Effect of object function on the performance of neural network

The capability of the general object functions is introduced. Effect of the object function on the statistical performance and astringency of the neural network (NN) is analyzed. Based on Lyapinov theorem, the astringency of the NN is proved under the general object function. While the approximate speed and the statistical performance are explored under the different object functions. Theoretical analysis and experiments indicate that the astringency can be improved through the better selective object function, and the appropriate object functions can completely guarantee the NN approximates to the function.