The Human Brain as a Combinatorial Complex

2025-11-22

AI Summary

Conventional graph models capture only pairwise neural interactions, failing to represent irreducible higher-order synergistic dependencies prevalent in brain networks. Method: We propose the first data-driven, statistical-dependence-based framework for constructing combinatorial complexes (CCs) from fMRI time series. Leveraging O-information and S-information, our method quantifies higher-order synergy and redundancy, directly extracting triplet-, quadruplet-, and other multi-node topological cells from empirical data—beyond pairwise edges. Contribution/Results: This approach transcends graph limitations by encoding both pairwise and multi-way neural interactions within a unified topological structure. Validation via NetSim simulations and empirical analyses demonstrates that the learned CCs robustly capture critical higher-order topological features missed by graph models, significantly enhancing the representational capacity of downstream topological deep learning models for characterizing complex brain network dynamics.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Capturing higher-order neural interactions beyond pairwise dependencies in fMRI data
• Constructing combinatorial complexes using information-theoretic measures from neural signals
• Providing unified representation for multi-scale neural processing through topological structures

Innovation

• Constructs combinatorial complexes from fMRI data
• Uses O-information and S-information measures
• Captures both pairwise and higher-order neural interactions