Abstract
Tightness of upper bounds on neural network approximation is investigated in the framework of variable-basis approximation. Conditions are given on a variable basis that do not allow a possibility of improving such bounds beyond \(O\left( {{n^{ - \left( {\frac{1}{2} + \frac{1}{d}} \right)}}} \right)\) where d is the number of variables of the functions to be approximated. Such conditions are satisfied by Lipschitz sigmoidal perceptrons.
Both authors were partially supported by NATO Grant PST.CLG.976870. V. KůFrková was partially supported grant GA ČR 201/00/1489. M. Sanguineti was partially supported by the Italian Ministry for the University and Research (MURST) and by grant D.R.42 of the Univ. of Genoa.
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Kůrková, V., Sanguineti, M. (2001). Tightness of Upper Bounds on Rates of Neural-Network Approximation. In: Kůrková, V., Neruda, R., Kárný, M., Steele, N.C. (eds) Artificial Neural Nets and Genetic Algorithms. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6230-9_7
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DOI: https://doi.org/10.1007/978-3-7091-6230-9_7
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