Extension of approximation capability of three layered neural networks to derivatives
Yoshifusa Ito · 2002
The author considers the problem of approximating arbitrary differentiable functions defined on compact sets of R/sup d/, as well as their derivatives, by finite sums of the form a/sub 0/+ Sigma /sub i=1//sup p/ a/sub i/g(W/sub i/*x+b), where W/sub 1/ are vectors of R/sup d/ and g is an arbitrary nonpolynomial C/sup infinity /-function fixed beforehand. If f is a polynomial of order n, the upper bound of p is n/sub n+d-1/C/sub n/. The linear combinations can be realized by three-layer neural networks.>