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 White},
  journal={Neural Networks},
  year={1990},
  volume={3},
  pages={551-560}
}
-We give conditions ensuring that multilayer jeedJorward networks with as Jew as a single hidden layer and an appropriately smooth hidden layer activation fimction are capable o f arbitrarily accurate approximation to an arbitrao' function and its derivatives. In fact, these networks can approximate functions that are not dtifferentiable in the classical sense, but possess only a generalized derivative, as is the case jor certain piecewise dtlf[erentiable Junctions. The conditions imposed on… CONTINUE READING
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