Approximation by superpositions of a sigmoidal function Export

@article{citeulike:3561150, abstract = {Abstract\ \ In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks.}, author = {Cybenko, G.}, citeulike-article-id = {3561150}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF02551274}, citeulike-linkout-1 = {http://www.springerlink.com/content/n873j15736072427}, day = {1}, doi = {10.1007/BF02551274}, journal = {Mathematics of Control, Signals, and Systems (MCSS)}, keywords = {approximation}, month = {December}, number = {4}, pages = {303--314}, posted-at = {2008-11-25 07:48:38}, priority = {2}, title = {Approximation by superpositions of a sigmoidal function}, url = {http://dx.doi.org/10.1007/BF02551274}, volume = {2}, year = {1989} }

TY - JOUR ID - citeulike:3561150 L3 - citeulike-article-id:3561150 N2 - Abstract  In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks. IS - 4 JF - Mathematics of Control, Signals, and Systems (MCSS) EP - 314 TI - Approximation by superpositions of a sigmoidal function VL - 2 SP - 303 KW - approximation AU - Cybenko, G PY - 1989/12/01/ UR - http://dx.doi.org/10.1007/BF02551274 ER -