Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to exploit more complex relationships. In particular, the hypergraph collaborative networks yield superior results compared to other hypergraph neural networks for various semi-supervised learning tasks. The collaborative network can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given hypergraph. In this paper, we aim to establish the algorithmic stability of the core layer of the collaborative network and provide generalization guarantees. The analysis sheds light on the design of hypergraph filters in collaborative networks, for instance, how the data and hypergraph filters should be scaled to achieve uniform stability of the learning process. Some experimental results on real-world datasets are presented to illustrate the theory.

翻译：图神经网络已被证明在利用样本间的成对关系方面非常有效。近年来，已有若干成功的研究将图神经网络推广至超图神经网络，以挖掘更复杂的关系。特别地，超图协作网络在各种半监督学习任务中展现出优于其他超图神经网络的结果。该协作网络通过将顶点嵌入与超边嵌入的生成构建为联合优化问题，并利用它们在重构给定超图中的一致性，共同提供高质量的顶点嵌入和超边嵌入。本文旨在建立协作网络核心层的算法稳定性，并给出泛化性能保证。该分析揭示了协作网络中超图滤波器的设计原理，例如，如何对数据和超图滤波器进行缩放以实现学习过程的统一稳定性。我们在真实数据集上展示了部分实验结果，以阐释相关理论。