Orientation Selective Cells Emerge in a Sparsely Coding Boltzmann Machine

In our contribution we investigate a sparse coded Boltzmann machine as a model for the formation of orientation selective receptive elds in primary visual cortex. The model consists of two layers of neurons which are recurrently connected and which represent the lateral geniculate nucleus and primary visual cortex. Neu-rons have ternary activity values +1, ?1, and 0, where the 0-state is degenerate being assumed with higher prior probability. The probability for a (stochastic) activation vector on the net obeys the Boltzmann distribution and maximum-likelihood leads to the standard Boltzmann learning rule. We apply a mean-eld version of this model to natural image processing and nd that neurons develop localized and oriented receptive elds.