Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks

TL;DR

This paper introduces OAVNN, a rotation-equivariant neural network that effectively resolves symmetry ambiguities, enabling accurate segmentation of symmetric objects by incorporating symmetry detection and orientation-aware mechanisms.

Contribution

The paper proposes OAVNN, a novel extension of Vector Neuron Networks, with components for detecting symmetries and handling symmetry ambiguities while maintaining rotational equivariance.

Findings

OAVNN accurately segments symmetric objects.

The network quickly learns symmetry-dependent tasks.

It maintains rotational equivariance despite symmetry challenges.

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.