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SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter
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Proposes SLOG, an inductive spectral GNN with a real-valued-order graph filter (beyond polynomial) combined with subgraph sampling, plus non-linear (SLOG(N)) and locally adaptive (SLOG(L)) variants, evaluated on 16 node classification datasets.
Problem
Existing spectral GNNs are limited to integer-order polynomial filters and cannot be applied inductively to large-scale node-level tasks, since they require eigen-decomposition or precomputed operators on the full graph.
Approach
A filter with real-valued order, (I - 1/2 L)^p (I + (L - I)^2)^q with trainable p and q, applied on sampled K-hop subgraphs around each node so it works inductively; SLOG(L) interpolates global and per-partition local filter parameters to handle varying heterophily.
Key results
- SLOG(B) achieves the best accuracy on all 8 heterophilic datasets in the inductive setting, e.g., 0.581 on Chameleon vs 0.578 for best baseline BernNet.
- On Reddit (115M edges), SLOG(N) reaches 0.962 accuracy versus 0.957 for GATv2, and SLOG(B) reaches 0.723 on Ogbn-arxiv vs 0.717 for GraphSAGE.
- SLOG(B) and SLOG(N) achieve the best result on 11 of 13 small-scale datasets, though they are marginally below the best baseline on Cora (by 1.4%) and Coauthor-Physics (by 0.4%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SLOG(B) instead of the strongest listed baseline | Inductive node classification · Squirrel | accuracy: 0.387±0.011 -> 0.392±0.006 | Helped |
| Use SLOG(B) instead of the strongest listed baseline | Inductive node classification · Chameleon | accuracy: 0.578±0.007 -> 0.581±0.024 | Helped |
| Use SLOG(B) instead of the strongest listed baseline | Inductive node classification · Squirrel-filtered | accuracy: 0.366±0.021 -> 0.427±0.013 | Helped |
| Use SLOG(N) instead of the strongest listed baseline | Inductive node classification · Chameleon-filtered | accuracy: 0.411±0.031 -> 0.431±0.026 | Helped |
| Use SLOG(N) instead of the strongest listed baseline | Inductive node classification · Minesweeper | accuracy: 0.824±0.001 -> 0.844±0.008 | Helped |
| Use SLOG(N) instead of the strongest listed baseline | Inductive node classification · Tolokers | accuracy: 0.794±0.003 -> 0.810±0.006 | Helped |
| Use SLOG(N) instead of the strongest listed baseline | Inductive node classification · Amazon-ratings | accuracy: 0.436±0.005 -> 0.456±0.006 | Helped |
| Use SLOG(B) instead of MLP | Inductive node classification · Questions | accuracy: 0.972±0.000 -> 0.972±0.001 | No clear effect |
| Use SLOG(B) instead of GPRGNN | Inductive node classification · Cora | accuracy: 0.874±0.010 -> 0.865±0.011 | Hurt |
| Use SLOG(B) instead of H2GCN | Inductive node classification · Citeseer | accuracy: 0.757±0.010 -> 0.766±0.026 | Helped |
| Use SLOG(B) instead of BernNet | Inductive node classification · DBLP | accuracy: 0.849±0.004 -> 0.850±0.005 | No clear effect |
| Use SLOG(N) instead of GPRGNN | Inductive node classification · Coauthor-CS | accuracy: 0.942±0.001 -> 0.944±0.005 | No clear effect |
Surprising findings
- SLOG(N) with added non-linearity and residuals does not uniformly beat the simpler linear SLOG(B); e.g., it is much lower on Cora (0.761 vs 0.865).
Limitations
- Only evaluated on node classification; link prediction and other tasks left for future work.
- SLOG(L) gives no gain on datasets with low locality (e.g., Squirrel), and its added local parameters complicate the model.
Experimental setup
Datasets: Chameleon Squirrel Squirrel-filtered Chameleon-filtered Minesweeper Tolokers Amazon-ratings Questions Cora Citeseer DBLP Coauthor-CS
Benchmarks: Chameleon Squirrel Squirrel-filtered Chameleon-filtered Minesweeper Tolokers Amazon-ratings Questions Cora Citeseer DBLP Coauthor-CS
Metrics: accuracy standard deviation
Baselines: MLP GCN ChebNet GraphSAGE GAT APPNP SGC GATv2 GPRGNN H2GCN FAGCN BernNet
Builds on: TeDGCN BernNet SGC GraphSAGE METIS
Closest papers by meaning
- Position: Spectral GNNs Rely Less on Graph Fourier Basis than Conceived (ICML 2025 · similarity 0.91)
- Unifying Homophily and Heterophily for Spectral Graph Neural Networks via Triple Filter Ensembles (NeurIPS 2024 · similarity 0.91)
- Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective (ICLR 2025 · similarity 0.91)
- How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing (ICML 2024 · similarity 0.90)
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.90)
- Spectral Graph Neural Networks are Incomplete on Graphs with a Simple Spectrum (NeurIPS 2025 · similarity 0.90)
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