Impact of internal noise on deep neural networks

We analyze the fundamental impact of noise propagation in deep neural network (DNN) comprising nonlinear neurons and with connections optimized by training. Our motivation is to understand the impact of noise in analogue neural network realizations. We consider the influence of additive and multiplicative, correlated and uncorrelated types of internal noise in DNNs. We find general properties of the noise impact depending on the noise type, activation function, depth and the statistics of connection matrices and show that noise accumulation can be efficiently avoided. Our work is based on analytical methods predicting the noise levels in all layers of the network.