研究卷积网络的对称性与等变性，发现显式打破对称性能提升多种任务性能。
Probing Equivariance and Symmetry Breaking in Convolutional Networks
- 设计统一架构Rapidash，公平对比不同等变与非等变模型。
- 在分割、回归和生成任务中，等变模型性能更优，且容量增加无法消除差距。
- 通过几何参考系显式打破对称性，可稳定提升模型表现，适合几何敏感任务。
本文探讨了显式结构先验（尤其是群等变性）的权衡问题，通过理论分析与全面实证研究展开。为实现可控且公平的比较，我们提出 exttt{Rapidash}——一种统一的群卷积架构，支持多种等变与非等变模型变体。结果表明，当模型与任务几何特性对齐时，约束更强的等变模型优于较宽松的替代方案；增加表示能力也无法完全消除性能差距。在分割、回归和生成等任务中，具备等变性和对称性破缺的模型表现更优。通过几何参考帧显式实现对称性破缺能持续提升性能；而通过几何输入特征破坏等变性，在与任务几何匹配时亦有帮助。研究揭示了任务相关的性能趋势，为模型选择提供更精细的指导。
原文摘要 · Abstract (English)
In this work, we explore the trade-offs of explicit structural priors, particularly group equivariance. We address this through theoretical analysis and a comprehensive empirical study. To enable controlled and fair comparisons, we introduce \texttt{Rapidash}, a unified group convolutional architecture that allows for different variants of equivariant and non-equivariant models. Our results suggest that more constrained equivariant models outperform less constrained alternatives when aligned with the geometry of the task, and increasing representation capacity does not fully eliminate performance gaps. We see improved performance of models with equivariance and symmetry-breaking through tasks like segmentation, regression, and generation across diverse datasets. Explicit \textit{symmetry breaking} via geometric reference frames consistently improves performance, while \textit{breaking equivariance} through geometric input features can be helpful when aligned with task geometry. Our results provide task-specific performance trends that offer a more nuanced way for model selection.
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