Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one possible representation to another. These are the passive symmetries; they include coordinate freedom, gauge symmetry and units covariance, all of which have led to important results in physics. Our goal is to understand the implications of passive symmetries for machine learning: Which passive symmetries play a role (e.g., permutation symmetry in graph neural networks)? What are dos and don'ts in machine learning practice? We assay conditions under which passive symmetries can be implemented as group equivariances. We also discuss links to causal modeling, and argue that the implementation of passive symmetries is particularly valuable when the goal of the learning problem is to generalize out of sample. While this paper is purely conceptual, we believe that it can have a significant impact on helping machine learning make the transition that took place for modern physics in the first half of the Twentieth century.

翻译：任何数据表示都涉及研究者任意选择的因素。由于这些选择外生于数据生成过程，每个选择都会导致精确对称性，对应将一种可能表示转换为另一种表示的变换群。这些就是被动对称性，包括坐标自由度、规范对称性和单位协变性，这些在物理学中都产生了重要成果。我们的目标是理解被动对称性对机器学习的启示：哪些被动对称性发挥作用（如图神经网络中的置换对称性）？机器学习实践中的注意事项是什么？我们评估了将被动对称性实现为群等变性的条件。我们还讨论了与因果建模的联系，并论证当学习目标是样本外泛化时，实现被动对称性尤为重要。尽管本文纯属概念性研究，但我们相信它将对推动机器学习实现二十世纪上半叶现代物理学经历的重大转型产生重要影响。