The Optimal Retrieval in Boolean Neural Networks

We have determined a generalized majority rule which optimizes the error reduction for the retrieval of noisy input patterns in Boolean networks for associative memory and have evaluated the consequential storage capacity, which is very robust against training noise disruption, when compared with previously proposed stepwise algorithms. We have indicated how the rule can be implemented using a multi-state algorithm. We compare such Boolean and conventional networks, whose respective short- and long-ranged retrieval behaviour are associated with low and high training noises, and also demonstrate that Hebb rule minimizes the output error for extremely noisy conventional networks.