标题： 通过深度雅可比估计表征相互作用子系统之间的控制 显示英文标题

标题： Characterizing control between interacting subsystems with deep Jacobian estimation

摘要： 生物功能通过多个子系统的动态相互作用产生，包括脑区之间的相互作用、基因调控网络内部的相互作用等。 理解这些系统的一种常见方法是建模每个子系统的动态特性，并表征它们之间的通信。 另一种方法是通过控制理论的视角：子系统之间如何相互控制。 这种方法涉及推断子系统之间控制的方向性、强度以及上下文调制。 然而，目前用于理解子系统控制的方法通常是线性的，无法充分描述非线性复杂系统所支持的丰富上下文效应。 为弥补这一差距，我们设计了一个数据驱动的非线性控制理论框架，通过动力学的雅可比矩阵来表征子系统之间的相互作用。 我们通过提出一种名为雅可比ODE的深度学习方法，解决了从时间序列数据中学习雅可比矩阵的挑战，该方法利用雅可比矩阵的性质，仅从数据中直接估计任意动力学系统的雅可比矩阵。 我们证明，雅可比ODE在具有挑战性的系统（包括高维混沌系统）上优于现有的雅可比估计方法。 我们将该方法应用于一个在工作记忆选择任务上训练的多区域循环神经网络（RNN），结果表明，在学习过程中，“感觉”区域对“认知”区域的控制增强。 此外，我们利用雅可比ODE直接控制训练好的RNN，从而实现了对其行为的精确操控。 我们的研究为生物子系统之间相互作用的理论基础和数据驱动的理解奠定了基础。 显示英文摘要

摘要： Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics of each subsystem and characterize communication between them. An alternative approach is through the lens of control theory: how the subsystems control one another. This approach involves inferring the directionality, strength, and contextual modulation of control between subsystems. However, methods for understanding subsystem control are typically linear and cannot adequately describe the rich contextual effects enabled by nonlinear complex systems. To bridge this gap, we devise a data-driven nonlinear control-theoretic framework to characterize subsystem interactions via the Jacobian of the dynamics. We address the challenge of learning Jacobians from time-series data by proposing the JacobianODE, a deep learning method that leverages properties of the Jacobian to directly estimate it for arbitrary dynamical systems from data alone. We show that JacobianODEs outperform existing Jacobian estimation methods on challenging systems, including high-dimensional chaos. Applying our approach to a multi-area recurrent neural network (RNN) trained on a working memory selection task, we show that the "sensory" area gains greater control over the "cognitive" area over learning. Furthermore, we leverage the JacobianODE to directly control the trained RNN, enabling precise manipulation of its behavior. Our work lays the foundation for a theoretically grounded and data-driven understanding of interactions among biological subsystems.