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

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.