How noise impacts on trained echo-state neural network

In this paper we analyse the impact of additive and multiplicative uncorrelated white Gaussian noise on trained echo-state neural network. The network was trained to predict chaotic time series of Mackey-Glass equation. Here we show that mean squared error and dispersion of the output signal produced by trained echo-state network, grows with dispersion of noise sources linearly. Moreover, we show how these two types of noise impact on the statistics of the output signal on the example of dependency of dispersion of the output signal on its mean value.