Research map / Graph learning / GNN architectures
TopoTune: A Framework for Generalized Combinatorial Complex Neural Networks
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 Generalized Combinatorial Complex Networks (GCCNs), which turn any neural network into a topological deep learning model via an ensemble of strictly augmented Hasse graphs, and releases the TopoTune software for building them.
Problem
Topological deep learning (TDL) lacks standardized, principled frameworks; existing CCNNs are message-passing only and graph-based simulations of them collapse rank information and lose topological symmetry.
Approach
Expand a combinatorial complex into one strictly augmented Hasse graph per neighborhood (ensemble of synchronized models), apply any GNN or Transformer as the neighborhood message function, and aggregate across neighborhoods; per-rank neighborhoods further allow rank-specific message passing. The framework provably generalizes and subsumes CCNNs and is more expressive.
Key results
- GCCNs outperform the best CCNN by more than one standard deviation in 11 of 16 domain/dataset combinations (5 seeds).
- On ZINC, a GCCN with GIN as neighborhood message function reaches MAE 0.19 vs. 0.34 for the best cellular CCNN.
- On Citeseer, a GCCN with GraphSAGE outperforms the best existing CCNN while being 28% smaller.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an ensemble of strictly augmented Hasse graphs instead of a single augmented Hasse graph | GCCN · Cellular and simplicial benchmark datasets | performance | Helped |
| Use per-rank neighborhood structures | GCCN · PROTEINS | parameter count: 48% | Helped |
| Use GIN as the neighborhood message function | GCCN · ZINC | MAE | Helped |
Surprising findings
- GCCNs run on the ensemble of strictly augmented Hasse graphs often improve results over a single augmented Hasse graph, and GCCNs are sometimes outperformed by the best GNN from TopoBench on 2 combinations.
- Training time for GCCNs slows on larger datasets, attributed to on-the-fly graph expansion.
Limitations
- Training time grows on larger datasets due to on-the-fly graph expansion.
- Node-level tasks show less parameter savings because of larger graphs and high-dimensional features.
- Dataset-specific: no single neighborhood structure or message function dominates across tasks.
Experimental setup
Datasets: MUTAG PROTEINS NCI1 NCI109 ZINC Cora CiteSeer PubMed
Benchmarks: MUTAG PROTEINS NCI1 NCI109 ZINC Cora CiteSeer PubMed
Metrics: accuracy MAE
Baselines: CCNN (best model on TopoBench) SCCN CWN GNN (best model on TopoBench)
Builds on: combinatorial complex neural networks augmented Hasse graphs TopoBench TopoX Weisfeiler-Leman test
Closest papers by meaning
- Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivity (ICLR 2025 · similarity 0.90)
- Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes (AAAI 2024 · similarity 0.89)
- HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations (NeurIPS 2026 · similarity 0.88)
- E(n) Equivariant Topological Neural Networks (ICLR 2025 · similarity 0.88)
- Topological Neural Networks go Persistent, Equivariant, and Continuous (ICML 2024 · similarity 0.88)
- Deep Homomorphism Networks (NeurIPS 2024 · similarity 0.88)
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.