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Unifying Homophily and Heterophily for Spectral Graph Neural Networks via Triple Filter Ensembles
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Proposes TFE-GNN, a polynomial-based spectral GNN that ensembles base low-pass and high-pass graph filters with learnable coefficients to adaptively handle homophily and heterophily without polynomial computation or coefficient constraints.
Problem
Polynomial-based learnable spectral GNNs face a trade-off: better polynomial approximation and sophisticated graph learning or coefficient constraints improve benchmark accuracy but cause overfitting and poor generalization across graphs of varying homophily.
Approach
A triple filter ensemble: a learnable sum of base low-pass filter powers and a learnable sum of base high-pass filter powers are combined with two learnable scalars to form a graph convolution, avoiding polynomial recurrences and coefficient constraints. The authors argue theoretically it can match ChebNet's approximation ability and can be seen as a combination of two unfolded polynomial GNNs.
Key results
- On full-supervised node classification, TFE-GNN-sum reaches 96.96 on CS and 98.85 on Physics, and outperforms ChebNetII on Chameleon and Squirrel by 5.79% and 14.85% (absolute).
- Ablation shows removing the low-pass ensemble (TFE-GNN\TFE1) drops Citeseer accuracy to 61.00 while removing the high-pass ensemble drops Texas and Chameleon results, supporting the need for both filter types.
- On semi-supervised splits, TFE-GNN-sum reports 84.11 on Cora and 74.53 on Citeseer, and outperforms FavardGNN on Wisconsin, Texas and Cornell by 8.99%, 12.01% and 6.78%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the low-pass ensemble TFE1 (ablation) | TFE-GNNsum · Citeseer | accuracy: 61.00±1.19 -> 82.83±1.24 | Helped |
| add the low-pass ensemble TFE1 (ablation) | TFE-GNNsum · Cora-Full | accuracy: 64.09±0.41 -> 73.60±0.21 | Helped |
| add the low-pass ensemble TFE1 (ablation) | TFE-GNNsum · Squirrel | accuracy: 57.06±1.03 -> 72.27±1.32 | Helped |
| add the low-pass ensemble TFE1 (ablation) | TFE-GNNsum · Coauthor CS | accuracy: 96.96±0.17 -> 96.96±0.17 | No clear effect |
| add the high-pass ensemble TFE2 (ablation) | TFE-GNNsum · Chameleon | accuracy: 61.05±2.45 -> 77.16±1.41 | Helped |
| add the high-pass ensemble TFE2 (ablation) | TFE-GNNsum · Squirrel | accuracy: 41.91±0.69 -> 72.27±1.32 | Helped |
| add the high-pass ensemble TFE2 (ablation) | TFE-GNNsum · Wisconsin | accuracy: 81.62±8.40 -> 97.38±1.42 | Helped |
| add the high-pass ensemble TFE2 (ablation) | TFE-GNNsum · Texas | accuracy: 68.36±7.10 -> 94.87±2.66 | Helped |
| use the random-walk normalized Laplacian as the high-pass filter (ablation) | TFE-GNNsum · Cora | accuracy: 90.73±1.11 -> 89.57±1.26 | Hurt |
| use the random-walk normalized Laplacian as the high-pass filter (ablation) | TFE-GNNsum · Wisconsin | accuracy: 97.38±1.42 -> 96.00±1.34 | Hurt |
| use concatenation instead of summation for the third ensemble | TFE-GNN · Cora | accuracy: 90.73±1.11 vs 90.11±1.27 | No clear effect |
| use concatenation instead of summation for the third ensemble | TFE-GNN · Chameleon | accuracy: 77.16±1.41 vs 77.03±1.47 | No clear effect |
Surprising findings
- The ablation with the high-pass ensemble removed gives the same Citeseer result as the full model in some settings, attributed by the authors to the choice of hyperparameters K_lp and K_hp.
- Removing the low-pass ensemble (TFE-GNN\TFE1) causes a large accuracy drop on Citeseer (61.00 vs. 82.83), a larger effect than the high-pass ablation.
Limitations
- K_lp and K_hp are chosen by experience or by estimated homophily, which is unreliable when many nodes are unlabeled.
- The theoretical equivalence to ChebNet holds only under specific conditions (summation ensembles, specific base filters, matched orders).
- Hyperparameter selection and choice of base filters strongly affect performance; reported results depend on DGL/PyTorch versions.
Experimental setup
Datasets: Cora Citeseer Pubmed Cora-Full Coauthor CS Coauthor Physics Chameleon Squirrel Texas Cornell Wisconsin roman-empire
Benchmarks: Cora Citeseer Pubmed Cora-Full Coauthor CS Coauthor Physics Chameleon Squirrel Texas Cornell Wisconsin roman-empire
Metrics: mean accuracy standard deviation over random splits training and validation loss gap
Baselines: GCN ARMA APPNP ChebNet GPR-GNN BernNet ChebNetII Specformer EvenNet FavardGNN PCNet GCNII
Builds on: ChebNet ChebNetII PCNet BernNet GPR-GNN
Closest papers by meaning
- How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing (ICML 2024 · similarity 0.93)
- Position: Spectral GNNs Rely Less on Graph Fourier Basis than Conceived (ICML 2025 · similarity 0.91)
- SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter (ICML 2024 · similarity 0.91)
- HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations (NeurIPS 2025 · similarity 0.90)
- HoloNets: Spectral Convolutions do extend to Directed Graphs (ICLR 2024 · similarity 0.90)
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.89)
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