Research map / Graph learning / GNN architectures
How Particle System Theory Enhances Hypergraph Message Passing
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes HAMP, a hypergraph message passing framework based on interacting particle systems (attraction, repulsion, Allen-Cahn forcing, and Brownian noise), in first-order (HAMP-I) and second-order (HAMP-II) variants, with a theoretical lower bound on hypergraph Dirichlet energy against over-smoothing.
Problem
Hypergraph neural networks suffer from over-smoothing when made deep and perform poorly on heterophilic hypergraphs, since purely attractive, diffusion-style message passing drives node features to collapse.
Approach
Treat each hyperedge as a field inducing shared node dynamics governed by attraction and repulsion between nodes plus an Allen-Cahn damping term, with first-order (feature) or second-order (velocity-coupled) particle ODEs and an optional Brownian noise term (SDE); repulsion and Allen-Cahn forcing give a provable positive lower bound on Dirichlet energy.
Key results
- HAMP-II reaches 75.33% on Citeseer and 89.05% on Pubmed, and HAMP-I reaches 81.18% on Cora, the best accuracy on those homophilic datasets in the reported table.
- On heterophilic hypergraphs HAMP-II achieves 70.14% on Senate and 69.94% on Walmart, and HAMP-I 72.72% on House, with the largest gain of about 3% on Walmart over ED-HNN.
- Ablation shows removing both repulsion and Allen-Cahn forcing drops HAMP-I on Cora from 81.18% to 75.67%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HAMP-I or HAMP-II instead of the strongest listed baseline | HAMP on heterophilic benchmarks · Congress, Senate, Walmart, and House | accuracy (%): 95.00$\pm$0.99 -> 95.26$\pm$1.34; 66.90$\pm$5.52 -> 70.14$\pm$6.08; 66.91$\pm$0.41 -> 69.94$\pm$0.37; 72.45$\pm$2.28 -> | Helped |
| Use HAMP instead of the strongest listed baseline | HAMP on homophilic benchmarks · Cora, Citeseer, Pubmed, Cora-CA, and DBLP-CA | accuracy (%): 80.65$\pm$1.22 -> 81.18$\pm$1.30; 74.87$\pm$1.12 -> 75.33$\pm$1.61; 89.03$\pm$0.53 -> 89.05$\pm$0.41; 84.95$\pm$0.98 -> | Mixed |
| Add repulsion and Allen-Cahn forces (ablation) | HAMP-I · Cora and Senate | accuracy (%): 75.67 -> 81.18; 60.14 -> 69.44 | Helped |
| Add repulsion alone, without Allen-Cahn force (ablation) | HAMP-I · Cora and Senate | accuracy (%): 75.67 -> 75.97; 60.14 -> 61.69 | Helped |
| Add Allen-Cahn force alone, without repulsion (ablation) | HAMP-I · Cora and Senate | accuracy (%): 75.67 -> 80.59; 60.14 -> 65.63 | Helped |
| Add repulsion and Allen-Cahn forces (ablation) | HAMP-II · Cora | accuracy (%): 77.18 -> 80.80 | Helped |
| Add repulsion alone, without Allen-Cahn force (ablation) | HAMP-II · Cora | accuracy (%): 77.18 -> 77.40 | Helped |
| Add Allen-Cahn force alone, without repulsion (ablation) | HAMP-II · Cora | accuracy (%): 77.18 -> 79.50 | Helped |
| Add stochastic noise to deterministic message passing (ablation) | HAMP-I and HAMP-II · Senate | accuracy | Helped |
| Increase message-passing depth (ablation) | HAMP-II · Cora, Citeseer, and Congress | accuracy | Helped |
| Use second-order rather than first-order particle dynamics | HAMP-II versus HAMP-I · Congress | clustering quality | Helped |
Surprising findings
- Ablation shows repulsion alone gives little benefit on Walmart and House for HAMP-I, and the Allen-Cahn term alone is needed for most of the gains on Cora and Citeseer.
- On heterophilic Walmart, HAMP-I and HAMP-II differ by only about 0.04 points, and HAMP-I with repulsion alone slightly underperforms its no-repulsion variant on Pubmed-level metrics in some rows.
Limitations
- Assumes a static hypergraph topology; temporal hypergraphs with evolving structure are not handled.
- Theoretical separation results rely on strong assumptions (two groups, symmetric interactions, large group sizes).
Experimental setup
Datasets: Cora Citeseer Pubmed Cora-CA DBLP-CA Congress Senate Walmart House
Benchmarks: Cora Citeseer Pubmed Cora-CA DBLP-CA Congress Senate Walmart House
Metrics: accuracy
Baselines: HGNN HCHA HNHN HyperGCN HyperND UniGCNII AllDeepSets AllSetTransformer ED-HNN HDS-ode
Builds on: ED-HNN HGNN Neural ODEs ACMP HDS-ode
Closest papers by meaning
- HyperMixup: Hypergraph-Augmented with Higher-order Information Mixup (NeurIPS 2025 · similarity 0.87)
- Training-Free Message Passing for Learning on Hypergraphs (ICLR 2025 · similarity 0.87)
- Hypergraph Generation via Structured Stochastic Diffusion (NeurIPS 2026 · similarity 0.86)
- Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching (ICML 2025 · similarity 0.85)
- HYGENE: A Diffusion-Based Hypergraph Generation Method (AAAI 2025 · similarity 0.84)
- SPHINX: Structural Prediction using Hypergraph Inference Network (ICML 2025 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.