The Human Brain as a Combinatorial Complex

• URL: http://arxiv.org/abs/2511.20692v1
• Date: Sat, 22 Nov 2025 19:04:13 GMT
• Title: The Human Brain as a Combinatorial Complex
• Authors: Valentina Sánchez, Çiçek Güven, Koen Haak, Theodore Papamarkou, Gonzalo Nápoles, Marie Šafář Postma,
• Abstract summary: Current graph-based representations of brain networks miss the higher-order dependencies that characterize neural complexity.<n>We propose a framework for constructing complexes (CCs) from fMRI time series data that captures both pairwise and higher-order neural interactions.<n>This work provides a framework for brain network representation that preserves fundamental higher-order structure invisible to traditional graph methods.
• Score: 3.849079578881503
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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