  Deep learning methods relying on multi-layered networks have been actively
studied in a wide range of fields in recent years, and deep Boltzmann
machines(DBMs) is one of them. In this study, a model of DBMs with some
properites of weight parameters obtained by learning is studied theoretically
by a statistical-mechanical approach based on the replica method. The phases
characterizing the role of DBMs as a generator and their phase diagram are
derived, depending meaningfully on the numbers of layers and units in each
layer. It is found, in particular, that the correlation between the weight
parameters in the hidden layers plays an essential role and that an increase in
the layer number has a negative effect on DBM's performance as a generator when
the correlation is smaller than a certain threshold value.
