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Training-Free Message Passing for Learning on Hypergraphs
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Proposes TF-HNN, a hypergraph neural network whose message-passing module is training-free and precomputed as a linearized, degree-weighted clique-expansion propagation operator, cutting training cost while matching node classification and hyperlink prediction accuracy.
Problem
Message passing in hypergraph neural networks requires computationally intensive joint training, which limits scalability to large hypergraphs.
Approach
Decouple hypergraph structure processing from training: remove learnable parameters and nonlinearities from four existing HNN aggregation functions, unify them into a single precomputed propagation matrix S over a hyperedge-size-weighted clique expansion, and train only an MLP classifier or predictor.
Key results
- TF-HNN achieves the highest average node classification accuracy (82.50%) across six datasets, versus 81.38% for the best baseline Deep-HGNN.
- On Trivago node classification, TF-HNN reaches 94.03% accuracy in 38.09 s versus 84.06% for Deep-HGNN at 3352 s, about 10% higher accuracy with roughly 1% of the training time.
- On Trivago hyperlink prediction, TF-HNN attains 95.71% AUC in 484 s, compared with 84.26% AUC for Deep-HGNN at 1873.67 s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use TF-HNN instead of PhenomNN | node classification · Cora-CA | accuracy (%): 85.81 ± 0.90 -> 86.54 ± 1.32 | Helped |
| use TF-HNN instead of PhenomNN | node classification · DBLP-CA | accuracy (%): 91.91 ± 0.21 -> 91.80 ± 0.30 | No clear effect |
| use TF-HNN instead of PhenomNN | node classification · Citeseer | accuracy (%): 75.10 ± 1.59 -> 74.82 ± 1.67 | No clear effect |
| use TF-HNN instead of ED-HNN | node classification · Congress | accuracy (%): 95.00 ± 0.99 -> 95.09 ± 0.89 | Helped |
| use TF-HNN instead of Deep-HGNN | node classification · House | accuracy (%): 75.26 ± 1.76 -> 76.29 ± 1.99 | Helped |
| use TF-HNN instead of Deep-HGNN | node classification · Senate | accuracy (%): 68.39 ± 4.79 -> 70.42 ± 2.74 | Helped |
| replace Deep-HGNN with TF-HNN | node classification on Trivago · Trivago | accuracy (%): 84.06 ± 1.70 -> 94.03 ± 0.51 | Helped |
| replace Deep-HGNN with TF-HNN | node classification on Trivago · Trivago | training time (s): 3352.35 ± 1039.83 -> 38.09 ± 6.65 | Helped |
| replace Deep-HGNN with TF-HNN | hyperlink prediction on Trivago · Trivago | AUC (%): 84.26 ± 1.62 -> 95.71 ± 1.00 | Helped |
| replace Deep-HGNN with TF-HNN | hyperlink prediction on Trivago · Trivago | training time (s): 1873.67 ± 559.55 -> 484.00 ± 110.99 | Helped |
| replace TF-MP-Module with SGC on clique expansion (ablation) | TF-HNN · node classification, Cora-CA, Citeseer, Senate, and House | accuracy (%): Cora-CA: 81.60 ± 1.68 vs 86.54 ± 1.32; Citeseer: 71.42 ± 2.15 vs 74.82 ± 1.67; Senate: 47.18 ± 6.48 vs 70.42 ± 2.74; Hou | Hurt |
| replace TF-MP-Module with SIGN on clique expansion (ablation) | TF-HNN · node classification, Cora-CA, Citeseer, Senate, and House | accuracy (%): Cora-CA: 86.04 ± 1.53 vs 86.54 ± 1.32; Citeseer: 73.62 ± 1.79 vs 74.82 ± 1.67; Senate: 64.93 ± 3.15 vs 70.42 ± 2.74; Hou | Hurt |
Surprising findings
- Removing the learnable MLP-free propagation and classifier-only training outperforms the learnable HNN baselines on several datasets, suggesting fewer parameters reduce overfitting.
- SGC with clique expansion is a special case of the proposed operator with alpha=0 and performs worse than the full TF-MP-Module.
Limitations
- Evaluated only on node-level and hyperedge-level tasks; hypergraph-level tasks not covered.
- Efficiency gain is smaller for hyperlink prediction because the task-specific predictor is more expensive.
- Hyperparameter search (layers, alpha) is not automated.
Experimental setup
Datasets: Cora-CA DBLP-CA Citeseer Congress House Senate Trivago
Benchmarks: Cora-CA DBLP-CA Citeseer Congress House Senate Trivago
Metrics: classification accuracy AUC relative training time
Baselines: HGNN HCHA HNHN UniGCNII AllDeepSets AllSetTransformer PhenomNN ED-HNN Deep-HGNN SGC with CE SIGN with CE
Builds on: HGNN UniGCNII AllDeepSets ED-HNN SGC SIGN APPNP
Closest papers by meaning
- Parameter-Free Hypergraph Neural Network for Few-Shot Node Classification (NeurIPS 2025 · similarity 0.90)
- LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100x Faster Inference (ICLR 2024 · similarity 0.89)
- Hypergraph Neural Architecture Search (AAAI 2024 · similarity 0.89)
- When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline (AAAI 2025 · similarity 0.89)
- SPHINX: Structural Prediction using Hypergraph Inference Network (ICML 2025 · similarity 0.88)
- Deep Hypergraph Neural Networks with Tight Framelets (AAAI 2025 · similarity 0.88)
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