Statistical Mechanics of Mexican-Hat-Type Horizontal Connection

We propose a multi-hypercolumn model consisting of M hypercolumns. Adjacent hypercolumns interact with each other through horizontal connections. This model consists of inter-hypercolumn and intra-hypercolumn Mexican-hat-type interactions. We analyze our model using statistical-mechanical methods. In this model, we theoretically show that the free energy is equivalent to the posterior distribution in the Bayesian framework in extremely weak inter-hypercolumn interactions. A numerical experiment supports this equivalence. The results of this study reveal the relationship between a microscopic neural structure and a macroscopic computational theory.