LEARNING ALGORITHMS FOR PERCEPTRONS FROM STATISTICAL PHYSICS

Learning algorithms for perceptrons are deduced from statistical mechanics. Thermodynamical quantities are used as cost functions which may be extremalized by gradient dynamics to find the synaptic efficacies that store the learning set of patterns. The learning rules so obtained are classified in two categories, following the statistics used to derive the cost functions, namely, Boltzmann statistics, and Fermi statistics. In the limits of zero or infinite temperatures some of the rules behave like already known algorithms, but new strategies for learning are obtained at finite temperatures, which minimize the number of errors on the training set.