Learning Networks of Neurons with Boolean Logic

We realized a model which self-organizes to perform a task via a learning-by-example scheme. The system is a network of Boolean operators which, in some of our computations, has been able to achieve an error-free design for addition between integer binary numbers when shown only a small subset of all possible additions. The training procedure, based on optimizing the network on the given sampling using simulated annealing, is completely general and allows in principle to treat any binary mapping. We recognize different regimes in learning, i.e. the system can both memorize patterns (with a capacity which is numerically estimated) and generalize information to construct rules and algorithms. Some scaling relations are conjectured and numerically tested for these different regimes.