Universal approximation in p-mean by neural networks

• Published in: Neural networks Vol. 11; no. 4; pp. 661 - 667
• Main Authors: Burton, Robert M., Dehling, Herold G.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.06.1998; Elsevier Science
• Subjects: Applied sciences; Approximation theory; Approximations and expansions; Electric, optical and optoelectronic circuits; Electronics; Exact sciences and technology; L p-approximation; Mathematical analysis; Mathematics; Neural networks; Sciences and techniques of general use; Single hidden layer network; Universal transfer functions; Single hidden layer network; Approximation theory; L p -approximation; Neural networks; Universal transfer functions; Universal algebra; Lp approximation; Approximation by function; Neural network; Experimental study; Transfer function; Layer
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/S0893-6080(98)00009-4

A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by g(x 1, …, x d)= ∑ j=1 n a jσ ∑ i=1 d w jix i−θ j , where a j , θ j , w ji ∈ R. In this paper we study the approximation of arbitrary functions f: R d → R by a neural net in an L p (μ) norm for some finite measure μ on R d . We prove that under natural moment conditions, a neural net with non-polynomial function can approximate any given function.