Higher-order graph neural networks (HOGNNs) 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.

高阶图神经网络（HOGNNs）是一类重要的 GNN 模型，能够利用顶点之间的多系关系来解决过度平滑或过度压缩等问题，显著提高 GNN 预测准确性，改进 GNN 架构，并能帮助选择最适合特定场景的 GNN 模型，提出了具有挑战与机遇的 HOGNN 进一步研究的全面列表。

高阶图神经网络揭秘

Demystifying Higher-Order Graph Neural Networks

Although recent advances in higher-order Graph Neural Networks (GNNs) improve
the theoretical expressiveness and molecular property predictive performance,
they often fall short of the empirical performance of models that explicitly
use fragment information as inductive bias. However, for these approaches,
there exists no theoretic expressivity study. In this work, we propose the
Fragment-WL test, an extension to the well-known Weisfeiler & Leman (WL) test,
which enables the theoretic analysis of these fragment-biased GNNs. Building on
the insights gained from the Fragment-WL test, we develop a new GNN
architecture and a fragmentation with infinite vocabulary that significantly
boosts expressiveness. We show the effectiveness of our model on synthetic and
real-world data where we outperform all GNNs on Peptides and have 12% lower
error than all GNNs on ZINC and 34% lower error than other fragment-biased
models. Furthermore, we show that our model exhibits superior generalization
capabilities compared to the latest transformer-based architectures,
positioning it as a robust solution for a range of molecular modeling tasks.

通过理论分析和扩展 Fragment-WL 测试，我们提出了一种基于片段信息的高阶图神经网络架构，大大增强了理论表达力，并在合成和真实数据中优于其它片段偏置模型，以及与最新的基于 Transformer 的架构相比表现出更强大的泛化能力，成为分子建模任务的可靠解决方案。