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Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks
Sidhika Balachandar · Adrien Poulenard · Congyue Deng · Leonidas Guibas

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in Symmetry and Geometry in Neural Representations (NeurReps) »
Event URL: https://openreview.net/forum?id=8AmObRRabss »

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 Deng et al. (2021). 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.

Keywords: 3-D learning · O(3) equivariance · point cloud analysis · planar symmetry

Author Information

Sidhika Balachandar (Department of Computer Science, Cornell University)
Sidhika Balachandar

I am a first-year Computer Science PhD candidate at Cornell University. I work on problems at the intersection of machine learning and healthcare. I am currently rotating with [Prof. Emma Pierson](https://www.cs.cornell.edu/~emmapierson/) and [Prof. Nikhil Garg](https://gargnikhil.com/). I am working on using machine learning and statistical models to detect bias in medical decision making. I received my undergraduate degree in Computer Science at Stanford University. At Stanford, I worked on two research projects. First, I worked with [Prof. Ron Dror](http://drorlab.stanford.edu/) and his student [Alex Powers](https://lxpowers33.github.io/about) on a drug docking project. Second, I worked with [Prof. Leonidas Guibas](https://geometry.stanford.edu/index.html) and his postdoc Adrien Poulenard on a project about rotation equivariant machine learning for 3D point clouds. My hobbies include dance (I've been trained in classical Indian dance), hiking, traveling, and reading.

Adrien Poulenard (Stanford)
Congyue Deng (Stanford University)
Leonidas Guibas (stanford.edu)

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