Essential rate for approximation by spherical neural networks
โ Scribed by Shaobo Lin; Feilong Cao; Zongben Xu
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 272 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-6080
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let D/R d be a compact set and let 8 be a uniformly bounded set of D ร R functions. For a given real-valued function f defined on D and a given natural number n, we are looking for a good uniform approximation to f of the form n i=1 a i , i , with , i # 8, a i # R. Two main cases are considered: (1)
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 R(d), there exist three layers of neFNNs with the fixed number of hidden neurons that attain the
A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by where a j , v j , w ji สฆ R. In this paper we study the approximation of arbitrary functions f: R d โ R by a neural net in an L p (m) norm for some finite measure m on R d . We prove that under natu