Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks
This addresses a fundamental limitation in 3-D learning for researchers and practitioners using equivariant networks, though it is an incremental improvement over existing methods.
The paper tackled the problem of symmetry ambiguities in equivariant neural networks, which prevent tasks like left-right segmentation of symmetric objects, and introduced OAVNN, an extension that resolves these ambiguities while preserving rotational equivariance, achieving accurate segmentations.
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.