Xie, Ting Fan et Cao, Fei Long, The ridge function representation of polynomials and an application to neural networks, Acta mathematica Sinica. English series (Print) , 27(11), 2011, pp. 2169-2176
The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.