# CCMamba: Topologically-Informed Selective State-Space Networks on Combinatorial Complexes for Higher-Order Graph Learning

arXiv: https://arxiv.org/abs/2601.20518 · HTML: https://mlsanity.com/paper/2601.20518/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Video, motion and generative Mamba models, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 6 of its 62 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Placed in

- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 6 of 6)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)

## Abstract (arXiv)

Topological deep learning has emerged as a powerful paradigm for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. While combinatorial complexes (CCs) offer a unified topological foundation for the higher-order graph learning, existing topological deep learning methods rely heavily on local message passing and attention mechanisms. These suffer from quadratic complexity and local neighborhood constraints, limiting their scalability and capacity for rank-aware, long-range dependency modeling. To overcome these challenges, we propose Combinatorial Complex Mamba (CCMamba), the first unified Mamba-based neural framework for learning on combinatorial complexes. CCMamba reformulates higher-order message passing as a selective state-space modeling problem by linearizing multi-rank incidence relations into structured, rank-aware sequences. This architecture enables adaptive, directional, and long-range information propagation in linear time bypassing the scalability bottlenecks of self-attention. Theoretically, we further establish that the expressive power of CCMamba is upper-bounded by the 1-dimensional combinatorial complex Weisfeiler-Lehman (1-CCWL) test. Extensive experiments across graph, hypergraph, and simplicial benchmarks demonstrate that CCMamba consistently outperforms existing methods while exhibiting superior scalability and remarkable robustness against over-smoothing in deep architectures.