Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function

26 Pages Posted: 23 Oct 2008

See all articles by Moshe Leshno

Moshe Leshno

Independent

Valdimir Ya. Lin

affiliation not provided to SSRN

Allan Pinkus

affiliation not provided to SSRN

Shimon Schocken

affiliation not provided to SSRN

Date Written: March 1992

Abstract

Several researchers characterized the activation function under which multilayer feedforwardnetworks can act as universal approximators. We show that most of all the characterizationsthat were reported thus far in the literature are special cases of the followinggeneral result: a standard multilayer feedforward network with a locally bounded piecewisecontinuous activation function can approximate any continuous function to any degree ofaccuracy if and only if the network's activation function is not a polynomial. We alsoemphasize the important role of the threshold, asserting that without it the last theoremdoes not hold.

Keywords: Multilayer feedforward networks, Activation functions, role of threshold, Universal approximation capabilities, LP(μ) approximation

Suggested Citation

Leshno, Moshe and Lin, Valdimir Ya. and Pinkus, Allan and Schocken, Shimon, Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function (March 1992). NYU Working Paper No. IS-92-13, Available at SSRN: https://ssrn.com/abstract=1288490

Moshe Leshno (Contact Author)

Independent

No Address Available
United States

Valdimir Ya. Lin

affiliation not provided to SSRN

No Address Available

Allan Pinkus

affiliation not provided to SSRN

No Address Available

Shimon Schocken

affiliation not provided to SSRN

No Address Available

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