Boltzmann-machine learning of prior distributions of binarized natural images

Abstract

Prior distributions of binarized natural images are learned by using Boltzmann machine. We find that there emerges a structure with two sublattices in the interactions, and the nearest-neighbor and next-nearest-neighbor interactions correspondingly take two discriminative values, which reflects individual characteristics of three sets of pictures we treat. On the other hand, in a longer spacial scale, a longer-range (though still rapidly-decaying) ferromagnetic interaction commonly appear in all the cases. The characteristic length scale of the interactions is universally about up to four lattice spacing $\xi \approx 4$. These results are derived by using the mean-field method which effectively reduces the computational time required in Boltzmann machine. An improved mean-field method called the Bethe approximation also gives the same result, which reinforces the validity of our analysis and findings. Relations to criticality, frustration, and simple-cell receptive fields are also discussed.