Cubic approximation neural network for multivariate functions

Abstract

This paper introduces a novel neural network architecture—cubic approximation neural network (CANN), capable of local approximation of multivariate functions. It is particularly simple in concept and in structure. Its simplicity enables a quantitative evaluation of its approximation capabilities, namely, for a desired error bound the size of the needed network can be calculated. In addition, if a training session is used, a thorough analysis of the learning process performance is performed. The trade-off between the rate of learning and the steady-state performance is clearly demonstrated. On the other hand, this approach suffers from the problem common to all local approximation networks—the number of neurons grows exponentially with the dimension of the input vector.