Carsten Peterson and James R. Anderson A mean field theory learning algorithm for neural networks Complex Systems 1, 995-1019 (1987) Abstract: Based on the Boltzmann Machine concept, we derive a learning algorithm in which time-consuming stochastic measurements of correlations are replaced by solutions to deterministic mean field theory equations. The method is applied to the XOR (exclusive-or), encoder, and line symmetry problems with substantial success. We observe speedup factors ranging from 10 to 30 for these applications and a significantly better learning performance in general. LU TP 87-01 Addendum by author: This work appears to be the first variational inference approach in the literature, here in the context of neural networks. Together with further insights from statistical mechanics, it triggered variational inference approaches for a wide class of models. These research avenues have played important roles in developing e.g. "Deep Learning" methods.