TY - JOUR
T1 - New study on neural networks
T2 - The essential order of approximation
AU - Wang, Jianjun
AU - Xu, Zongben
PY - 2010/6
Y1 - 2010/6
N2 - For the nearly exponential type of feedforward neural networks (neFNNs), the essential order of their approximation is revealed. It is proven that for any continuous function defined on a compact set of Rd, there exist three layers of neFNNs with the fixed number of hidden neurons that attain the essential order. Under certain assumption on the neFNNs, the ideal upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only characterize the intrinsic property of approximation of the neFNNs, but also proclaim the implicit relationship between the precision (speed) and the number of hidden neurons of the neFNNs.
AB - For the nearly exponential type of feedforward neural networks (neFNNs), the essential order of their approximation is revealed. It is proven that for any continuous function defined on a compact set of Rd, there exist three layers of neFNNs with the fixed number of hidden neurons that attain the essential order. Under certain assumption on the neFNNs, the ideal upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only characterize the intrinsic property of approximation of the neFNNs, but also proclaim the implicit relationship between the precision (speed) and the number of hidden neurons of the neFNNs.
KW - Modulus of smoothness
KW - Nearly exponential type neural networks
KW - The essential order of approximation
UR - https://www.scopus.com/pages/publications/77952287368
U2 - 10.1016/j.neunet.2010.01.004
DO - 10.1016/j.neunet.2010.01.004
M3 - 文章
C2 - 20138734
AN - SCOPUS:77952287368
SN - 0893-6080
VL - 23
SP - 618
EP - 624
JO - Neural Networks
JF - Neural Networks
IS - 5
ER -