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.

该研究论文旨在建立协作网络核心层的算法稳定性，并提供泛化保证。分析揭示了协作网络中超图滤波器的设计原则，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。论文还通过实验结果在现实世界数据集上进行了说明。