Boltzmann-Machine Learning of Prior Distributions of Binarized Natural Images

12/16/2014
by   Tomoyuki Obuchi, et al.
0

Prior distributions of binarized natural images are learned by using a Boltzmann machine. According the results of this study, 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 the individual characteristics of the three sets of pictures that we process. Meanwhile, in a longer spatial scale, a longer-range, although still rapidly decaying, ferromagnetic interaction commonly appears in all cases. The characteristic length scale of the interactions is universally up to approximately four lattice spacings ξ≈ 4. These results are derived by using the mean-field method, which effectively reduces the computational time required in a Boltzmann machine. An improved mean-field method called the Bethe approximation also gives the same results, as well as the Monte Carlo method does for small size images. These reinforce the validity of our analysis and findings. Relations to criticality, frustration, and simple-cell receptive fields are also discussed.

READ FULL TEXT

page 6

page 7

page 14

page 21

page 27

research
02/07/2020

Short sighted deep learning

A theory explaining how deep learning works is yet to be developed. Prev...
research
02/01/2015

Advanced Mean Field Theory of Restricted Boltzmann Machine

Learning in restricted Boltzmann machine is typically hard due to the co...
research
09/10/2019

Boltzmann machine learning and regularization methods for inferring evolutionary fields and couplings from a multiple sequence alignment

The inverse Potts problem to infer the Boltzmann distribution for homolo...
research
11/17/2010

Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines

We describe a model for capturing the statistical structure of local amp...
research
09/25/2019

On the Contact and Nearest-Neighbor Distance Distributions for the n-Dimensional Matern Cluster Process

This letter provides exact characterization of the contact and nearest-n...
research
08/21/2023

A Deep Dive into the Connections Between the Renormalization Group and Deep Learning in the Ising Model

The renormalization group (RG) is an essential technique in statistical ...

Please sign up or login with your details

Forgot password? Click here to reset