Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre", 1, Largo S. Leonardo Murialdo, 00146 Rome, Italy.
Neural Netw. 2013 Dec;48:72-7. doi: 10.1016/j.neunet.2013.07.009. Epub 2013 Aug 6.
In this paper, we study pointwise and uniform convergence, as well as order of approximation, of a family of linear positive multivariate neural network (NN) operators with sigmoidal activation functions. The order of approximation is studied for functions belonging to suitable Lipschitz classes and using a moment-type approach. The special cases of NN operators, activated by logistic, hyperbolic tangent, and ramp sigmoidal functions are considered. Multivariate NNs approximation finds applications, typically, in neurocomputing processes. Our approach to NN operators allows us to extend previous convergence results and, in some cases, to improve the order of approximation. The case of multivariate quasi-interpolation operators constructed with sigmoidal functions is also considered.
在本文中，我们研究了一类具有 sigmoidal 激活函数的线性正多元神经网络（NN）算子的逐点和一致收敛以及逼近阶。使用矩型方法研究了属于适当 Lipschitz 类的函数的逼近阶。考虑了由 logistic、双曲正切和斜坡 sigmoidal 函数激活的 NN 算子的特殊情况。多元神经网络逼近通常在神经计算过程中找到应用。我们对 NN 算子的方法允许我们扩展以前的收敛结果，并在某些情况下提高逼近阶。还考虑了用 sigmoidal 函数构造的多元拟插值算子的情况。
