Visual Scene Representation with Hierarchical Equivariant Sparse Coding

We propose a hierarchical neural network architecture for unsupervised learning of equivariant part-whole decompositions of visual scenes. In contrast to the global equivariance of group-equivariant networks, the proposed architecture exhibits equivariance to part-whole transformations throughout the hierarchy, which we term hierarchical equivariance. The model achieves such internal representations via hierarchical Bayesian inference, which gives rise to rich bottom-up, top-down, and lateral information flows, hypothesized to underlie the mechanisms of perceptual inference in visual cortex. We demonstrate these useful properties of the model on a simple dataset of scenes with multiple objects under independent rotations and translations.