This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and generalize structurally to graph reasoning problems of arbitrary input sizes. Our first contribution is a fine-grained analysis of the expressiveness of HyperGNNs, that is, the set of functions that they can realize. Our result is a hierarchy of problems they can solve, defined in terms of various hyperparameters such as depths and edge arities. Next, we analyze the learning properties of these neural networks, especially focusing on how they can be trained on a finite set of small graphs and generalize to larger graphs, which we term structural generalization. Our theoretical results are further supported by the empirical results.

翻译：本扩展摘要描述了一个分析超图神经网络（HyperGNNs）表达性、学习能力及（结构）泛化能力的框架。具体而言，我们聚焦于超图神经网络如何从有限数据集中学习，并在任意输入规模的图推理问题上实现结构泛化。我们的首个贡献是对超图神经网络表达性的细粒度分析，即其能实现的函数集合。研究结果揭示了这些网络可解决的问题层级结构，该结构通过深度、边元数等多种超参数进行定义。其次，我们分析了这些神经网络的学习特性，特别关注其如何在小规模图的有限数据集上训练，并泛化至更大规模的图——我们将此称为结构泛化。我们的理论结果得到了实证结果的进一步支持。