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.

Internal noise in hardware deep and recurrent neural networks helps with learning

Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming the neural network into a tangible device. In this paper, we investigate how internal noise during the training of neural networks affects the final performance of recurrent and deep neural networks. We consider feedforward networks (FNN) and echo state networks (ESN) as examples. The types of noise examined originated from a real optical implementation of a neural network. However, these types were subsequently generalized to enhance the applicability of our findings on a broader scale. The noise types considered include additive and multiplicative noise, which depend on how noise influences each individual neuron, and correlated and uncorrelated noise, which pertains to the impact of noise on groups of neurons (such as the hidden layer of FNNs or the reservoir of ESNs). In this paper, we demonstrate that, in most cases, both deep and echo state networks benefit from internal noise during training, as it enhances their resilience to noise. Consequently, the testing performance at the same noise intensities is significantly higher for networks trained with noise than for those trained without it. Notably, only multiplicative correlated noise during training has minimal has almost no impact on both deep and recurrent networks.