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. In machine learning, the most visible passive symmetry is the relabeling or permutation symmetry of graphs. Our goal is to understand the implications for machine learning of the many passive symmetries in play. We discuss dos and don'ts for machine learning practice if passive symmetries are to be respected. We 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. This paper is conceptual: It translates among the languages of physics, mathematics, and machine-learning. We believe that consideration and implementation of passive symmetries might help machine learning in the same ways that it transformed physics in the twentieth century.

翻译：任何数据表示都涉及研究者任意的选择。由于这些选择独立于数据生成过程，每个选择都导致一个精确的对称性，对应于将一种可能表示转换为另一种的变换群。这些是被动对称性；它们包括坐标自由度、规范对称性和单位协变性，这些都在物理学中产生了重要成果。在机器学习中，最显著的被动对称性是图的重标号或置换对称性。我们的目标是理解众多被动对称性对机器学习的影响。我们讨论了若需尊重被动对称性，机器学习实践中应遵循的注意事项。我们探讨了与因果建模的联系，并论证了当学习问题的目标是样本外泛化时，实现被动对称性尤其有价值。本文属于概念性论文：它在物理学、数学和机器学习的语言之间进行翻译。我们相信，对被动对称性的考量与实现可能有助于机器学习，就如同它在二十世纪改变了物理学那样。