# The Human Brain as a Combinatorial Complex

arXiv: https://arxiv.org/abs/2511.20692 · HTML: https://mlsanity.com/paper/2511.20692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 22 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Position: Graph Learning Will Lose Relevance Due To Poor Benchmarks](https://mlsanity.com/paper/2502.14546/) (2025)
- [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)
- [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016)
- [JIDT: An information-theoretic toolkit for studying the dynamics of complex systems](https://mlsanity.com/paper/1408.3270/) (2014)
- [Greater than the parts: A review of the information decomposition approach to causal emergence](https://mlsanity.com/paper/2111.06518/) (2021)
- [Neuroscience needs Network Science](https://mlsanity.com/paper/2305.06160/) (2023)

## Abstract (arXiv)

We propose a framework for constructing combinatorial complexes (CCs) from fMRI time series data that captures both pairwise and higher-order neural interactions through information-theoretic measures, bridging topological deep learning and network neuroscience. Current graph-based representations of brain networks systematically miss the higher-order dependencies that characterize neural complexity, where information processing often involves synergistic interactions that cannot be decomposed into pairwise relationships. Unlike topological lifting approaches that map relational structures into higher-order domains, our method directly constructs CCs from statistical dependencies in the data. Our CCs generalize graphs by incorporating higher-order cells that represent collective dependencies among brain regions, naturally accommodating the multi-scale, hierarchical nature of neural processing. The framework constructs data-driven combinatorial complexes using O-information and S-information measures computed from fMRI signals, preserving both pairwise connections and higher-order cells (e.g., triplets, quadruplets) based on synergistic dependencies. Using NetSim simulations as a controlled proof-of-concept dataset, we demonstrate our CC construction pipeline and show how both pairwise and higher-order dependencies in neural time series can be quantified and represented within a unified structure. This work provides a framework for brain network representation that preserves fundamental higher-order structure invisible to traditional graph methods, and enables the application of topological deep learning (TDL) architectures to neural data.