Graph Rules for Recurrent Neural Network Dynamics
Graph Rules for Recurrent Neural Network Dynamics
复制标题
递归神经网络动力学的图规则
DOI：
10.1090/noti2661
复制
发表时间：
2023
影响因子：
--
通讯作者：
Morrison, Katherine
中科院分区：
文献类型：
--
作者：
Curto, Carina;Morrison, Katherine
大脑中的神经元不断闪烁活动，这些活动可以是自发的，也可以是对刺激的反应[LBH09]。由于正反馈回路和失控激励的可能性，真实的神经网络通常具有丰富的抑制作用，可用于塑造和稳定动态[YMSL05，KAY14]。这种网络中的兴奋性神经元表现出复杂的连接模式，其结构控制着允许的活动模式。因此，神经科学的一个中心问题是：网络连接如何塑造动态？对于给定的模型，这个问题变成了数学挑战。目标是发展一种将非线性动力系统的属性与其基础图直接联系起来的理论。这样的理论可以提供关于网络连接如何限制真实大脑活动的见解和假设。它还为以数学上易于处理的方式建模神经现象开辟了新的可能性。
Neurons in the brain are constantly flickering with activity, which can be spontaneous or in response to stimuli [LBH09]. Because of positive feedback loops and the potential for runaway excitation, real neural networks often possess an abundance of inhibition that serves to shape and stabilize the dynamics [YMSL05, KAY14]. The excitatory neurons in such networks exhibit intricate patterns of connectivity, whose structure controls the allowed patterns of activity. A central question in neuroscience is thus: how does network connectivity shape dynamics? For a given model, this question becomes a mathematical challenge. The goal is to develop a theory that directly relates properties of a nonlinear dynamical system to its underlying graph. Such a theory can provide insights and hypotheses about how network connectivity constrains activity in real brains. It also opens up new possibilities for modeling neural phenomena in a mathematically tractable way.