用拓扑方法分析神经元信息流向，揭示复杂任务下的深层交互模式。
Time Series Analysis of Spiking Neural Systems via Transfer Entropy and Directed Persistent Homology
- 结合转移熵与有向持久同调，捕捉神经活动中的方向性信息流。
- 在复杂或噪声条件下，高维拓扑特征更显著，反映非成对交互模式。
- 适用于人工与生物神经系统的时序尖峰数据，可解释性强。
我们提出一种拓扑框架，通过将转移熵（TE）与有向持久同调（PH）结合，分析神经时间序列中的信息流动。TE量化神经元间的定向影响，生成加权有向图以反映动态交互；这些图再经由PH分析，实现对多尺度、多维度结构复杂性的评估。该方法应用于训练逻辑门任务的合成脉冲网络、受结构化和扰动输入影响的图像分类网络，以及标注行为事件的小鼠皮层记录数据。在所有场景中，拓扑特征均能区分任务复杂度、刺激结构与行为状态。在复杂或噪声条件下，高维特征更为突出，揭示了超越成对连接的交互模式。研究结果提供了一种将定向信息流映射到全局组织结构的系统性方法，该框架具有通用性和可解释性，特别适合具有时间分辨和二进制尖峰数据的神经系统。
原文摘要 · Abstract (English)
We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence between neurons, producing weighted, directed graphs that reflect dynamic interactions. These graphs are then analyzed using PH, enabling assessment of topological complexity across multiple structural scales and dimensions. We apply this TE+PH pipeline to synthetic spiking networks trained on logic gate tasks, image-classification networks exposed to structured and perturbed inputs, and mouse cortical recordings annotated with behavioral events. Across all settings, the resulting topological signatures reveal distinctions in task complexity, stimulus structure, and behavioral regime. Higher-dimensional features become more prominent in complex or noisy conditions, reflecting interaction patterns that extend beyond pairwise connectivity. Our findings offer a principled approach to mapping directed information flow onto global organizational patterns in both artificial and biological neural systems. The framework is generalizable and interpretable, making it well suited for neural systems with time-resolved and binary spiking data.
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