  Hypergraphs are vital in modelling data with higher-order relations
containing more than two entities, gaining prominence in machine learning and
signal processing. Many hypergraph neural networks leverage message passing
over hypergraph structures to enhance node representation learning, yielding
impressive performances in tasks like hypergraph node classification. However,
these message-passing-based models face several challenges, including
oversmoothing as well as high latency and sensitivity to structural
perturbations at inference time. To tackle those challenges, we propose an
alternative approach where we integrate the information about hypergraph
structures into training supervision without explicit message passing, thus
also removing the reliance on it at inference. Specifically, we introduce
Hypergraph-MLP, a novel learning framework for hypergraph-structured data,
where the learning model is a straightforward multilayer perceptron (MLP)
supervised by a loss function based on a notion of signal smoothness on
hypergraphs. Experiments on hypergraph node classification tasks demonstrate
that Hypergraph-MLP achieves competitive performance compared to existing
baselines, and is considerably faster and more robust against structural
perturbations at inference.
