Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to eliminate issues such as over-smoothing or over-squashing, to significantly enhance the accuracy of GNN predictions, to improve the expressiveness of GNN architectures, and for numerous other goals. A plethora of HOGNN models have been introduced, and they come with diverse neural architectures, and even with different notions of what the "higher-order" means. This richness makes it very challenging to appropriately analyze and compare HOGNN models, and to decide in what scenario to use specific ones. To alleviate this, we first design an in-depth taxonomy and a blueprint for HOGNNs. This facilitates designing models that maximize performance. Then, we use our taxonomy to analyze and compare the available HOGNN models. The outcomes of our analysis are synthesized in a set of insights that help to select the most beneficial GNN model in a given scenario, and a comprehensive list of challenges and opportunities for further research into more powerful HOGNNs.

翻译：高阶图神经网络（HOGNNs）及其相关的拓扑深度学习架构是一类重要的GNN模型，它们利用超越普通边的顶点间多元关系。这些模型已被用于消除过平滑或过压缩等问题，显著提升GNN预测精度，增强GNN架构的表达能力，并实现众多其他目标。大量HOGNN模型已被提出，它们具有多样化的神经架构，甚至对“高阶”的定义也存在差异。这种丰富性使得准确分析和比较HOGNN模型、以及决定在何种场景使用特定模型变得极具挑战。为缓解这一问题，我们首先为HOGNN设计了深度分类体系与蓝图框架，这有助于构建性能最大化的模型。随后，我们运用该分类体系对现有HOGNN模型进行分析比较。分析成果凝聚为一组洞见，可帮助在给定场景中选择最有效的GNN模型，并形成涵盖挑战与机遇的全面清单，为更强大的HOGNN研究指明方向。