The Human Brain as a Combinatorial Complex

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 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.