具有时间模型和学习过程的神经网络动力学
Dynamics of neural networks with elapsed time model and learning processes
摘要：
我们介绍并研究了一种新的交互式神经网络模型，该模型结合了空间维度（例如，神经元在皮层上的位置）和一些学习过程。每个神经网络的动态是通过经过时间模型来描述的，也就是说，神经元是由自上次放电以来经过的时间来描述的，并且所选择的学习过程基本上是从Hebbian规则中得到的启发。然后我们得到一个积分微分方程系统，在弱关联的情况下，利用熵方法和Doeblin理论分析了该系统向定态的收敛性.我们还考虑了神经活动比学习过程更快的情况，并给出了可以近似动态的条件，即通过具有类似稳态轮廓的解决方案。对于更强的互连，我们提出了一些数值模拟，观察系统的参数如何可以给出不同的行为和图案的形成。
英文摘要：
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed time model, that is, the neurons are described by the elapsed time since their last discharge and the chosen learning processes are essentially inspired from the Hebbian rule. We then obtain a system of integro-differential equations, from which we analyze the convergence to stationary states by the means of entropy method and Doeblin's theory in the case of weak interconnections. We also consider the situation where neural activity is faster than the learning process and give conditions where one can approximate the dynamics by a solution with a similar profile of a steady state. For stronger interconnections, we present some numerical simulations to observe how the parameters of the system can give different behaviors and pattern formations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
