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HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations
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Proposes HeroFilter, an adaptive spectral GNN that learns polynomial filters to select spectrally relevant patch neighbors and mixes them with an MLP-Mixer, with a fast PageRank-style variant, reporting gains on 16 homophilic and heterophilic benchmarks.
Problem
Fixed low-pass or high-pass spectral filters are assumed to match homophily or heterophily levels monotonically, but the optimal frequency response of GNNs under varying heterophily is non-monotonic and graph-dependent.
Approach
Learn adaptive polynomial spectral filters that score node relevance to build top-p spectral patches per node, then mix patch and feature dimensions with an MLP-Mixer; a Fast variant replaces eigendecomposition with a truncated Neumann/PageRank-style diffusion for ranking.
Key results
- HeroFilter reaches 64.2% on Snap-Patents and 85.0% on Texas, best among compared methods in the heterophilic table.
- On Squirrel and Snap-Patents, HeroFilter improves over the next-best model by 9.0% and 9.2% respectively, per the paper's claim.
- On homophilic graphs HeroFilter reaches 70.5% on OGBN-Arxiv, the top score in its table.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HeroFilter instead of the strongest reported baseline | node classification · Snap-Patents | accuracy: 55.0 ± 0.2 -> 64.2 ± 0.1 | Helped |
| Use HeroFilter instead of the strongest reported baseline | node classification · Squirrel | accuracy: 41.5 ± 1.0 -> 47.7 ± 2.2 | Helped |
| Use HeroFilter instead of the strongest reported baseline | node classification · Cora | accuracy: 86.7 ± 1.0 -> 86.8 ± 1.5 | Mixed |
| Use adaptive polynomial patcher instead of a bandpass filter (ablation) | HeroFilter patcher · Cora | accuracy: 71.3 ± 0.8 -> 77.3 ± 0.6 | Helped |
| Use adaptive polynomial patcher instead of a heat filter (ablation) | HeroFilter patcher · Chameleon | accuracy: 47.7 ± 1.7 -> 57.3 ± 1.2 | Helped |
| Rank patches instead of shuffling their order (ablation) | HeroFilter · Cora | accuracy: 71.4 ± 1.1 -> 77.3 ± 0.6 | Helped |
| Rank patches instead of shuffling their order (ablation) | HeroFilter · Chameleon | accuracy: 51.0 ± 1.2 -> 57.3 ± 1.1 | Helped |
| Add Patch-Mixing (ablation) | HeroFilter · Arxiv-Year | accuracy: 53.85 ± 0.20 -> 54.66 ± 0.28 | Helped |
| Add Feature-Mixing (ablation) | HeroFilter · Arxiv-Year | accuracy: 54.49 ± 0.04 -> 54.66 ± 0.28 | Helped |
| Add Patch-Mixing (ablation) | HeroFilter · Snap-Patents | accuracy: 63.00 ± 0.01 -> 65.05 ± 0.04 | Helped |
| Add Feature-Mixing (ablation) | HeroFilter · Snap-Patents | accuracy: 64.97 ± 0.05 -> 65.05 ± 0.04 | Helped |
| Add both Patch-Mixing and Feature-Mixing (ablation) | HeroFilter · Snap-Patents | accuracy: 62.95 ± 0.09 -> 65.05 ± 0.04 | Helped |
Surprising findings
- Theory and synthetic experiments indicate the average filter response does not follow a strict monotonic relation with heterophily degree.
- Randomly shuffling patch order degrades accuracy on all tested datasets, up to 6.3% on Chameleon.
Limitations
- Relies on eigendecomposition for the exact patcher, which is costly for large graphs (the Fast variant addresses this).
- Heterophily-spectrum theory relies on assumptions and bounds that may be loose; evidence is largely synthetic plus benchmark tables.
Experimental setup
Datasets: Cora CiteSeer PubMed OGBN-Arxiv Texas Squirrel Chameleon Cornell Wisconsin Actor Arxiv-Year Snap-Patents
Benchmarks: Cora CiteSeer PubMed OGBN-Arxiv Texas Squirrel Chameleon Cornell Wisconsin Actor Arxiv-Year Snap-Patents
Metrics: accuracy
Baselines: MLP GPRGNN ChebNet ChebNetII APPNP GCN GAT GraphSage FAGCN H2GCN BM-GCN BernNet
Builds on: GCN GPRGNN BernNet MLP-Mixer ChebNetII
Closest papers by meaning
- Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering (AAAI 2024 · similarity 0.91)
- PC-Conv: Unifying Homophily and Heterophily with Two-Fold Filtering (AAAI 2024 · similarity 0.90)
- How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing (ICML 2024 · similarity 0.90)
- Unifying Homophily and Heterophily for Spectral Graph Neural Networks via Triple Filter Ensembles (NeurIPS 2024 · similarity 0.90)
- When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline (AAAI 2025 · similarity 0.89)
- HoloNets: Spectral Convolutions do extend to Directed Graphs (ICLR 2024 · similarity 0.89)
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