  Equivariant networks have been adopted in many 3-D learning areas. Here we
identify a fundamental limitation of these networks: their ambiguity to
symmetries. Equivariant networks cannot complete symmetry-dependent tasks like
segmenting a left-right symmetric object into its left and right sides. We
tackle this problem by adding components that resolve symmetry ambiguities
while preserving rotational equivariance. We present OAVNN: Orientation Aware
Vector Neuron Network, an extension of the Vector Neuron Network. OAVNN is a
rotation equivariant network that is robust to planar symmetric inputs. Our
network consists of three key components. 1) We introduce an algorithm to
calculate symmetry detecting features. 2) We create a symmetry-sensitive
orientation aware linear layer. 3) We construct an attention mechanism that
relates directional information across points. We evaluate the network using
left-right segmentation and find that the network quickly obtains accurate
segmentations. We hope this work motivates investigations on the expressivity
of equivariant networks on symmetric objects.
