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Parameter-Free Hypergraph Neural Network for Few-Shot Node Classification
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Proposes ZEN, a parameter-free linear hypergraph neural network for few-shot node classification that uses a closed-form approximate weight matrix and redundancy-aware propagation.
Problem
Few-shot node classification on hypergraphs, where existing nonlinear hypergraph neural networks overfit and scale poorly when labels are scarce.
Approach
Linearizes representative HNNs into a single propagation matrix times a single weight matrix, replaces the pseudoinverse-based closed-form weight with an approximation (W ≈ (1/ε)(PX)^T D_trn Y, then normalized), and removes redundant self-information from multi-hop adjacency matrices (redundancy-aware propagation) so that self- and neighbor-information can be tuned separately.
Key results
- ZEN achieves the best 5-shot average rank (1.7) across 10 hypergraph benchmarks, ahead of AllSetTransformer (3.6) and UniGCN (3.9).
- ZEN is up to 696x faster than the fastest competitor (on Senate), per the reported running time ratios.
- Ablation shows removing both TCS and RAP lowers average rank from 1.7 to 3.7 on the 5-shot setting.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ZEN instead of the strongest per-dataset baseline | 5-shot hypergraph node classification · 10 benchmark hypergraphs | accuracy (%) | Mixed |
| Use ZEN instead of the fastest competing HNN | hypergraph node classification · 10 benchmark hypergraphs | runtime ratio (lower is better): 696× | Helped |
| add tractable closed-form solution (TCS) (ablation) | ZEN · Cora, 5-shot | accuracy (%): 46.9_{\pm 5.5} -> 51.9_{\pm 10.1} | Helped |
| add redundancy-aware propagation (RAP) (ablation) | ZEN · Cora, 5-shot | accuracy (%): 50.6_{\pm 8.8} -> 51.9_{\pm 10.1} | Helped |
| add both TCS and RAP (ablation) | ZEN without TCS or RAP · Cora, 5-shot | accuracy (%): 44.3_{\pm 7.2} -> 51.9_{\pm 10.1} | Helped |
| add multi-hop message combination (ablation) | linearized HGNN · Cora, 5-shot | accuracy (%): 42.7_{\pm 8.4} -> 51.9_{\pm 10.1} | Helped |
| add RAP (ablation) | ZEN · Congress and Senate | accuracy (%) | Hurt |
| add TCS (ablation) | ZEN · 20News and MN40 | accuracy (%) | Hurt |
| remove TCS (ablation) | ZEN · 10 benchmark hypergraphs | accuracy (%) | Mixed |
| remove RAP (ablation) | ZEN · 10 benchmark hypergraphs | accuracy (%) | Mixed |
| remove both TCS and RAP (ablation) | ZEN · 10 benchmark hypergraphs | accuracy (%) | Hurt |
| replace ZEN with linearized HGNN without multi-hop message combination (ablation) | ZEN · 10 benchmark hypergraphs | accuracy (%) | Hurt |
Surprising findings
- Linearized HGNN baseline performs notably worse than the full nonlinear HGNN on several datasets, and RAP tends to hurt on dense datasets such as Congress and Senate.
Limitations
- Designed only for node classification; not applicable to hyperedge prediction, local clustering, or hyperedge disambiguation.
- Closed-form weight relies on approximation assumptions (normalized embeddings, small epsilon) that may not hold for all datasets; approximation error grows with number of classes.
- RSI computation is restricted to 2 hops; deeper propagation is only sketched via approximations.
Experimental setup
Datasets: Cora Citeseer Pubmed Cora-CA 20News ModelNet40 Congress Walmart Senate House Zoo
Benchmarks: Cora Citeseer Pubmed Cora-CA 20News ModelNet40 Congress Walmart Senate House
Metrics: classification accuracy average rank running time ratio
Baselines: HGNN HNHN HCHA UniGCN UniGCNII AllDeepSets AllSetTransformer ED-HNN
Builds on: HGNN HNHN UniGCNII AllDeepSets ED-HNN SGC APPNP
Closest papers by meaning
- Training-Free Message Passing for Learning on Hypergraphs (ICLR 2025 · similarity 0.90)
- When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline (AAAI 2025 · similarity 0.89)
- Hypergraph Neural Architecture Search (AAAI 2024 · similarity 0.88)
- LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100x Faster Inference (ICLR 2024 · similarity 0.87)
- Hypergraph-enhanced Dual Semi-supervised Graph Classification (ICML 2024 · similarity 0.87)
- Deep Hypergraph Neural Networks with Tight Framelets (AAAI 2025 · similarity 0.86)
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