Noise Benefits in Complex-Valued Neural Networks

In this paper, we investigate the effectiveness of noise that is injected into the output of complex-valued neural networks. We first establish the equivalence between the complex backpropagation algorithm and the complex expectation maximization algorithm from the perspective of maximum probability likelihood estimation, then based on this equivalence we establish the separation hyperplane to distinguish the beneficial noise from the harmful noise in the sense of speeding up the training. The theoretical findings are validated by numerical simulations on the MNIST and Fashion MNIST data sets.