  Inspired by constraints from physical law, equivariant machine learning
restricts 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 article, we introduce the topic and explain a couple of
methods to explicitly parameterize equivariant functions that are being used in
machine learning applications. In particular, we explicate a general procedure,
attributed to Malgrange, to express all polynomial maps between linear spaces
that are equivariant under 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.
