In equivariant machine learning the idea is to restrict the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory are typically used to parameterize the space of such functions. In this note, we explicate a general procedure, attributed to Malgrange, to express all polynomial maps between linear spaces that are equivariant with respect to the action of a group $G$, given a characterization of the invariant polynomials on a bigger space. The method also parametrizes smooth equivariant maps in the case that $G$ is a compact Lie group.

翻译：在等式机器学习时,其想法是将学习限制在假设类,即所有功能对于某些集体行动都是等式的。通常使用不惯性表示或无常理论来参数化这些功能的空间。在本说明中,我们解释一个归结于Malgrange的一般程序,以表达对于一个集团的动作具有等式的线性空间之间的所有多数值图,因为对较大空间的异性多数值图作了定性。如果$G是紧凑的组合,这种方法也使用平滑的等式地图。