# Multilayer feedforward networks are universal approximators

@article{Hornik1989MultilayerFN, title={Multilayer feedforward networks are universal approximators}, author={K. Hornik and M. Stinchcombe and H. White}, journal={Neural Networks}, year={1989}, volume={2}, pages={359-366} }

Abstract This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.

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#### References

SHOWING 1-10 OF 24 REFERENCES

Universal approximation using feedforward networks with non-sigmoid hidden layer activation functions

- Mathematics
- International 1989 Joint Conference on Neural Networks
- 1989

269- PDF

There exists a neural network that does not make avoidable mistakes

- Mathematics, Computer Science
- IEEE 1988 International Conference on Neural Networks
- 1988

194

Approximation by superpositions of a sigmoidal function

- Mathematics, Computer Science
- Math. Control. Signals Syst.
- 1989

4,036- PDF

Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations

- Computer Science
- 1986

15,317- PDF

Approximation by superpositions of a sigmoidaifunction

- Urbana
- 1988

Capabilities of three layer percep - trans

- IEEE Second International Conference on Neural Networks
- 1988

Multilayer feedforward networks are universal approximators (Discussion Paper 88-45)

- Multilayer feedforward networks are universal approximators (Discussion Paper 88-45)
- 1988