Geodesic
Neural network approximation of several variable functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 9-21

Voir la notice de l'article provenant de la source Math-Net.Ru

The main result of the work is as follows: in the Chebyshev–Hermite weighted integral metric, it is possible to approximate any function of sufficiently general form by neural network. The approximating net consists of two layers, where the first uses any predefined sigmoid function of activation and second uses linear-threshold function. The Chebyshev–Hermit weight is chosen because it lets one to imitate receptors distribution for example in an eye of a human or some mammal. 
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     author = {D. V. Alexeev},
     title = {Neural network approximation of several variable functions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
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     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a2/}
}
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D. V. Alexeev. Neural network approximation of several variable functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 9-21. http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a2/