Abstract This paper addresses the following question of neural network identifiability: Does input–output map realized by a feed-forward with respect to given nonlinearity uniquely specify architecture, weights, and biases? The existing literature on subject (Sussman in Neural Netw 5(4):589–593, 1992; Albertini et al. Artificial networks for speech vision, 1993; Fefferman Rev Mat Iberoam 10(3):...