Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on topological higher-order GNNs overcome that boundary, these models often depend on assumptions about sub-structures of graphs. Specifically, topological GNNs leverage the prevalence of cliques, cycles, and rings to enhance the message-passing procedure. Our study presents a novel perspective by focusing on simple paths within graphs during the topological message-passing process, thus liberating the model from restrictive inductive biases. We prove that by lifting graphs to path complexes, our model can generalize the existing works on topology while inheriting several theoretical results on simplicial complexes and regular cell complexes. Without making prior assumptions about graph sub-structures, our method outperforms earlier works in other topological domains and achieves state-of-the-art results on various benchmarks.

翻译：图神经网络（GNN）尽管在不同任务上取得了显著性能，但在理论上受限于1-韦菲勒-莱曼测试，导致图表达能力存在局限。尽管先前关于拓扑高阶GNN的研究突破了这一界限，但这些模型往往依赖于对图子结构的假设。具体而言，拓扑GNN利用团、环和圈等结构的普遍性来增强消息传递过程。本研究提出了一种新颖视角，在拓扑消息传递过程中聚焦于图中的简单路径，从而使模型摆脱了限制性的归纳偏置。我们证明，通过将图提升为路径复形，我们的模型能够泛化现有拓扑相关工作，同时继承单纯复形和正则胞腔复形上的若干理论结果。无需预先假设图子结构，我们的方法在先前其他拓扑领域的成果上表现更优，并在多种基准测试上取得了最先进的结果。