论文标题
具有随机线性相互作用的神经元网络的渐近行为
Asymptotic behavior of a network of neurons with random linear interactions
论文作者
论文摘要
我们研究了线性霍普菲尔德神经元网络中非对称神经元动力学的渐近行为。神经元之间的相互作用是由以随机耦合为中心的I.I.D.建模的。随机变量，具有所有订单的有限矩。我们证明，如果网络的初始条件是一组I.I.D.随机变量和独立于突触权重，极限系统的每个组件都被描述为具有中心高斯过程的初始条件的相应坐标的总和，其协方差函数可以用修改后的贝塞尔函数来描述。这个过程不是马尔可夫人。在随机重量方面，几乎肯定是法律上的收敛。我们的方法基本上是基于矩的方法来获得中心限制定理的方法。
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of all orders. We prove that if the initial condition of the network is a set of i.i.d. random variables and independent of the synaptic weights, each component of the limit system is described as the sum of the corresponding coordinate of the initial condition with a centered Gaussian process whose covariance function can be described in terms of a modified Bessel function. This process is not Markovian. The convergence is in law almost surely with respect to the random weights. Our method is essentially based on the method of moments to obtain a Central Limit Theorem.
