Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes. However, existing Weisfeiler-Leman type expressivity analyses are typically developed on different structural domains and rely on domain-specific neighborhood systems, making their expressive powers difficult to compare within a common formalism. In this paper, we introduce the Combinatorial Complex Weisfeiler-Leman (CCWL) framework, a unified expressive power refinement defined on combinatorial complexes. By exploiting the ability of combinatorial complexes to represent both set-type relations and part-whole hierarchies, CCWL performs topological color refinement through four structural neighborhoods: boundary, co-boundary, lower adjacency, and upper adjacency. We show that, under specified lifting maps, CCWL can simulate several domain-specific WL-type refinements, thereby providing a common theoretical baseline for analyzing topological message passing. We further study the neighborhood sufficiency problem and prove that, under explicit coverage conditions, a reduced refinement using only lower- and upper-adjacent bridge information preserves the distinguishing power of the full four-neighborhood CCWL refinement. Guided by this theoretical result, we instantiate the reduced refinement as the Combinatorial Complex Isomorphism Network (CCIN). Experiments on synthetic and real-world benchmarks demonstrate that CCIN achieves competitive performance against representative graph and topological neural network baselines. Ablation studies and resource-efficiency analyses further support the effectiveness of the proposed lower/upper-neighborhood design.

翻译：拓扑神经网络已涌现为建模超图、单纯复形、胞腔复形等超越成对图结构的高阶关系结构的有效工具。然而，现有Weisfeiler-Lehman类型表达能力分析通常针对不同结构域开发，并依赖特定于该域的邻域系统，导致其表达能力难以在统一形式体系下进行比较。本文提出组合复形Weisfeiler-Lehman（CCWL）框架，这是一种定义在组合复形上的统一表达能力精化方法。通过利用组合复形既能表征集合型关系又能表征部分-整体层次结构的能力，CCWL通过四种结构邻域（边界、共边界、下邻接和上邻接）执行拓扑颜色精化。我们证明，在特定提升映射下，CCWL可模拟多种特定域WL类型精化，从而为分析拓扑消息传递提供统一理论基线。进一步研究邻域充分性问题，证明在显式覆盖条件下，仅使用下邻接与上邻接桥信息的约简精化可保留完整四邻域CCWL精化的区分能力。基于该理论结果，我们将该约简精化实例化为组合复形同构网络（CCIN）。在合成与真实世界基准上的实验表明，CCIN在代表性图神经网络和拓扑神经网络基线中取得具有竞争力的性能。消融实验与资源效率分析进一步验证了所提出的下/上邻域设计的有效性。