Group Equivariant Sparse Coding.

We describe a sparse coding model of visual cortex that encodes image transformations in an equivariant and hierarchical manner. The model consists of a group-equivariant convolutional layer with internal recurrent connections that implement sparse coding through neural population attractor dynamics, consistent with the architecture of visual cortex. The layers can be stacked hierarchically by introducing recurrent connections between them. The hierarchical structure enables rich bottom-up and top-down information flows, hypothesized to underlie the visual system’s ability for perceptual inference. The model’s equivariant representations are demonstrated on time-varying visual scenes.