CCMamba: Selective State-Space Models for Higher-Order Graph Learning on Combinatorial Complexes
This work addresses scalability and information aggregation limitations in topological deep learning for researchers and practitioners dealing with complex relational data, representing a novel method rather than an incremental improvement.
The authors tackled the problem of modeling higher-order relational structures in topological deep learning by proposing CCMamba, a unified mamba-based neural framework for combinatorial complexes, which achieved consistent performance improvements over existing methods on benchmarks while offering linear-time scalability and robustness to depth.
Topological deep learning has emerged for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. Although combinatorial complexes offer a unified topological framework, most existing topological deep learning methods rely on local message passing via attention mechanisms, which incur quadratic complexity and remain low-dimensional, limiting scalability and rank-aware information aggregation in higher-order complexes.We propose Combinatorial Complex Mamba (CCMamba), the first unified mamba-based neural framework for learning on combinatorial complexes. CCMamba reformulates message passing as a selective state-space modeling problem by organizing multi-rank incidence relations into structured sequences processed by rank-aware state-space models. This enables adaptive, directional, and long range information propagation in linear time without self attention. We further establish the theoretical analysis that the expressive power upper-bound of CCMamba message passing is the 1-Weisfeiler-Lehman test. Experiments on graph, hypergraph, and simplicial benchmarks demonstrate that CCMamba consistently outperforms existing methods while exhibiting improved scalability and robustness to depth.