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SPHINX: Structural Prediction using Hypergraph Inference Network
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Proposes SPHINX, an end-to-end differentiable model that infers latent discrete hypergraphs from node-level signals using sequential slot attention and k-subset sampling, evaluated on particle simulation, NBA trajectory prediction, and ModelNet40/NTU object classification.
Problem
Hypergraph structure is rarely available or annotated, while many systems exhibit higher-order interactions. Existing latent hypergraph predictors are either not differentiable, produce only soft/weighted structures, need regularization losses, or only work transductively.
Approach
Model hyperedge discovery as sequential soft clustering with slot attention, where each new hyperedge is conditioned on previously predicted ones, and sample exactly-k-node discrete incidences with differentiable k-subset sampling, yielding a discrete hypergraph that plugs into any hypergraph network without regularization losses.
Key results
- On the NBA inductive setup, SPHINX reaches 0.30/0.43 minADE20/minFDE20 at 1 second, beating the listed hypergraph baselines at short horizons.
- On the synthetic Particle Simulation, the inferred hyperedges reach about 90% overlap with ground truth versus 67% for TDHNN.
- Sequential slot attention and k-subset sampling are both reported as improving over the w/o sequential and Gumbel-Softmax variants on NBA and particle data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use sequential, history-aware slot prediction instead of simultaneous slot prediction (ablation) | SPHINX · NBA | ADE/FDE: 0.62/0.94 -> 0.59/0.92 | Helped |
| replace Gumbel-Softmax with constrained k-subset sampling (ablation) | SPHINX · NBA | ADE/FDE: 1.29/1.81 -> 0.59/0.92 | Helped |
| use sequential slot prediction (ablation) | SPHINX · Particle Simulation | downstream performance | Helped |
| replace Gumbel-Softmax with constrained k-subset sampling (ablation) | SPHINX · Particle Simulation | downstream performance | Helped |
| infer the latent hypergraph with SPHINX rather than TDHNN | hypergraph prediction · Particle Simulation | hyperedge overlap: 67% -> 90% | Helped |
| use 1 slot rather than 2 (ablation) | SPHINX · Particle Simulation | MSE: 0.00002 -> 0.00007 | Hurt |
| increase slots from 2 to 3 (ablation) | SPHINX · Particle Simulation | MSE: 0.00002 -> 0.000017 | Helped |
| increase slots from 2 to 4 (ablation) | SPHINX · Particle Simulation | MSE: 0.00002 -> 0.000007 | Helped |
| use SPHINX instead of GroupNet | NBA trajectory prediction · NBA 1sec and 2sec | minADE20: 0.34 -> 0.30; 0.62 -> 0.59 | Helped |
| use SPHINX instead of GroupNet | NBA trajectory prediction · NBA 3sec and 4sec | minADE20: 0.87 -> 0.88; 1.13 -> 1.16 | Mixed |
Surprising findings
- TDHNN learned hyperedges that each contain all nodes in the dataset, suggesting attention coefficients rather than a sparse structure.
- Providing more slots than the true number of hyperedges produced redundant duplicates of existing hyperedges rather than spurious new relations.
Limitations
- Only k-regular hyperedges (fixed cardinality k) can be predicted, requiring domain knowledge for varied sizes.
- Number of hyperedges M must be fixed a priori; a single static hypergraph is predicted per trajectory rather than a dynamic one.
- Real-world hyperedge accuracy cannot be verified because the datasets lack higher-order annotations.
Experimental setup
Datasets: Particle Simulation NBA SportVU ModelNet40 NTU
Benchmarks: Particle Simulation NBA SportVU trajectory prediction ModelNet40 NTU
Metrics: minADE20 minFDE20 ADE FDE hyperedge overlap classification accuracy
Baselines: NRI DNRI EvolveGraph STGAT Trajectron++ EvolveHypergraph GroupNet TDHNN GCN GAT HGNN HGNN+
Builds on: slot attention SIMPLE k-subset sampling AIMLE DeepSets GroupNet
Closest papers by meaning
- Beyond Graphs: Can Large Language Models Comprehend Hypergraphs? (ICLR 2025 · similarity 0.90)
- Training-Free Message Passing for Learning on Hypergraphs (ICLR 2025 · similarity 0.88)
- LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100x Faster Inference (ICLR 2024 · similarity 0.88)
- Hypergraph Representation Learning with Hyperlink Random Effects (NeurIPS 2026 · similarity 0.88)
- HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs (ICLR 2024 · similarity 0.87)
- Hypergraph Learning for Unsupervised Graph Alignment via Optimal Transport (AAAI 2025 · similarity 0.87)
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