Noise Impact on a Recurrent Neural Network with a Linear Activation Function

In recent years, more and more researchers in the field of artificial neural networks have been interested in creating hardware implementations where neurons and the connection between them are realized physically. Such networks solve the problem of scaling and increase the speed of obtaining and processing information, but they can be affected by internal noise.
In this paper we analyze an echo state neural network (ESN) in the presence of uncorrelated additive and multiplicative white Gaussian noise. Here we consider the case where artificial neurons have a linear activation function with different slope coefficients. We consider the influence of the input signal, memory and connection matrices on the accumulation of noise. We have found that the general view of variance and the signal-to-noise ratio of the ESN output signal is similar to only one neuron. The noise is less accumulated in ESN with a diagonal reservoir connection matrix with a large “blurring” coefficient. This is especially true of uncorrelated multiplicative noise.