Lift me up: the impact of liftings on hypergraph neural networks

Marco Montagna, Simone Scardapane, Lev Telyatnikov
Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling, PMLR 326:456-474, 2026.

Abstract

Hypergraph neural networks (HNNs) have become a powerful tool for modeling higher-order interactions in relational data. However, most HNN methods assume that the hypergraph structure is given. Whenever the data originates from a graph or a point cloud (which is common in practice) this requires a transformation step known as \textit{lifting}. Despite its crucial role, the lifting process remains largely understudied and is often handled via ad hoc heuristics. In this work, we present the first systematic evaluation of hypergraph lifting strategies. We study seven diverse lifting methods and assess their impact on downstream classification tasks across a variety of datasets and three state-of-the-art hypergraph models. Moreover, we compare these lifting-based approaches against standard graph neural networks, demonstrating that finding the appropriate higher-order structure allows hypergraph models to outperform traditional graph baselines. Notably, our findings reveal that the choice of lifting often has a greater impact on performance than the choice of model architecture. While some liftings perform better than others, no single lifting consistently dominates on all datasets. These results suggest that further advances in hypergraph learning may come less from architectural innovations and more from better ways of constructing hypergraph structures.

Cite this Paper

BibTeX
@InProceedings{pmlr-v326-montagna26a, title = {Lift me up: the impact of liftings on hypergraph neural networks}, author = {Montagna, Marco and Scardapane, Simone and Telyatnikov, Lev}, booktitle = {Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling}, pages = {456--474}, year = {2026}, editor = {Pouplin, Alison and Vadgama, Sharvaree and Bekkers, Erik and Kaba, Sékou-Oumar and Lawrence, Hannah and Lecha, Manuel and Baker, Elizabeth and Suk, Julian and Walters, Robin and Tomczak, Jakub and Jegelka, Stefanie}, volume = {326}, series = {Proceedings of Machine Learning Research}, month = {26 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v326/main/assets/montagna26a/montagna26a.pdf}, url = {https://proceedings.mlr.press/v326/montagna26a.html}, abstract = {Hypergraph neural networks (HNNs) have become a powerful tool for modeling higher-order interactions in relational data. However, most HNN methods assume that the hypergraph structure is given. Whenever the data originates from a graph or a point cloud (which is common in practice) this requires a transformation step known as \textit{lifting}. Despite its crucial role, the lifting process remains largely understudied and is often handled via ad hoc heuristics. In this work, we present the first systematic evaluation of hypergraph lifting strategies. We study seven diverse lifting methods and assess their impact on downstream classification tasks across a variety of datasets and three state-of-the-art hypergraph models. Moreover, we compare these lifting-based approaches against standard graph neural networks, demonstrating that finding the appropriate higher-order structure allows hypergraph models to outperform traditional graph baselines. Notably, our findings reveal that the choice of lifting often has a greater impact on performance than the choice of model architecture. While some liftings perform better than others, no single lifting consistently dominates on all datasets. These results suggest that further advances in hypergraph learning may come less from architectural innovations and more from better ways of constructing hypergraph structures.} }
Endnote
%0 Conference Paper %T Lift me up: the impact of liftings on hypergraph neural networks %A Marco Montagna %A Simone Scardapane %A Lev Telyatnikov %B Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling %C Proceedings of Machine Learning Research %D 2026 %E Alison Pouplin %E Sharvaree Vadgama %E Erik Bekkers %E Sékou-Oumar Kaba %E Hannah Lawrence %E Manuel Lecha %E Elizabeth Baker %E Julian Suk %E Robin Walters %E Jakub Tomczak %E Stefanie Jegelka %F pmlr-v326-montagna26a %I PMLR %P 456--474 %U https://proceedings.mlr.press/v326/montagna26a.html %V 326 %X Hypergraph neural networks (HNNs) have become a powerful tool for modeling higher-order interactions in relational data. However, most HNN methods assume that the hypergraph structure is given. Whenever the data originates from a graph or a point cloud (which is common in practice) this requires a transformation step known as \textit{lifting}. Despite its crucial role, the lifting process remains largely understudied and is often handled via ad hoc heuristics. In this work, we present the first systematic evaluation of hypergraph lifting strategies. We study seven diverse lifting methods and assess their impact on downstream classification tasks across a variety of datasets and three state-of-the-art hypergraph models. Moreover, we compare these lifting-based approaches against standard graph neural networks, demonstrating that finding the appropriate higher-order structure allows hypergraph models to outperform traditional graph baselines. Notably, our findings reveal that the choice of lifting often has a greater impact on performance than the choice of model architecture. While some liftings perform better than others, no single lifting consistently dominates on all datasets. These results suggest that further advances in hypergraph learning may come less from architectural innovations and more from better ways of constructing hypergraph structures.
APA
Montagna, M., Scardapane, S. & Telyatnikov, L.. (2026). Lift me up: the impact of liftings on hypergraph neural networks. Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling, in Proceedings of Machine Learning Research 326:456-474 Available from https://proceedings.mlr.press/v326/montagna26a.html.

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