用扩散引导张量网络，实现神经系统的多尺度自组织建模。
Diffusion-Guided Renormalization of Neural Systems via Tensor Networks
- 通过扩散过程生成跨尺度对称性破缺表示，结合张量网络实现可扩展粗粒化。
- 从部分观测数据中恢复神经活动的社区结构，并构建元图与联合概率函数。
- 适用于高维神经网络的非平衡动力学建模，适合系统神经科学与AI研究者。
远离平衡态时，神经系统在多尺度上自我组织。要利用神经科学和人工智能中的多尺度自组织现象，需要一个计算框架来建模随机神经轨迹的有效非平衡动力学。非平衡热力学和表征几何提供了理论基础，但我们需要可扩展的数据驱动技术，从部分子采样观测中建模高维神经网络的集体属性。重整化是一种核心的粗粒化技术，用于研究多体和非线性动力系统的涌现尺度特性。尽管在物理和机器学习中广泛应用，复杂动态网络的粗粒化仍无解，影响诸多计算科学领域。最近基于扩散的重整化方法受量子统计力学启发，在熵跃迁点（以比热或信息传输最大变化为标志）附近对网络进行粗粒化。本文探索通过生成跨尺度对称性破缺表示，使用张量网络实现神经系统的扩散引导重整化。该方法连接耗散神经系统的微观与介观动力学。在微观尺度，开发了可扩展的图推断算法，从子采样神经活动发现社区结构；利用基于社区的节点排序，扩散引导重整化通过元图和联合概率函数生成重整化群流。在介观尺度，目标是学习占据低维子空间的耗散神经轨迹的有效非平衡动力学，支持系统神经科学与人工智能中的粗粒度到精细控制。
原文摘要 · Abstract (English)
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium dynamics of stochastic neural trajectories. Non-equilibrium thermodynamics and representational geometry offer theoretical foundations, but we need scalable data-driven techniques for modeling collective properties of high-dimensional neural networks from partial subsampled observations. Renormalization is a coarse-graining technique central to studying emergent scaling properties of many-body and nonlinear dynamical systems. While widely applied in physics and machine learning, coarse-graining complex dynamical networks remains unsolved, affecting many computational sciences. Recent diffusion-based renormalization, inspired by quantum statistical mechanics, coarse-grains networks near entropy transitions marked by maximal changes in specific heat or information transmission. Here I explore diffusion-based renormalization of neural systems by generating symmetry-breaking representations across scales and offering scalable algorithms using tensor networks. Diffusion-guided renormalization bridges microscale and mesoscale dynamics of dissipative neural systems. For microscales, I developed a scalable graph inference algorithm for discovering community structure from subsampled neural activity. Using community-based node orderings, diffusion-guided renormalization generates renormalization group flow through metagraphs and joint probability functions. Towards mesoscales, diffusion-guided renormalization targets learning the effective non-equilibrium dynamics of dissipative neural trajectories occupying lower-dimensional subspaces, enabling coarse-to-fine control in systems neuroscience and artificial intelligence.
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