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Status: Unchecked ×Keyword: sigmoidal function ×Clear all

2 claims from 1 paper

1. Computer Science › Neural Networks and Applications

   Approximation by superpositions of a sigmoidal function

   Cybenko · Mathematics of Control Signals and Systems · 1989

   Unchecked2 claims
   Show 2 claims

   1. UncheckedSums of a fixed one-variable function applied to linear combinations of inputs can approximate any continuous function on the unit hypercube arbitrarily closely.“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 fu…”
   2. UncheckedAny decision region can be approximated as closely as wanted by a feedforward network with one hidden layer and any continuous sigmoidal activation.“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.”