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：由于这些选择是数据生成过程的外部选择,每一种选择都会导致精确的对称性,与一个可能的转换组合相对应。这些是被动的对称性;它们包括协调自由、测量的对称性和单位的共变性,所有这些都导致物理方面的重要结果。我们的目标是了解被动对称性对称性对机器学习的影响:被动的对称性会起到某种作用(例如,图形神经网络中的对称性)?在机器学习实践中做什么和不做什么?我们分析被动对称性在何种条件下可以作为群体对称性执行。我们还讨论与因果建模的联系,并争论说,当学习问题的目的是要将抽样概括化时,实施被动对称性特别有用。尽管本文纯属概念性,但我们认为它能够对帮助机器学习在二十世纪前半叶的现代物理学转型产生重大影响。