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**Estimation of approximating rate for neural network in \(L^p_w\) spaces.**
*(English)*
Zbl 1244.93155

Summary: A class of Sobolev type multivariate function is approximated by feedforward network with one hidden layer of sigmoidal units and a linear output. By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bound on the degree of approximation can be obtained for the class of Sobolev functions. The results obtained are helpful in understanding the approximation capability and topology construction of the sigmoidal neural networks.

### MSC:

93E10 | Estimation and detection in stochastic control theory |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{J.-J. Wang} et al., J. Appl. Math. 2012, Article ID 636078, 8 p. (2012; Zbl 1244.93155)

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### References:

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