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.

翻译：超图在建模包含两个以上实体的高阶关系数据中至关重要，在机器学习和信号处理领域日益凸显其重要性。许多超图神经网络利用超图结构上的消息传递来增强节点表示学习，在超图节点分类等任务中取得了显著成效。然而，这些基于消息传递的模型面临若干挑战，包括过平滑问题以及推理时的高延迟和对结构扰动的敏感性。为应对这些挑战，我们提出一种替代方法：将超图结构信息整合到训练监督中，避免显式消息传递，从而在推理时也无需依赖它。具体而言，我们引入Hypergraph-MLP，一种针对超图结构数据的新型学习框架，该学习模型为简单的多层感知器（MLP），通过基于超图信号平滑性概念的损失函数进行监督。在超图节点分类任务上的实验表明，Hypergraph-MLP在性能上与现有基线方法相当，且在推理时速度显著更快且对结构扰动更具鲁棒性。