Impact of internal noise on convolutional neural networks

In this paper, we investigate the impact of noise on a simplified trained convolutional network. The types of noise studied originate from a real optical implementation of a neural network, but we generalize these types to enhance the applicability of our findings on a broader scale. The noise types considered include additive and multiplicative noise, which relate to how noise affects individual neurons, as well as correlated and uncorrelated noise, which pertains to the influence of noise across one layers. We demonstrate that the propagation of uncorrelated noise primarily depends on the statistical properties of the connection matrices. Specifically, the mean value of the connection matrix following the layer impacted by noise governs the propagation of correlated additive noise, while the mean of its square contributes to the accumulation of uncorrelated noise. Additionally, we propose an analytical assessment of the noise level in the network's output signal, which shows a strong correlation with the results of numerical simulations.