## Neural Computation

November 2008, Vol. 20, No. 11, Pages 2757-2791
(doi: 10.1162/neco.2008.03-07-494)
© 2008 Massachusetts Institute of Technology
Simultaneous Approximations of Polynomials and Derivatives and Their Applications to Neural Networks
Article PDF (208.19 KB)
Abstract

We have constructed one-hidden-layer neural networks capable of approximating polynomials and their derivatives simultaneously. Generally, optimizing neural network parameters to be trained at later steps of the BP training is more difficult than optimizing those to be trained at the first step. Taking into account this fact, we suppressed the number of parameters of the former type. We measure degree of approximation in both the uniform norm on compact sets and the Lp-norm on the whole space with respect to probability measures.