Learning by message passing in networks of discrete synapses

We show that a message-passing process allows us to store in binary ‘‘material’’ synapses a number of random patterns which almost saturate the information theoretic bounds. We apply the learning algorithm to networks characterized by a wide range of different connection topologies and of size comparable with that of biological systems (e.g., n = 10^5–10^6). The algorithm can be turned into an online—fault tolerant—learning protocol of potential interest in modeling aspects of synaptic plasticity and in building neuromorphic devices.