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Equivariant networks have been adopted in many 3-D learning areas. Here weidentify a fundamental limitation of these networks: their ambiguity tosymmetries. Equivariant networks cannot complete symmetry-dependent tasks likesegmenting a left-right symmetric object into its left and right sides. Wetackle this problem by adding components that resolve symmetry ambiguitieswhile preserving rotational equivariance. We present OAVNN: Orientation AwareVector Neuron Network, an extension of the Vector Neuron Network. OAVNN is arotation equivariant network that is robust to planar symmetric inputs. Ournetwork consists of three key components. 1) We introduce an algorithm tocalculate symmetry detecting features. 2) We create a symmetry-sensitiveorientation aware linear layer. 3) We construct an attention mechanism thatrelates directional information across points. We evaluate the network usingleft-right segmentation and find that the network quickly obtains accuratesegmentations. We hope this work motivates investigations on the expressivityof equivariant networks on symmetric objects.

Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks