Analytical form of Fisher information matrix of bipoloar-activation-function-based multilayer perceptrons

For the widely used multilayer perceptrons (MLPs), the existed singularities in the parameter space have seriously affected the learning dynamics of MLPs, which cause several singular learning behaviors. Since the Fisher information matrix (FIM) plays a significant role in analyzing the singular learning dyanmics of MLPs, it is very worthy to obtain the analytical form of FIM to do further investigation. In this paper, by choosing the bipolar error function as the activation function, the analytical form of FIM are obtained, where the validity of the obtained results are verified by taking three experiments.