Neural Networks for Functional Approximation and System Identification
Abstract
We construct generalized translation networks to approximate uniformly a class of nonlinear, continuous functionals defined on Lp([—1, 1]s) for integer s ≥ 1, 1 ≤ p < ∞, or C([—1, 1]s). We obtain lower bounds on the possible order of approximation for such functionals in terms of any approximation process depending continuously on a given number of parameters. Our networks almost achieve this order of approximation in terms of the number of parameters (neurons) involved in the network. The training is simple and noniterative; in particular, we avoid any optimization such as that involved in the usual backpropagation.
Cite
Text
Mhaskar and Hahm. "Neural Networks for Functional Approximation and System Identification." Neural Computation, 1997. doi:10.1162/NECO.1997.9.1.143Markdown
[Mhaskar and Hahm. "Neural Networks for Functional Approximation and System Identification." Neural Computation, 1997.](https://mlanthology.org/neco/1997/mhaskar1997neco-neural/) doi:10.1162/NECO.1997.9.1.143BibTeX
@article{mhaskar1997neco-neural,
title = {{Neural Networks for Functional Approximation and System Identification}},
author = {Mhaskar, Hrushikesh Narhar and Hahm, Nahmwoo},
journal = {Neural Computation},
year = {1997},
pages = {143-159},
doi = {10.1162/NECO.1997.9.1.143},
volume = {9},
url = {https://mlanthology.org/neco/1997/mhaskar1997neco-neural/}
}