In this paper, in order to optimize neural network architecture and generalization, after analyzing the reasons of overfitting and poor generalization of the neural networks, we presented a class of constructive decay RBF neural networks to repair the singular value of a continuous function with finite number of jumping discontinuity points. We proved that a function with m jumping discontinuity points can be approximated by a simplest neural network and a decay RBF neural network in L 2 ( ℝ ) by each ɛ error, and a function with m jumping discontinuity point y = f ( x ) , x ∈ E ⊂ ℝ d can be constructively approximated by a decay RBF neural network in L 2 ( ℝ d ) by each ε > 0 error. Then the whole networks will have less hidden neurons and well generalization in the same of the first part. A real world problem about stock closing price with jumping discontinuity have been presented and verified the correctness of the theory. 
A new constructive neural network method for noise processing and its application on stock market prediction