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We show that a message-passing process allows to store in binary "material"synapses a number of random patterns which almost saturates the informationtheoretic bounds. We apply the learning algorithm to networks characterized bya wide range of different connection topologies and of size comparable withthat of biological systems (e.g. $n\simeq10^{5}-10^{6}$). The algorithm can beturned into an on-line --fault tolerant-- learning protocol of potentialinterest in modeling aspects of synaptic plasticity and in buildingneuromorphic devices.Comment: 4 pages, 3 figures; references updated and minor corrections;  accepted in PR

Learning by Message Passing in Networks of Discrete Synapses