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.

翻译：我们提出了一种从fMRI时间序列数据构建组合复形的框架，该框架通过信息论度量同时捕捉成对和高阶神经相互作用，从而桥接拓扑深度学习与网络神经科学。当前基于图的大脑网络表示系统性地遗漏了表征神经复杂性的高阶依赖关系，其中信息处理常涉及无法分解为成对关系的协同相互作用。与将关系结构映射到高阶域的拓扑提升方法不同，我们的方法直接从数据的统计依赖关系构建组合复形。我们的组合复形通过纳入表示脑区间集体依赖关系的高阶单元来推广图结构，自然地适应神经处理的多尺度、分层特性。该框架使用从fMRI信号计算得到的O-信息和S-信息度量构建数据驱动的组合复形，基于协同依赖关系同时保留成对连接和高阶单元（如三元组、四元组）。通过使用NetSim模拟作为受控概念验证数据集，我们展示了组合复形构建流程，并说明了神经时间序列中的成对和高阶依赖关系如何能在统一结构中进行量化和表示。这项工作提供了一种大脑网络表示框架，该框架保留了传统图方法不可见的基本高阶结构，并使拓扑深度学习架构能够应用于神经数据。