Theoretical Study of Mean-Field Boltzmann Machine Learning by Information Geometry

Mean-field Boltzmann machine learning is recognized as a practical method to circumvent the difficulty that Boltzmann machine learning is very time-consuming. However, its theoretical meaning is still not clear. In this paper, based on information geometry, we give an information-theoretic interpretation of mean-field Boltzmann machine learning and a clear geometrical explanation of the approximation used there. Based on this interpretation, computer simulations for evaluating the effectiveness of mean-field Boltzmann machine learning are carried out for two-unit Boltzmann machines. The necessity of geometrical analysis in demonstrating the effectiveness of mean-field Boltzmann machine learning is discussed. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(8): 30–39, 1999