Approximations of Functions by a Multilayer Perceptron: a New Approach

@article{Attali1997ApproximationsOF,
  title={Approximations of Functions by a Multilayer Perceptron: a New Approach},
  author={Jean-Gabriel Attali and Gilles Pag{\`e}s},
  journal={Neural networks : the official journal of the International Neural Network Society},
  year={1997},
  volume={10 6},
  pages={1069-1081}
}
We provide a radically elementary proof of the universal approximation property of the one-hidden layer perceptron based on the Taylor expansion and the Vandermonde determinant. It works for both L(q) and uniform approximation on compact sets. This approach naturally yields some bounds for the design of the hidden layer and convergence results (including some rates) for the derivatives. A partial answer to Hornik's conjecture on the universality of the bias is proposed. An extension to vector… CONTINUE READING

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