Mini-max initialization for function approximation

Neural networks have been successfully applied to various pattern recognition and function approximation problems. However, the training process remains a time-consuming procedure that often gets stuck in a local minimum. The optimum network size and topology are usually unknown. In this paper, we formulate the concept of extrema equivalence for estimating the complexity of a function. Based on this formulation, the optimal network size and topology can be selected according to the number of extrema. Mini-max initialization method is then proposed to select the initial values of the weights for the network that is proven to greatly speed up training. The superior performance of our method in terms of convergence and generalization has been substantiated by experimental results.