{"ID":2838338,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20692","arxiv_id":"2511.20692","title":"The Human Brain as a Combinatorial Complex","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.","short_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 sys...","url_abs":"https://arxiv.org/abs/2511.20692","url_pdf":"https://arxiv.org/pdf/2511.20692v2","authors":"[\"Valentina Sánchez\",\"Çiçek Güven\",\"Koen Haak\",\"Theodore Papamarkou\",\"Gonzalo Nápoles\",\"Marie Šafář Postma\"]","published":"2025-11-22T19:04:13Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\",\"cs.LG\"]","methods":"[]","has_code":false}