论文标题
具有经过的时间模型和学习过程的神经网络的动态
Dynamics of neural networks with elapsed time model and learning processes
论文作者
论文摘要
我们介绍并研究了一种相互作用的神经网络的新模型，该模型结合了空间维度（例如神经元在皮层中的位置）和一些学习过程。每个神经网络的动态都是通过经过的时间模型来描述的，也就是说，自上次放电以来，神经元描述了神经元，并且所选的学习过程基本上是从Hebbian规则中启发的。然后，我们获得了一个差异方程的系统，在弱互连的情况下，通过熵方法和多伯林理论分析了固定状态的收敛。我们还考虑了神经活动比学习过程更快的情况，并给出可以通过具有相似稳态状态的解决方案近似动力学的条件。对于更强的互连，我们提供了一些数值模拟，以观察系统的参数如何提供不同的行为和模式形成。
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.
