The Stone-Weierstrass theorem and its application to neural networks

@article{Cotter1990TheST,
  title={The Stone-Weierstrass theorem and its application to neural networks},
  author={Neil E. Cotter},
  journal={IEEE transactions on neural networks},
  year={1990},
  volume={1 4},
  pages={290-5}
}
The Stone-Weierstrass theorem and its terminology are reviewed, and neural network architectures based on this theorem are presented. Specifically, exponential functions, polynomials, partial fractions, and Boolean functions are used to create networks capable of approximating arbitrary bounded measurable functions. A modified logistic network satisfying the theorem is proposed as an alternative to commonly used networks based on logistic squashing functions. 
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References

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“ On the approximate realization of continuous mappings by neural networks

  • M. Stinchcombe Hornik
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  • 1989

Multilayer feedfonvard networks are universal approximators

  • G. E. Hinton Rumelhart, R. J. Williams
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