Weak Convergence of Cardaliaguet-Euvrard Neural Network Operators Studied Asymptotically


An Nth order asymptotic expansion is established for the error of weak approximation of a special class of functions by the well-known Cardaliaguet-Euvrard neural network operators. This class is made out of functions f that are N times continuously differentiable over R, so that all f,f′,…, f(N) have the same compact support and f(N) is of bounded variation. This asymptotic expansion involves products of integrals of the network activation bell-shaped function b and f. The rate of the above convergence depends only on the first derivative of involved functions.

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Results in Mathematics