Universal approximation in p-mean by neural networks
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...
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Published in | Neural networks Vol. 11; no. 4; pp. 661 - 667 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Oxford
Elsevier Ltd
01.06.1998
Elsevier Science |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0893-6080 1879-2782 |
DOI: | 10.1016/S0893-6080(98)00009-4 |