The Human Brain as a Combinatorial Complex
Valentina S\'anchez, \c{C}i\c{c}ek G\"uven, Koen Haak, Theodore Papamarkou, Gonzalo N\'apoles, Marie \v{S}af\'a\v{r} Postma

TL;DR
This paper introduces a novel framework for constructing combinatorial complexes from fMRI data to capture higher-order neural interactions, bridging network neuroscience and topological deep learning.
Contribution
It presents a method to directly build combinatorial complexes from neural data, incorporating higher-order dependencies that traditional graph models miss.
Findings
Successfully demonstrated the CC construction pipeline with NetSim data.
Quantified higher-order dependencies in neural signals using information-theoretic measures.
Provided a unified structure for representing both pairwise and higher-order neural interactions.
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…
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Taxonomy
TopicsTopological and Geometric Data Analysis · Functional Brain Connectivity Studies · Advanced Graph Neural Networks
