Nadal, JP; Brunel, N; Parga, N, *Nonlinear feedforward networks with stochastic outputs: infomax implies redundancy reduction.*,
Network: Computation in Neural Systems (Informa), vol. 9 no. 2
(May, 1998),
pp. 207-217 [doi] .
**Abstract:**

*We prove that maximization of mutual information between the output and the input of a feedforward neural network leads to full redundancy reduction under the following sufficient conditions: (i) the input signal is a (possibly nonlinear) invertible mixture of independent components; (ii) there is no input noise; (iii) the activity of each output neuron is a (possibly) stochastic variable with a probability distribution depending on the stimulus through a deterministic function of the inputs (where both the probability distributions and the functions can be different from neuron to neuron); (iv) optimization of the mutual information is performed over all these deterministic functions. This result extends that obtained by Nadal and Parga (1994) who considered the case of deterministic outputs.*