Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks

• URL: http://arxiv.org/abs/2210.16646v1
• Date: Sat, 29 Oct 2022 16:28:59 GMT
• Title: Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks
• Authors: Sidhika Balachandar, Adrien Poulenard, Congyue Deng, Leonidas Guibas
• Abstract summary: 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.
• Score: 4.147346416230272
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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