Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce a canonical representation of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform canonicalization is better than using predefined heuristics. Our results show that learning the canonicalization function indeed leads to better results and that the approach achieves excellent performance in practice.

翻译：基于对称性的神经网络通常通过约束网络架构来实现对变换群的不变性或等变性。本文提出了一种替代方法，通过学习生成数据的规范化表示来避免这种架构约束。这些规范化函数可以便捷地嵌入到非等变骨干架构中。我们针对多种常见变换群提供了具体的实现方案。研究表明，该方法不仅具备通用性，同时能提供可解释的洞察。核心假设在于，学习神经网络执行规范化操作比使用预定义启发式方法更优。实验结果表明，学习规范化函数确实能带来性能提升，且该方法在实践中表现出优异效果。