On the utility of Equivariance and Symmetry Breaking in Deep learning architectures on point clouds

Sharvaree Vadgama, Mohammad Mohaiminul Islam, Domas Buracas, Christian A Shewmake, Erik J Bekkers

Keywords: deep learning architectures, geometric deep learning, equivariance, group convolutional networks, generative modeling

Abstract: This paper explores the key factors that influence the performance of models working with point clouds, \edit{across different tasks of varying geometric complexity.} In this work, we explore the trade-offs between flexibility and weight-sharing introduced by equivariant layers, assessing when equivariance boosts or detracts from performance. It is often argued that providing more information as input improves a model's performance. However, if this additional information breaks certain properties, such as $SE(3)$ equivariance, does it remain beneficial? We identify the key aspects of equivariant and non-equivariant architectures that drive success in different tasks by benchmarking them on segmentation, regression, and generation tasks across multiple datasets with increasing complexity. We observe a positive impact of equivariance, which becomes more pronounced with increasing task complexity, even when strict equivariance is not required.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 5192