Uniqueness of the weights for minimal feedforward nets with a given input-output map

Abstract: We show that, for feedforward nets with a single hidden layer, a single output node, and a "transfer function" Tanh s, the net is uniquely determined by its input-output map, up to an obvious finite group of symmetries (permutations of the hidden nodes, and changing the sign of all the weights associated to a particular hidden node), provided that the net is irreducible (i.e., that there does not exist an inner node that makes a zero contribution to the output, and there is no pair of hidden nodes that could be collapsed to a single node without altering the inputoutput map).