Approximation capability in C(R¯n) by multilayer feedforward networks and related problems

  title={Approximation capability in C(R¯n) by multilayer feedforward networks and related problems},
  author={Tianping Chen and Hong Chen and Ruey-Wen Liu},
  journal={IEEE transactions on neural networks},
  volume={6 1},
In this paper, we investigate the capability of approximating functions in C(R (n)) by three-layered neural networks with sigmoidal function in the hidden layer. It is found that the boundedness condition on the sigmoidal function plays an essential role in the approximation, as contrast to continuity or monotonity condition. We point out that in order to prove the neural network in the n-dimensional case, all one needs to do is to prove the case for one dimension. The approximation in L(p… CONTINUE READING
Highly Cited
This paper has 208 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications citing this paper.
Showing 1-10 of 79 extracted citations

Neuro-Fuzzy Function Approximations Using Feedforward Networks - An Application of Sigmoidal Signal

2010 Ninth International Conference on Machine Learning and Applications • 2010
View 12 Excerpts
Highly Influenced

The errors of approximation for feedforward neural networks in the Lp metric

Mathematical and Computer Modelling • 2009
View 4 Excerpts
Highly Influenced

Classification ability of single hidden layer feedforward neural networks

IEEE Trans. Neural Netw. Learning Syst. • 2000
View 4 Excerpts
Highly Influenced

An overview on weight initialization methods for feedforward neural networks

2016 International Joint Conference on Neural Networks (IJCNN) • 2016
View 1 Excerpt

208 Citations

Citations per Year
Semantic Scholar estimates that this publication has 208 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 14 references

Approximation by Superposition of Sigmoidal and Radial Functions,

H. N. Mhaskar, C. A. Micchelli
Advances on Applied Mathematics, pp. 350-373, • 1992

Constructive Proof of Cybenko's Approximation Theorem and Its Extensions," pp. 163 - 168 in Computing Science and Statistics (editors LePage and Page)

T. Chen, H. Chen, R.-W. Liu

Construction of neural nets using the radon transform

International 1989 Joint Conference on Neural Networks • 1989

Capabilities of three-layered perceptrons

IEEE 1988 International Conference on Neural Networks • 1988

Similar Papers

Loading similar papers…