Information maximization principle explains the emergence of complex cell-like neurons

We propose models and a method to qualitatively explain the receptive field properties of complex cells in the primary visual cortex. We apply a learning method based on the information maximization principle in a feedforward network, which comprises an input layer of image patches, simple cell-like first-output-layer neurons, and second-output-layer neurons (Model 1). The information maximization results in the emergence of the complex cell-like receptive field properties in the second-output-layer neurons. After learning, second-output-layer neurons receive connection weights having the same size from two first-output-layer neurons with sign-inverted receptive fields. The second-output-layer neurons replicate the phase invariance and iso-orientation suppression. Furthermore, on the basis of these results, we examine a simplified model showing the emergence of complex cell-like receptive fields (Model 2). We show that after learning, the output neurons of this model exhibit iso-orientation suppression, cross-orientation facilitation, and end stopping, which are similar to those found in complex cells. These properties of model neurons suggest that complex cells in the primary visual cortex become selective to features composed of edges to increase the variability of the output.