TopoU-Net: a U-Net architecture for topological domains
Gaurav Gaurav, Ibrahem ALJabea, Yaroslav Zakomornyy, Eric Frank, Mohamed Elhamdadi, Theodore Papamarkou, Mustafa Hajij

TL;DR
TopoU-Net introduces a topological domain-aware U-Net architecture that leverages combinatorial complexes and rank-paths to effectively process higher-order structured data, outperforming traditional methods.
Contribution
It presents a novel rank-path U-Net design for topological domains, replacing spatial scales with rank-based paths, and clarifies the role of skip connections through bottleneck support ratios.
Findings
Achieves the strongest mean accuracy on 6 of 8 node-classification datasets.
Outperforms baselines on 4 of 5 hypergraph datasets.
Removing skip connections harms performance under severe bottleneck compression.
Abstract
Many modern datasets mix points, edges, regions, groups, objects, events, hyperedges, and relations. Yet neural architectures often force such data into grids, graphs, or sequences, obscuring higher-order structure and making encoder-decoder designs domain-specific. We view U-Net not as a grid-specific architecture, but as a hierarchical encoder-decoder principle: representation spaces, transport maps between levels, and skip connections between matched levels. Combinatorial complexes naturally supply these ingredients through cells, incidences, and ranks. We introduce TopoU-Net, a rank-path U-Net for topological domains. Given a path from an input rank to a bottleneck rank and back, the encoder lifts cochains upward along incidence maps, the decoder transports them downward, and skip connections merge features at matched ranks. Rank replaces spatial scale: choosing paths through nodes,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
