A new learning algorithm is derived which performs online stochas(cid:173) tic gradient ascent in the mutual information between outputs and inputs of a network. In the absence of a priori knowledge about the'signal' and'noise' components of the input, propagation of information depends on calibrating network non-linearities to the detailed higher-order moments of the input density functions. As an example application, we have achieved near-perfect separation of ten digi(cid:173) tally mixed speech signals. Our simulations lead us to believe that our network performs better at blind separation than the Herault(cid:173) J utten network, reflecting the fact that it is derived rigorously from the mutual information objective.

With the exception of (Becker 1992), there has been little attempt to use non-linearity in networks to achieve something a linear network could not. Nonlinear networks, however, are capable of computing more general statistics than those second-order ones involved in decorrelation, and as a consequence they are capable of dealing with signals (and noises) which have detailed higher-order structure. The success of the'H-J' networks at blind separation (Jutten & Herault 1991) suggests that it should be possible to separate statistically independent components, by using learning rules which make use of moments of all orders. This paper takes a principled approach to this problem, by starting with the question of how to maximise the information passed on in nonlinear feed-forward network. Starting with an analysis of a single unit, the approach is extended to a network mapping N inputs to N outputs. In the process, it will be shown that, under certain fairly weak conditions, the N ---. N network forms a minimally redundant encoding ofthe inputs, and that it therefore performs Independent Component Analysis (ICA). 2 Information maximisation The information that output Y contains about input X is defined as: I(Y, X) H(Y) - H(YIX) (1) where H(Y) is the entropy (information) in the output, while H(YIX) is whatever information the output has which didn't come from the input. In the case that we have no noise (or rather, we don't know what is noise and what is signal in the input), the mapping between X and Y is deterministic and H(YIX) has its lowest possible value of

With the exception of (Becker 1992), there has been little attempt to use non-linearity in networks to achieve something a linear network could not. Nonlinear networks, however, are capable of computing more general statistics than those second-order ones involved in decorrelation, and as a consequence they are capable of dealing with signals (and noises) which have detailed higher-order structure. The success of the'H-J' networks at blind separation (Jutten & Herault 1991) suggests that it should be possible to separate statistically independent components, by using learning rules which make use of moments of all orders. This paper takes a principled approach to this problem, by starting with the question of how to maximise the information passed on in nonlinear feed-forward network. Starting with an analysis of a single unit, the approach is extended to a network mapping N inputs to N outputs. In the process, it will be shown that, under certain fairly weak conditions, the N ---. N network forms a minimally redundant encoding ofthe inputs, and that it therefore performs Independent Component Analysis (ICA). 2 Information maximisation The information that output Y contains about input X is defined as: I(Y, X) H(Y) - H(YIX) (1) where H(Y) is the entropy (information) in the output, while H(YIX) is whatever information the output has which didn't come from the input. In the case that we have no noise (or rather, we don't know what is noise and what is signal in the input), the mapping between X and Y is deterministic and H(YIX) has its lowest possible value of

With the exception of (Becker 1992), there has been little attempt to use non-linearity in networks to achieve something a linear network could not. Nonlinear networks, however, are capable of computing more general statistics than those second-order ones involved in decorrelation, and as a consequence they are capable of dealing with signals (and noises) which have detailed higher-order structure. The success of the'H-J' networks at blind separation (Jutten & Herault 1991)suggests that it should be possible to separate statistically independent components, by using learning rules which make use of moments of all orders. This paper takes a principled approach to this problem, by starting with the question ofhow to maximise the information passed on in nonlinear feed-forward network. Startingwith an analysis of a single unit, the approach is extended to a network mapping N inputs to N outputs. In the process, it will be shown that, under certain fairly weak conditions, the N ---. N network forms a minimally redundant encodingofthe inputs, and that it therefore performs Independent Component Analysis (ICA). 2 Information maximisation The information that output Y contains about input X is defined as: I(Y, X) H(Y) - H(YIX) (1) where H(Y) is the entropy (information) in the output, while H(YIX) is whatever information the output has which didn't come from the input. In the case that we have no noise (or rather, we don't know what is noise and what is signal in the input), the mapping between X and Y is deterministic and H(YIX) has its lowest possible value of