arXiv:2511.20692q-bio.NCcs.LG2025-11中稿 · NeurIPS

用信息论方法构建脑网络的高阶组合结构,捕捉传统图模型遗漏的协同活动。

The Human Brain as a Combinatorial Complex

  • 从fMRI数据中直接构建组合复形,融合成对与高阶神经耦合关系。
  • 通过O信息和S信息量化协同依赖,保留三元组、四元组等高阶单元。
  • 适合研究脑功能连接复杂性或想应用拓扑深度学习的人。

我们提出一种从fMRI时间序列构建组合复形(CCs)的框架,利用信息论度量捕捉神经活动中的成对及高阶相互作用,连接拓扑深度学习与网络神经科学。现有基于图的脑网络表示方法系统性忽略了表征神经复杂性的高阶依赖,而信息处理常涉及无法分解为成对关系的协同互动。不同于将关系结构映射到高阶域的拓扑提升方法,我们的方法直接从数据统计依赖构建CCs。CCs通过包含代表多区域集体依赖的高阶胞腔,扩展了图结构,自然适应神经处理的多尺度、层次化特性。该框架使用从fMRI信号计算的O信息和S信息度量,构建数据驱动的组合复形,保留成对连接与高阶单元(如三元组、四元组),基于协同依赖。以NetSim模拟数据作为受控验证,我们展示了该构建流程,并证明成对与高阶依赖可在统一结构中被量化与表征。本工作提供了一种保留传统图方法所忽视的高阶结构的脑网络表示框架,使拓扑深度学习(TDL)架构可应用于神经数据。

原文摘要 · Abstract (English)

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.

脑网络高阶交互拓扑学习

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