# Multilayer feedforward networks are universal approximators

@article{Hornik1989MultilayerFN, title={Multilayer feedforward networks are universal approximators}, author={Kurt Hornik and Maxwell B. Stinchcombe and Halbert L. White}, journal={Neural Networks}, year={1989}, volume={2}, pages={359-366} }

## 17,525 Citations

Approximation capabilities of multilayer feedforward networks

- Computer ScienceNeural Networks
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Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function

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Neural networks for localized approximation

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- 1994

We prove that feedforward artificial neural networks with a single hidden layer and an ideal sigmoidal response function cannot provide localized approximation in a Euclidean space of dimension…

Neural networks with a continuous squashing function in the output are universal approximators

- Computer Science, MathematicsNeural Networks
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A constructive method for multivariate function approximation by multilayer perceptrons

- Computer ScienceIEEE Trans. Neural Networks
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It is shown how to construct a perceptron with two hidden layers for multivariate function approximation, which can perform function approximation in the same manner as networks based on Gaussian potential functions, by linear combination of local functions.

Constructive Approximation of Discontinuous Functions by Neural Networks

- Computer ScienceNeural Processing Letters
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A constructive proof that a real, piecewise continuous function can be almost uniformly approximated by single hidden-layer feedforward neural networks (SLFNNs) is given.

Function approximation using a partition of the input space

- Computer Science, Mathematics[Proceedings 1992] IJCNN International Joint Conference on Neural Networks
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It is shown that a simple geometric proof of this theorem can be extended to networks of units using a smooth output function, and a recent result on the approximation of polynomials by fixed size networks is improved.

Generalization and Approximation Capabilities of Multilayer Networks

- Computer ScienceNeural Computation
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The theory allows one to specify a finite discrete set of training data and a network structure that generalizes and approximates any given continuous mapping between sets of contours on a plane within any given permissible error.

NEURAL NETWORKS FOR OPTIMAL APPROXIMATION OF SMOOTH

- Mathematics, Computer Science
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We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation…

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