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Disentangling Hyperedges through the Lens of Category Theory
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Proposes a category-theoretic naturality-based criterion (factor representation consistency) for hyperedge disentanglement and a proof-of-concept Natural-HNN that is evaluated on TCGA cancer subtype classification with genetic pathways as hyperedges.
Problem
Hyperedge disentanglement in hypergraphs lacks a criterion for determining factor relevance; existing similarity-based criteria from graph disentanglement rely on data-specific assumptions and may not fit group interactions such as genetic pathways.
Approach
Derives from category theory (naturality condition between entangled and disentangled functors on PISet to DLRep) that a hyperedge factor representation should be consistent whether computed by aggregating then disentangling or disentangling then aggregating; the consistency score is used as a per-factor relevance weight in message passing.
Key results
- Natural-HNN achieves Macro F1 0.804 on BRCA, about 5% above the second-best model (HSDN 0.757), and is top on BRCA, STAD, SARC, LGG, and HNSC.
- On CESC, Natural-HNN (0.881) is second to ED-HNNII (0.895).
- Natural-HNN outperforms the hypergraph-structure-level disentanglement model HSDN on all six cancer datasets reported.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use naturality-guided hyperedge disentanglement instead of HSDN's factor-similarity criterion | Natural-HNN vs HSDN · BRCA | Macro F1: 0.757 -> 0.804 | Helped |
| Use naturality-guided hyperedge disentanglement instead of HSDN's factor-similarity criterion | Natural-HNN vs HSDN · STAD | Macro F1: 0.629 -> 0.659 | Helped |
| Use naturality-guided hyperedge disentanglement instead of the strongest baseline, UniGCNII | Natural-HNN vs UniGCNII · SARC | Macro F1: 0.728 -> 0.745 | Helped |
| Use naturality-guided hyperedge disentanglement instead of the strongest baseline, ED-HNN | Natural-HNN vs ED-HNN · LGG | Macro F1: 0.700 -> 0.707 | Helped |
| Use naturality-guided hyperedge disentanglement instead of the strongest baseline, ED-HNNII | Natural-HNN vs ED-HNNII · HNSC | Macro F1: 0.845 -> 0.862 | Helped |
| Use naturality-guided hyperedge disentanglement instead of the strongest baseline, ED-HNNII | Natural-HNN vs ED-HNNII · CESC | Macro F1: 0.895 -> 0.881 | Hurt |
| Add factor discrimination loss (ablation) | Natural-HNN · Cancer subtype classification | Performance | Helped |
| Use the aggregation-first branch output instead of the disentangle-first branch output for final hyperedge factor representations (ablation) | Natural-HNN · Cancer subtype classification | Performance | No clear effect |
| Vary the number of factors to 2 or 8 (ablation) | Natural-HNN · BRCA functional-context similarity | Similarity to ground truth | Mixed |
| Vary the factor discrimination loss weight (ablation) | Natural-HNN · BRCA functional-context similarity | Similarity to ground truth | No clear effect |
| Increase representation dimensionality too much (ablation) | Natural-HNN · BRCA functional-context similarity | Similarity to ground truth | Mixed |
| Reduce representation dimensionality too much (ablation) | Natural-HNN · BRCA functional-context similarity | Similarity to ground truth | Hurt |
Limitations
- Proof-of-concept model only; evaluated on a single biological hypergraph domain (pathways and TCGA cancers).
- Functional-context validation relies on indirect comparison with GO-based Lin's similarity rather than ground-truth factor annotations.
- Factor discrimination loss adds a hyperparameter lambda requiring tuning; the paper treats it as optional.
Experimental setup
Datasets: TCGA BRCA TCGA STAD TCGA SARC TCGA LGG TCGA HNSC TCGA CESC KEGG PID Reactome BioCarta
Benchmarks: TCGA cancer subtype classification (BRCA, STAD, SARC, LGG, HNSC, CESC)
Metrics: Macro F1 SHAP value cluster functional similarity correlation (Lin's method BMA)
Baselines: HGNN HCHA HNHN UniGCNII AllDeepSets AllSetTransformer HyperGAT SHINE ED-HNN ED-HNNII HSDN
Builds on: DisenGCN HSDN ED-HNN Pathformer HGNN
Closest papers by meaning
- Defining and Discovering Hyper-meta-paths for Heterogeneous Hypergraphs (NeurIPS 2025 · similarity 0.88)
- SPHINX: Structural Prediction using Hypergraph Inference Network (ICML 2025 · similarity 0.87)
- Hypergraph Learning for Unsupervised Graph Alignment via Optimal Transport (AAAI 2025 · similarity 0.86)
- Hypergraph-enhanced Dual Semi-supervised Graph Classification (ICML 2024 · similarity 0.86)
- HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs (ICLR 2024 · similarity 0.86)
- Hypergraph Joint Representation Learning for Hypervertices and Hyperedges via Cross Expansion (AAAI 2024 · similarity 0.85)
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