Function Approximation by Three-Layered Networks and Its Error Bounds | An Integral Representation Theorem

Neural Networks are widely noticed to provide a nonlinear function approximation method. In order to make its approximation ability clear, a new theorem on an integral transform of ridge functions is presented. By using this theorem, an approximation bound, which clari es the quantitative relationship between the approximation accuracy and the number of elements in the hidden layer, can be obtained. This result shows that the approximation accuracy depends on the smoothness of target functions. It also shows that the approximation methods which use ridge functions are free from \curse of dimensionality".