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.