information across frequency components, given no existing metric or benchmark for this.
Approach
Use frequency-specific supervision (eigenvector-bin targets with zero-energy input bands) to show GNNs as a whole can produce target frequencies absent from input, then benchmark GNNs by binning Laplacian eigenvectors into spectral bins converted to node-classification labels and summarizing accuracy curves with a Normalized AUAC metric, supported by a Lipschitz/discretization analysis.
Key results
- GCN with only low-frequency input can output high-frequency components matching the target, showing GNN outputs are not dominated by the aggregation filter.
- On the spectral benchmark, SAGE ranks best on average (3.17), followed by GCNII and GATv2; middle-frequency bins are hardest for all models with V-shaped accuracy curves.
- Benchmark-derived rankings approximate the actual ranking on new heterophilous datasets better than random or original-task rankings in most cases (lower Kendall-Tau distance).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train GCN to predict high-frequency targets from low-frequency input features | GCN · Coauthor-CS | Output high-frequency energy alignment | Helped |
| Train GCN to predict low-frequency targets from high-frequency input features | GCN · Coauthor-CS | Output low-frequency energy alignment | Helped |
| Increase GNN depth from two to four layers (ablation) | GNNs in the spectral benchmark · Coauthor-CS and other evaluated datasets | Accuracy-curve spectral tendency | No clear effect |
| Increase hidden dimension from 64 to 128 (ablation) | GNNs in the spectral benchmark · Coauthor datasets | Frequency adaptation | No clear effect |
Surprising findings
- Standard GNNs like GCN can recover target frequency components absent from their input, challenging the view that aggregation filters determine spectral behavior.
- Spatial models such as SAGE rank highest on the spectral benchmark, while many spectral-filter models like FA and APPNP are weak in the middle frequency range.
Limitations
- Theoretical analysis bounds only the discretization deviation in energy distribution, and its constants are loosely justified.
- Benchmark uses fixed 2-layer, 64-dim, 500-epoch settings with only 3 runs and no early stopping.
- Frequency binning into node-classification labels is a constructed proxy target rather than natural task labels.
Experimental setup
Datasets: Cora DBLP Coauthor CS Coauthor Physics Amazon Computers Amazon Photo Airport-Brazil Wisconsin Cornell Squirrel Chameleon
Benchmarks: Cora DBLP CS Physics Computers Photo Airport-Brazil Wisconsin Cornell Squirrel Chameleon
Metrics: node classification accuracy Normalized AUAC Kendall's tau
Baselines: GCN GAT GATv2 SAGE GCNII APPNP ChebNet GIN SGC FA
Builds on: GCN GPRGNN ChebNet GCNII APPNP
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