A counterexample regarding "New study on neural networks: The essential order of approximation". (March 2020) - Goebbels, Steffen
Abstract: The paper "New study on neural networks: the essential order of approximation" by Jianjun Wang and Zongben Xu, which appeared in Neural Networks 23 (2010), deals with upper and lower estimates for the error of best approximation with sums of nearly exponential type activation functions in terms of moduli of smoothness. In particular, the presented lower bound is astonishingly good. However, the proof is incorrect and the bound is wrong.