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K-hop Hypergraph Neural Network: A Comprehensive Aggregation Approach
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Proposes KHGNN, a K-hop hypergraph neural network that uses bisection nested convolution over shortest paths (built on the HyperGINE layer) to propagate information between distant nodes and hyperedges.
Problem
Existing hypergraph neural networks rely on clique-expansion two-stage message passing with limited receptive fields, which causes over-squashing and over-smoothing and underuses hypergraph information, especially for long-range dependencies.
Approach
HyperGINE extends GINE to hypergraphs with node, hyperedge and structure features; KHGNN recursively applies bisection nested convolutions at the centers of shortest paths, reusing low-order convolutions as path features to guide K-hop aggregation for nodes and hyperedges, plus a relative degree encoding.
Key results
- KHGNN reaches 80.67% on Cora and 100.00% on Mushroom, with average rank 1.29 across seven hypergraph datasets.
- On Peptides-func KHGNN achieves 70.11 AP and on ZINC an MAE of 0.074, outperforming graph transformers in the reported tables.
- On LRGB, KHGNN reports 38.30 F1 on PascalVOC-SP and 35.60 MRR on PCQM-Contact, best among listed models.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Expand node aggregation from Kv=1 to Kv=6 (with Ke=2 and relative degree encoding) (ablation) | KHGNN · Peptides-func | AP: 0.5965 -> 0.7011 | Helped |
| Expand node and hyperedge aggregation from Kv=4, Ke=1 to Kv=6, Ke=2 (ablation) | KHGNN · Peptides-func | AP: 0.6866 -> 0.7011 | Helped |
| Remove relative degree encoding (ablation) | KHGNN (Kv=6, Ke=2) · Peptides-func | AP: 0.7011 -> 0.6922 | Hurt |
| Use KHGNN instead of the strongest listed baseline | Cora, Citeseer, Cora-CA, Mushroom, NTU2012, ModelNet40 · Hypergraph datasets | accuracy | Helped |
| Use KHGNN instead of the strongest listed baseline | Pubmed · Pubmed | accuracy: 89.03 -> 88.47 | Hurt |
| Use KHGNN instead of the strongest listed baseline | ZINC, MNIST, CIFAR10, MolHIV · Short-range graph benchmarks | task metric | Helped |
| Use KHGNN instead of the strongest listed baseline | MolPCBA · MolPCBA | AP: 0.2961 -> 0.2906 | Hurt |
| Use KHGNN instead of the strongest listed baseline | PascalVOC-SP, Peptides-func, Peptides-struct, PCQM-Contact · Long-Range Graph Benchmark | task metric | Helped |
Surprising findings
- Adding hyperedge-hop aggregation (Ke) with node hops does not always help on its own; ablations show gains mostly from increasing both Kv and Ke together, with training time scaling roughly linearly with hops.
Limitations
- Complexity depends on the number of shortest paths and average high-order hyperedge size, which may be costly on dense graphs.
- Gains on hypergraph node classification are smaller on Pubmed where KHGNN is only competitive rather than best.
Experimental setup
Datasets: Cora Citeseer Pubmed Cora-CA Mushroom NTU2012 ModelNet40 ZINC MNIST CIFAR10 MolHIV MolPCBA
Benchmarks: Cora Citeseer Pubmed Cora-CA Mushroom NTU2012 ModelNet40 ZINC MNIST CIFAR10 MolHIV MolPCBA
Metrics: accuracy MAE AUROC AP F1 MRR
Baselines: HGNN HyperGCN UniGCNII AllSet HGNN+ TriCL ED-HNN Hypergraph-MLP HyperGINE GCN GIN GatedGCN
Builds on: GINE HGNN PathNN clique expansion
Closest papers by meaning
- Hypergraph Neural Architecture Search (AAAI 2024 · similarity 0.89)
- Deep Hypergraph Neural Networks with Tight Framelets (AAAI 2025 · similarity 0.88)
- Training-Free Message Passing for Learning on Hypergraphs (ICLR 2025 · similarity 0.88)
- Improved Expressivity of Hypergraph Neural Networks through High-Dimensional Generalized Weisfeiler-Leman Algorithms (ICML 2025 · similarity 0.88)
- LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100x Faster Inference (ICLR 2024 · similarity 0.88)
- When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline (AAAI 2025 · similarity 0.88)
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