Learning Horizontal Connections in a Sparse Coding Model of Natural Images

Abstract

It has been shown that adapting a dictionary of basis functions to the statistics of natural images so as to maximize sparsity in the coefficients results in a set of dictionary elements whose spatial properties resemble those of V1 (primary vi-sual cortex) receptive fields. However, the resulting sparse coefficients still exhibit pronounced statistical dependencies, thus violating the independence assumption of the sparse coding model. Here, we propose a model that attempts to capture the dependencies among the basis function coefficients by including a pairwise coupling term in the prior over the coefficient activity states. When adapted to the statistics of natural images, the coupling terms learn a combination of facilitatory and inhibitory interactions among neighboring basis functions. These learned in-teractions may offer an explanation for the function of horizontal connections in V1 in terms of a prior over natural images. 1