Regularization and feedforward artificial neural network training with noise

Regularization is a method used for controlling the complexity of models. Explicit regularization uses a modifier term, incorporating a-priori knowledge about the function to be approximated by Feedforward Artificial Networks, that is added to the risk functional and implicit regularization where noise is added to the system variables during training, are two of the commonly used techniques for model complexity control. The relationship between these two type of regularization is explained. A regularization term is derived based on the general noise model. The interplay between the various noise mediated regularization terms is described.