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From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module
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Introduces Latent Topology Inference via the Differentiable Cell Complex Module (DCM), which learns sparse, non-regular cell complexes (graph plus polygons) with alpha-entmax sampling and trains them end-to-end with GNN/cell complex message passing for node classification.
Problem
Latent graph inference methods only learn regular graph topologies and need an input graph, while topological deep learning relies on fixed deterministic lifts and exhaustive, unscalable cell search when no graph is given.
Approach
A two-step differentiable procedure: an alpha-entmax-based graph module (alpha-DGM) samples sparse, non-regular edges, then a Polygon Inference Module samples polygons among induced cycles, with a reward-based loss that lets the downstream task loss guide edge and polygon selection.
Key results
- On Texas with input graph, DCM improves over DGM-M by more than 20% (84.87 vs 62.78 test accuracy).
- Without input graph on Cora, DCM reaches 78.80% vs 70.85% for DGM-M.
- Learned latent graphs on Texas reach homophily 0.99 from input 0.11.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DCM rather than latent graph inference with the input graph on Texas | DCM vs DGM-M · Texas, w graph | accuracy: 62.78 $\pm$ 9.31 -> 84.87 $\pm$ 10.04 | Helped |
| Use DCM rather than latent graph inference without the input graph on Texas | DCM vs DGM-M · Texas, w/o graph | accuracy: 81.67 $\pm$ 7.05 -> 85.71 $\pm$ 7.87 | Helped |
| Replace α-entmax sampling with Gumbel Top-k (ablation) | DCM · Homophilic and heterophilic datasets | accuracy | Hurt |
| Set α=1 and take all polygons (ablation) | DCM · Homophilic and heterophilic datasets | accuracy | No clear effect |
| Vary the number of message-passing layers from 1 to 2–4 (ablation) | DCM · Homophilic and heterophilic datasets | accuracy | Mixed |
| Vary maximum cycle length Kmax from 4 to 3 or 5 (ablation) | DCM · Homophilic and heterophilic datasets | accuracy | Mixed |
Surprising findings
- Learned latent graphs have higher homophily than the input graph even on homophilic datasets, and the DCM with input graph remains stable even when the given heterophilic graph is misaligned.
Limitations
- Main bottlenecks are message passing and induced cycle search, limiting scalability to very large datasets.
- Evaluated only on transductive node classification; inductive tasks not tested.
- Restricted to cell complexes with polygons up to length K_max, not hypergraphs or combinatorial complexes.
Experimental setup
Datasets: Cora CiteSeer PubMed Physics CS Texas Wisconsin Squirrel Chameleon
Benchmarks: Cora CiteSeer PubMed Physics CS Texas Wisconsin Squirrel Chameleon
Metrics: test accuracy (avg over 10 splits) homophily level
Baselines: MLP GCN DGM-E DGM-M Top-k DCM
Builds on: Differentiable Graph Module (DGM) alpha-entmax cell complex neural networks GCN
Closest papers by meaning
- TopoTune: A Framework for Generalized Combinatorial Complex Neural Networks (ICML 2025 · similarity 0.87)
- Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivity (ICLR 2025 · similarity 0.87)
- Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes (AAAI 2024 · similarity 0.86)
- Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries (ICLR 2024 · similarity 0.85)
- TopoGCL: Topological Graph Contrastive Learning (AAAI 2024 · similarity 0.85)
- A Graph Dynamics Prior for Relational Inference (AAAI 2024 · similarity 0.85)
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