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.