On the Utility of Equivariance and Symmetry Breaking in Deep Learning Architectures on Point Clouds

• URL: http://arxiv.org/abs/2501.01999v1
• Date: Wed, 01 Jan 2025 07:00:41 GMT
• Title: On the Utility of Equivariance and Symmetry Breaking in Deep Learning Architectures on Point Clouds
• Authors: Sharvaree Vadgama, Mohammad Mohaiminul Islam, Domas Buracus, Christian Shewmake, Erik Bekkers,
• Abstract summary: This paper explores the key factors that influence the performance of models working with point clouds. We identify the key aspects of equivariant and non-equivariant architectures that drive success in different tasks.
• Score: 1.4079337353605066
• License:
• Abstract: This paper explores the key factors that influence the performance of models working with point clouds, 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.

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