Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function
@inproceedings{Leshno1993MultilayerFN, title={Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function}, author={M. Leshno and Vladimir Ya. Lin and A. Pinkus and S. Schocken}, booktitle={Neural Networks}, year={1993} }
Several researchers characterized the activation functions under which multilayer feedforwardnetworks can act as universal approximators. We show that all the characterizationsthat were reported thus far in the literature ark special cases of the following general result:a standard multilayer feedforward network can approximate any continuous functionto any degree of accuracy if and only if the network's activation functions are not polynomial.We also emphasize the important role of the… CONTINUE READING
Topics from this paper
1,304 Citations
Neural Networks for Optimal Approximation of Smooth and Analytic Functions
- Mathematics, Computer Science
- Neural Computation
- 1996
- 255
- Highly Influenced
- PDF
Three-Layer Feedforward Structures Smoothly Approximating Polynomial Functions
- Mathematics, Computer Science
- ICANN
- 2010
Negative results for approximation using single layer and multilayer feedforward neural networks
- Mathematics, Computer Science
- 2018
- 4
- PDF
Approximation rates for neural networks with general activation functions
- Mathematics, Medicine
- Neural Networks
- 2020
- 15
- PDF
A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function
- Mathematics, Computer Science
- Neural Computation
- 2016
- 48
- PDF
Approximation by neural networks with weights varying on a finite set of directions
- Mathematics
- 2012
- 21
On the Approximation Properties of Neural Networks
- Mathematics, Computer Science
- ArXiv
- 2019
- 8
- Highly Influenced
References
SHOWING 1-10 OF 53 REFERENCES
Approximation capabilities of multilayer feedforward networks
- Mathematics, Computer Science
- Neural Networks
- 1991
- 3,872
- PDF
Approximating and learning unknown mappings using multilayer feedforward networks with bounded weights
- Mathematics, Computer Science
- 1990 IJCNN International Joint Conference on Neural Networks
- 1990
- 117
Multilayer feedforward networks are universal approximators
- Mathematics, Computer Science
- Neural Networks
- 1989
- 15,300
- PDF
Approximation by superpositions of a sigmoidal function
- Mathematics, Computer Science
- Math. Control. Signals Syst.
- 1989
- 4,049
- Highly Influential
- PDF
On the approximate realization of continuous mappings by neural networks
- Mathematics, Computer Science
- Neural Networks
- 1989
- 4,037
- PDF
There exists a neural network that does not make avoidable mistakes
- Mathematics, Computer Science
- IEEE 1988 International Conference on Neural Networks
- 1988
- 194
Capabilities of three-layered perceptrons
- Computer Science
- IEEE 1988 International Conference on Neural Networks
- 1988
- 398