A symmetry-breaking generative model of a simple-cell/complex-cell hierarchy

We present a generative model for a three-layer hierarchy consisting of a retinal layer, a simple-cell layer, and a complex-cell layer. The weights in the model are trained using supervised learning on the retinal layer and complex cells. Once the weights are learned, the model is able to perform bottom-up classification of images, as well as top-down reconstruction from a specified category. The symmetry-breaking aspect of the model prevents the top-down reconstruction from generating images with a mixture of incompatible features. We illustrate the performance of this model with an image space consisting of vertical and horizontal bars in varying positions, in which the complex-cell layer learns the invariance that groups all horizontal bars into one category and all vertical into another.