  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. Symmetry perception requires abstraction of long-range
spatial dependencies between image regions, and its underlying neural
mechanisms remain elusive. 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 DNNs are architected to capture long-range
spatial dependencies, such as through `dilated' convolutions and the recently
introduced `transformers' design. By contrast, we find that recurrent
architectures are capable of learning to perceive symmetry by decomposing the
long-range spatial dependencies into a sequence of local operations, that are
reusable for novel images. These results suggest that recurrent connections
likely play an important role in symmetry perception in artificial systems, and
possibly, biological ones too.
