Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer
作者： Xin Li
DOI: 10.1016/0925-2312(95)00070-4
关键词: Activation function 、 Artificial neural network 、 Open set 、 Function (mathematics) 、 Compact space 、 Discrete mathematics 、 Order (group theory) 、 Mathematics 、 Combinatorics 、 Approximations of π 、 Partial derivative
摘要: Abstract Let σ be a non-polynomial activation function of neural network that has nth order continuous derivatives on R. The objective this paper is to show for any compact set K Rs, s ≥ 1, and multivariate f defined an open containing K, with one hidden layer can so constructed all its existing kth partial derivatives, k = (k1, …, ks) ϵ Z+s satisfying ∑i 1ski ≤ n, simultaneously uniformly approximated by the network.
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