Dynamics of driven networks: computation in recurrent neural circuits

我研究的长期目标是使用动力系统和信息论的数学工具来提出驱动递归网络计算的理论。*在这个提议中，我的目标是研究网络体系结构和网络内部由外部信号驱动的可变性之间的关系。*生物或人工神经元网络如果它们的连接是分布式的并包含反馈环路，则称为递归网络。这种网络可以执行非常复杂的计算，这一点从它们在大脑中的普遍存在和在机器学习中不断增加的使用中就可以看出。然而，它们是出了名的难以控制，而且它们的动态通常很少被理解，特别是在存在外部强迫的情况下。这是因为循环网络是典型的混沌系统，这意味着它们具有丰富而敏感的动态，导致对输入的不同反应。连接的排列和强度如何影响网络中混乱的严重性和分布性？这对调整连接以塑造网络功能的方式有何影响？我对这些问题进行了三个具体的研究，分别针对大脑和人工网络。目的1研究空间结构的连通性如何在速率模型和尖峰模型中形成混沌吸引子，并将理论结果与大脑皮层回路的研究联系起来。目的2探讨混沌和突触可塑性是如何相互作用形成递归网络的，并试图在正在进行的实验中预测来自脑机接口的人工输入如何引导运动皮质的连接。目标3开发了利用混沌和混沌吸引子在训练期间改变人工网络的连接权的方案。*我的研究计划有两个相辅相成的目标：(I)对驱动的循环网络动力学有数学上的严格理解，以及(Ii)开发一个分析和建模框架来解释和指导神经科学实验。两者都有切实的多学科应用，从开发可以直接与大脑中的神经电路通信的植入物，到设计人工神经网络。**

The long-term goal of my research is to advance a theory of driven recurrent network computation using mathematical tools from dynamical systems and information theory. ***In this proposal, my goal is to investigate the relationship between network architecture and the variability that emerges within networks driven by external signals.******Networks of neurons either biological or artificial are called recurrent if their connections are distributed and contain feedback loops. Such networks can perform remarkably complex computations, as evidenced by their ubiquity throughout the brain and ever-increasing use in machine learning. They are, however, notoriously hard to control and their dynamics are generally poorly understood, especially in the presence of external forcing. This is because recurrent networks are typically chaotic systems, meaning they have rich and sensitive dynamics leading to variable responses to inputs. How do the arrangement and strength of connections affect how severe and distributed chaos is in a network? What is the influence on the way connections are modulated to shape network function? I investigate these questions in three specific research aims directed at both the brain, and artificial networks. Aim 1 investigates how spatially structured connectivity shapes chaotic attractors in both rate and spiking models, and connects theoretical results to the study of cortical circuits. Aim 2 probes how chaos and synaptic plasticity interact to shape recurrent networks, and seeks to predict how artificial inputs from brain-computer interfaces steer motor cortex connectivity in ongoing experiments. Aim 3 develops schemes to take advantage of chaos and chaotic attractors to alter connection weights of artificial networks during training. ******My research program has two complementary objectives: (i) a mathematically rigorous understanding of driven recurrent network dynamics and (ii) the development of an analysis and modelling framework to interpret and guide neuroscience experiments. Both have tangible multidisciplinary applications ranging from the development of implants that can directly communicate with neural circuits in the brain, to the design of artificial neural networks. **