Recurrent connections facilitate symmetry perception in deep networks

Symmetry is omnipresent in nature and perceived by the visual system of many species, as it facilitates detecting ecologically important classes of objects in our environment. Yet, the neural underpinnings of symmetry perception remain elusive, as they require abstraction of long-range spatial dependencies between image regions and are acquired with limited experience. In this paper, we evaluate Deep Neural Network (DNN) architectures on the task of learning symmetry perception from examples. We demonstrate that feed-forward DNNs that excel at modelling human performance on object recognition tasks, are unable to acquire a general notion of symmetry. This is the case even when the feed-forward DNNs are architected to capture long-range spatial dependencies, such as through 'dilated' convolutions and the 'transformers' design. By contrast, we find that recurrent architectures are capable of learning a general notion of symmetry by breaking down the symmetry's long-range spatial dependencies into a progression of local-range operations. These results suggest that recurrent connections likely play an important role in symmetry perception in artificial systems, and possibly, biological ones too.