# Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks

@article{Hornik1990UniversalAO, title={Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks}, author={Kurt Hornik and Maxwell B. Stinchcombe and Halbert L. White}, journal={Neural Networks}, year={1990}, volume={3}, pages={551-560} }

## 1,818 Citations

Application of an artificial neural network to the control of an active external orthosis of the lower limb

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A real-time application of an artificial neural network for motorised orthosis with six degrees-of-freedom for use by a paraplegic; a ‘walking machine’ is presented.

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Extension of approximation capability of three layered neural networks to derivatives

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The author considers the problem of approximating arbitrary differentiable functions defined on compact sets of R/sup d/, as well as their derivatives, by finite sums of the form a/sub 0/+ Sigma /sub i=1//sup p/ a/ sub i/g(W/sub i/*x+b), where g is an arbitrary nonpolynomial C/sup infinity /-function fixed beforehand.

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- Computer ScienceArXiv
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It is demonstrated that the feed-forward architecture, for most commonly used activation functions, is incapable of approximating functions comprised of multiple sub-patterns while simultaneously respecting their composite-pattern structure, so a simple architecture modification is implemented that reallocates the neurons of any singleFeed-forward network across several smaller sub-networks, each specialized on a distinct part of the input-space.

Orthogonal least squares algorithm for the approximation of a map and its derivatives with a RBF network

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Approximation of Curves Contained on the Surface by Freed-Forward Neural Networks

- Computer ScienceAICI
- 2011

Based on Freed-forward Neural Networks, a new method to approximate curves contained on the given surface is developed to convert the problems of space curve approximation on surfaces into the plane curve approximation by point projection.

Differentiating Functions of the Jacobian with Respect to the Weights

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The J-prop algorithm is introduced, an efficient general method for computing the exact partial derivatives of a variety of simple functions of the Jacobian of a model with respect to its free parameters.

The errors in simultaneous approximation by feed-forward neural networks

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- 2010

Degree of Approximation Results for Feedforward Networks Approximating Unknown Mappings and Their Derivatives

- Computer ScienceNeural Computation
- 1994

This work extends Barron's results to feedforward networks with possibly nonsigmoid activation functions approximating mappings and their derivatives simultaneously, showing that the approximation error decreases at rates as fast as n1/2, where n is the number of hidden units.

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