Application of the error function in analyzing the learning dynamics near singularities of the multilayer perceptrons

Analyzing the learning dynamics near singularities of the feedforward neural networks is a research hotspot in recent years, but the unintegrability of the log-sigmoid function make us hardly to detailed analyze the singular behaviors of the multilayer perceptrons. In this paper, the error function is adopted to the activation function of the multilayer perceptrons because of its integrability. We obtain the explicit expressions of two important expectations based on which we would easily obtain the averaged learning equations of the multilayer perceptrons and then could deeply analyzed the learning dynamics near singularities. The simulation results indicate that it is proper to use the error function to be the activation function of the multilayer perceptrons in analyzing the singular behaviors.