Feature grouping from spatially constrained multiplicative interaction

We present a feature learning model that learns to encode relationships between images. The model is defined as a Gated Boltzmann Machine, which is constrained such that hidden units that are nearby in space can gate each other's connections. We show how frequency/orientation "columns" as well as topographic filter maps follow naturally from training the model on image pairs. The model also helps explain why square-pooling models yield feature groups with similar grouping properties. Experimental results on synthetic image transformations show that spatially constrained gating is an effective way to reduce the number of parameters and thereby to regularize a transformation-learning model.