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

In this paper we analyze an echo state neural network (ESN) in the presence of uncorrelated additive and multiplicative white Gaussian noise. Here consider case where artificial neurons have a linear activation function with different slope coefficients. We influence input signal, memory connection matrices on accumulation found that general view variance signal-to-noise ratio ESN output signal is similar to only one neuron. The noise less accumulated diagonal reservoir matrix large “blurring” coefficient. This especially true