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 canonical representations of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for some groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis, supported by our empirical results, is that learning a small neural network to perform canonicalization is better than using predefined heuristics. Our experiments show that learning the canonicalization function is competitive with existing techniques for learning equivariant functions across many tasks, including image classification, $N$-body dynamics prediction, point cloud classification and part segmentation, while being faster across the board.

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。本文提出一种替代方案，通过学习生成数据的规范化表示来避免这一架构约束。这些规范化函数可轻松嵌入非等变骨干网络架构中。我们针对若干关键变换群给出了具体实现方法，证明该方法兼具通用性与可解释性。基于实验结果支持的核心假设表明：学习一个小型神经网络进行规范化优于使用预定义启发式方法。实验证明，在图像分类、N体动力学预测、点云分类及部件分割等多项任务中，学习规范化函数的方法与现有等变函数学习技术性能相当，且计算速度全面领先。