In recent years, more and more researchers in the field of neural networks are interested in creating hardware implementations where neurons and the connection between them are realized physically. The physical implementation of ANN fundamentally changes the features of noise influence. In the case hardware ANNs, there are many internal sources of noise with different properties. The purpose of this paper is to study the peculiarities of internal noise propagation in recurrent ANN on the example of echo state network (ESN), to reveal ways to suppress such noises and to justify the stability of networks to some types of noises. In this paper we analyse ESN in presence of uncorrelated additive and multiplicative white Gaussian noise. Here we consider the case when artificial neurons have linear activation function with different slope coefficients. Starting from studying only one noisy neuron we complicate the problem by considering how the input signal and the memory property affect the accumulation of noise in ESN. In addition, we consider the influence of the main types of coupling matrices on the accumulation of noise. So, as such matrices, we take a uniform matrix and a diagonal-like matrices with different coefficients called "blurring" coefficient. We have found that the general view of variance and signal-to-noise ratio of ESN output signal is similar to only one neuron. The noise is less accumulated in ESN with diagonal reservoir connection matrix with large "blurring" coefficient. Especially it concerns uncorrelated multiplicative noise.

翻译：近年来，神经网络领域越来越多的研究者致力于硬件实现，即神经元及其连接通过物理方式实现。人工神经网络的物理实现从根本上改变了噪声影响特征。在硬件神经网络中，存在大量具有不同特性的内部噪声源。本文旨在以回声状态网络为例，研究递归神经网络中内部噪声传播的特殊性，揭示抑制此类噪声的方法，并论证网络对特定类型噪声的稳定性。我们分析了存在不相关加性与乘性白高斯噪声时的回声状态网络性能。研究中假设人工神经元采用具有不同斜率系数的线性激活函数。从单个噪声神经元的研究出发，我们逐步增加复杂度，考察输入信号与记忆特性对回声状态网络噪声累积的影响。此外，我们还分析了主要耦合矩阵类型对噪声累积的作用。具体而言，采用均匀矩阵与具有不同“模糊”系数的类对角矩阵作为耦合矩阵。研究发现，回声状态网络输出信号的方差与信噪比整体表现与单神经元情况相似。当采用具有较大“模糊”系数的对角储层连接矩阵时，噪声累积较少，这一特性对不相关乘性噪声尤为显著。