Neural Network Identifiability for a Family of Sigmoidal Nonlinearities

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):507–555, 1994) suggests that answer should be yes, up certain symmetries induced nonlinearity, provided under consideration satisfy “genericity conditions.” results Sussman (1992) (1993) apply single hidden layer (1994) need fully connected. In an effort identifiability greater generality, we derive necessary genericity conditions arbitrary depth connectivity nonlinearity. Moreover, construct family nonlinearities which these are minimal , i.e., both sufficient . is large enough approximate many commonly encountered within precision uniform norm.