Geodesic
Some aspects of approximation and interpolation of functions artificial neural networks
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 38 (2022) no. 1, pp. 54-73

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The article deals with the issues of approximation and interpolation of functions f(x) = |x|, f(x) = sin(x), f(x) =1/(1+25x²) with the help of neural networks from those constructed on the basis of the Kolmogorov-Arnold and Tsybenko theorems. problems in training a neural network based on the initialization of weight coefficients in a random way are shown. The possibility of training a neural network to work with a variety is shown.
Keywords: approximation of functions, interpolation of functions, artificial neural networks, Tsybenko's theorem, Kolmogorov-Arnold's theorem. 
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     author = {V. A. Galkin and T. V. Gavrilenko and A. D. Smorodinov},
     title = {Some aspects of approximation and interpolation of functions artificial neural networks},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {54--73},
     publisher = {mathdoc},
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     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_38_1_a3/}
}
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V. A. Galkin; T. V. Gavrilenko; A. D. Smorodinov. Some aspects of approximation and interpolation of functions artificial neural networks. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 38 (2022) no. 1, pp. 54-73. http://geodesic.mathdoc.fr/item/VKAM_2022_38_1_a3/