Probing Equivariance and Symmetry Breaking in Convolutional Networks

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

Keywords: convolution networks, geometric deep learning, equivariance, symmetry-breaking, generative modeling

TL;DR: A study on equivariant and non-equivariant convolution networks for point clouds

Abstract:

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 focusing on point clouds. 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.
Code available at [github.com/Sharvaree/EquivarianceStudy](https://github.com/Sharvaree/EquivarianceStudy)

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 10608