Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets

doi:10.1109/tpami.2026.3743238

Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets

2026-10-13

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DOI：10.1109/tpami.2026.3743238

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Convolution has transferred successfully from images to hypergraphs, but the U-Net, the encoder-decoder architecture that has proved decisive in other domains, remains largely unavailable for hypergraph data, because hypergraphs lack well-defined pooling and unpooling operations. This paper introduces the HyperGraph U-Net (HGUN) together with the two operators it requires. Parallel Hierarchical Pooling (PHPool) fits one hierarchical clustering dendrogram to the hypergraph and reads all coarsening levels off it at once, selecting cut thresholds by hypergraph modularity; Parallel Hierarchical Unpooling (PHUnpool) inverts these maps to restore the original resolution. Selecting every level in parallel from a single hierarchy, instead of composing coarsenings sequentially, prevents structural distortion at one resolution from being inherited by the next, and we prove that it preserves at least as much information about the input hypergraph under matched first-level coarsening. We further propose a hypergraph cross-convolution (HGXConv) layer that captures polyadic interactions through degree-normalized multiplicative feature mixing. On hypergraph signal reconstruction, hypergraph classification across seven benchmarks, and node anomaly detection, HGUN outperforms state-of-the-art graph and hypergraph baselines and remains markedly more robust to network depth.

Keywords:

Geometric deep learning

hypergraph neural networks

hypergraph U-Nets

hypergraph convolution

hierarchical pooling and unpooling

hierarchical clustering

hypergraph modularity

node anomaly detection

Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets

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