Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks

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Abstract/Contents

Abstract: Equivariant neural networks have been adopted in a variety of 3-D learning areas. In this paper, we identify and address a fundamental problem of equivariant networks: their ambiguity to symmetries. For a left-right symmetric input, like an airplane, these networks cannot complete symmetry-dependent tasks like segmenting the 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. First, we introduce an algorithm to calculate features for detecting symmetries. Second, we create an orientation aware linear layer that is sensitive to symmetries. Finally, 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 to symmetric objects.

Author	Balachandar, Sidhika
Thesis advisor	Poulenard, Adrien
Thesis advisor	Guibas, Leonidas
Thesis advisor	Dror, Ron
Thesis advisor	Deng, Congyue
Degree granting institution	Stanford University
Department	Department of Computer Science

DOI	https://doi.org/10.25740/tn463rr9524
Location	https://purl.stanford.edu/tn463rr9524

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License: This work is licensed under a Creative Commons Attribution Non Commercial 4.0 International license (CC BY-NC).

Preferred citation: Balachandar, S. (2022). Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks. Stanford Digital Repository. Available at https://purl.stanford.edu/tn463rr9524

Undergraduate Theses, School of Engineering

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