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Recently, the spherical data processing has emerged in many applications and attracted a lot of attention. Among all the methods for dealing with the spherical data, the spherical neural networks (SNNs) method has been recognized as a very efficient tool due to SNNs possess both good approximation capability and spacial localization property. For better localized approximant, weighted approximation...
We consider the optimal rate of approximation by single hidden feed-forward neural networks on the unit sphere. It is proved that there exists a neural network with n neurons, and an analytic, strictly increasing, sigmoidal activation function such that the deviation of a Sobolev class W2r2(Sd) from the class of neural networks Φnϕ, behaves asymptotically as n−2rd−1. Namely, we prove that the essential...
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