Theoretical study of mean-field Boltzmann machine learning by information geometry

Mean-field Boltzmann machine learning is recognized as a practical method t o circumvent the difficulty that Boltzmann machine learning is very time;co nsuming. However, its theoretical meaning is still not clear In this paper, based on information geometry, we give an information-theoretic interpreta tion of mean-field Boltzmann machine learning and a clear geometrical expla nation of the approximation used there. Based on this interpretation, compu ter simulations for evaluating the effectiveness of mean-field Boltzmann ma chine learning are carried out for two-unit Boltzmann machines. The necessi ty of geometrical analysis in demonstrating the effectiveness of meanfield Boltzmann machine learning is, discussed. (C) 1999 Scripta Technica.