  Recently, there have been many works on the deep learning of statistical
ensembles to determine the critical temperature of a possible phase transition.
We analyze the detailed structure of an optimized deep learning machine and
prove the basic equalities among the optimized machine parameters and the
physical quantities of the statistical system. According to these equalities,
we conclude that the bias parameters of the final full connection layer record
the free energy of the statistical system as a function of temperature. We
confirm these equalities in one- and two-dimensional Ising spin models and
actually demonstrate that the deep learning machine reveals the critical
temperature of the phase transition through the second difference of bias
parameters, which is equivalent to the specific heat. Our results disprove the
previous works claiming that the weight parameters of the full connection might
play a role of the order parameter such as the spin expectation.
