SuperHype: Hypergraph Generation via Graph-Superposition Decomposition

Lucas Gantes, Abele Mălan, Roberto Gheda, Robert Birke, Lydia Chen
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:32969-32993, 2026.

Abstract

Hypergraphs are graph generalizations with key applications in domains such as healthcare, where strict data privacy requirements apply, or bioinformatics, where testing new compounds is costly. However, due to their combinatorial nature, hypergraph representations are often either intractable or lead to significant information loss. For this reason, research into hypergraph synthesis is limited, and state-of-the-art approaches yield poor generation quality in terms of overall structural patterns and graph-level validity. To address such shortcomings, we introduce SuperHype, an exact and tractable hypergraph diffusion model. The core of SuperHype is the graph-superposition decomposition, a novel representation that embeds a hypergraph into a multi-layer graph, enabling a tractable representation with no loss of generalization. To generate new samples from such representations, we introduce a Graph-Superposition Transformer that treats the superposition as an interconnected sequence of layers. Moreover, we enhance the model’s performance by incorporating hypergraph-specific auxiliary features and aggregating indirect node interactions via triplet pooling. Our evaluation across five datasets shows that SuperHype generally reproduces local and global connectivity patterns with superior fidelity compared to state-of-the-art baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-gantes26a, title = {{S}uper{H}ype: Hypergraph Generation via Graph-Superposition Decomposition}, author = {Gantes, Lucas and M\u{a}lan, Abele and Gheda, Roberto and Birke, Robert and Chen, Lydia}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {32969--32993}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/gantes26a/gantes26a.pdf}, url = {https://proceedings.mlr.press/v306/gantes26a.html}, abstract = {Hypergraphs are graph generalizations with key applications in domains such as healthcare, where strict data privacy requirements apply, or bioinformatics, where testing new compounds is costly. However, due to their combinatorial nature, hypergraph representations are often either intractable or lead to significant information loss. For this reason, research into hypergraph synthesis is limited, and state-of-the-art approaches yield poor generation quality in terms of overall structural patterns and graph-level validity. To address such shortcomings, we introduce SuperHype, an exact and tractable hypergraph diffusion model. The core of SuperHype is the graph-superposition decomposition, a novel representation that embeds a hypergraph into a multi-layer graph, enabling a tractable representation with no loss of generalization. To generate new samples from such representations, we introduce a Graph-Superposition Transformer that treats the superposition as an interconnected sequence of layers. Moreover, we enhance the model’s performance by incorporating hypergraph-specific auxiliary features and aggregating indirect node interactions via triplet pooling. Our evaluation across five datasets shows that SuperHype generally reproduces local and global connectivity patterns with superior fidelity compared to state-of-the-art baselines.} }
Endnote
%0 Conference Paper %T SuperHype: Hypergraph Generation via Graph-Superposition Decomposition %A Lucas Gantes %A Abele Mălan %A Roberto Gheda %A Robert Birke %A Lydia Chen %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-gantes26a %I PMLR %P 32969--32993 %U https://proceedings.mlr.press/v306/gantes26a.html %V 306 %X Hypergraphs are graph generalizations with key applications in domains such as healthcare, where strict data privacy requirements apply, or bioinformatics, where testing new compounds is costly. However, due to their combinatorial nature, hypergraph representations are often either intractable or lead to significant information loss. For this reason, research into hypergraph synthesis is limited, and state-of-the-art approaches yield poor generation quality in terms of overall structural patterns and graph-level validity. To address such shortcomings, we introduce SuperHype, an exact and tractable hypergraph diffusion model. The core of SuperHype is the graph-superposition decomposition, a novel representation that embeds a hypergraph into a multi-layer graph, enabling a tractable representation with no loss of generalization. To generate new samples from such representations, we introduce a Graph-Superposition Transformer that treats the superposition as an interconnected sequence of layers. Moreover, we enhance the model’s performance by incorporating hypergraph-specific auxiliary features and aggregating indirect node interactions via triplet pooling. Our evaluation across five datasets shows that SuperHype generally reproduces local and global connectivity patterns with superior fidelity compared to state-of-the-art baselines.
APA
Gantes, L., Mălan, A., Gheda, R., Birke, R. & Chen, L.. (2026). SuperHype: Hypergraph Generation via Graph-Superposition Decomposition. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:32969-32993 Available from https://proceedings.mlr.press/v306/gantes26a.html.

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