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

2025-01-01

AI Summary

The role of SE(3) equivariance and symmetry breaking in point cloud deep learning remains poorly understood, particularly regarding their task-dependent efficacy and practical applicability. Method: We establish a systematic, cross-task (segmentation, regression, generation), cross-architecture (PointNet++, SE(3)-Transformer, etc.), and cross-dataset evaluation framework to isolate and quantify the impact of SE(3) equivariant inductive biases. Contribution/Results: We first reveal that equivariance gains scale significantly with geometric task complexity. Crucially, we demonstrate that *moderate* incorporation of SE(3) equivariance—even without strict enforcement—substantially improves generalization, yielding an average 12.7% performance gain on high-complexity tasks and enhanced robustness to input symmetry perturbations. This work clarifies the practical boundaries and value of SE(3) equivariance, providing both theoretical insight and actionable design principles for point cloud models.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Data transparency and provenance

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.

Problem

• Equivariance
• Symmetry Breaking
• Point Cloud Tasks

Innovation

• Equivariance
• Symmetry Breaking
• Performance Enhancement