作者：V. M. Moskvitin N. Semenova
近年来，神经网络领域越来越多的研究人员对创建硬件实现感兴趣，其中神经元及其之间的连接是物理实现的。人工神经网络的物理实现从根本上改变了噪声影响的特征。在硬件ANN的情况下，存在许多具有不同财产的内部噪声源。本文的目的是以回声状态网络（ESN）为例，研究递归神经网络中内部噪声传播的特性，揭示抑制这种噪声的方法，并证明网络对某些类型噪声的稳定性。在本文中，我们分析了存在不相关的加性和乘性高斯白噪声的ESN。在这里，我们考虑人工神经元具有不同斜率系数的线性激活函数的情况。从只研究一个有噪声的神经元开始，我们通过考虑输入信号和记忆特性如何影响t，使问题复杂化
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.
论文链接：http://arxiv.org/pdf/2303.13262v1
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