Multivariate neural network operators with sigmoidal activation functions

Neural network operators: Constructive interpolation of multivariate functions

“…where the above series is convergent on the compact subsets of R. The proof of this claim can be made by following the line drawn in [28,29].…”

“…Subsequently, other results concerning the NN operators N σ n have been obtained in [16,17,28,29,31]. In particular, in [28,29] the approximation results proved in [2,3,4,6] have been extended, in order to consider NN operators activated by any sigmoidal function σ(x) belonging to a suitable class which contains also σ (x) and σ h (x).…”

“…In particular, in [28,29] the approximation results proved in [2,3,4,6] have been extended, in order to consider NN operators activated by any sigmoidal function σ(x) belonging to a suitable class which contains also σ (x) and σ h (x). Moreover, the results concerning the order of approximation have been improved therein.…”

Neural Expert Weighting: A NEW framework for dynamic forecast combination

“…Further information concerning the logs (logistic sigmoid) and tanh (hyperbolic tangent) functions can be found in Lewicki & Marino (2003), Cao & Chen (2009), Costarelli & Spigler (2013a, 2013b and Costarelli (2014). The formulation from (26) to (28) accounts for a…”

Approximation by network operators with logistic activation functions

“…Especially, more papers, such as [16][17][18][19][20][21][22][23], have studied the construction and approximation of network operators with the sigmoidal function. The main purpose of this paper is to study the construction and multivariate approximation of Cardaliaguet-Euvrard type network operators with the logistic function r. In fact, we will use appropriate translation and combination of function r and construct a class of even and bell-shaped function with support R. Then, we employ the constructed function as activation function to construct a kind of so-called Cardaliaguet-Euvrard type network operators.…”