  We consider the problem of symmetrising a neural network along a group
homomorphism: given a homomorphism $\varphi : H \to G$, we would like a
procedure that converts $H$-equivariant neural networks into $G$-equivariant
ones. We formulate this in terms of Markov categories, which allows us to
consider neural networks whose outputs may be stochastic, but with
measure-theoretic details abstracted away. We obtain a flexible, compositional,
and generic framework for symmetrisation that relies on minimal assumptions
about the structure of the group and the underlying neural network
architecture. Our approach recovers existing methods for deterministic
symmetrisation as special cases, and extends directly to provide a novel
methodology for stochastic symmetrisation also. Beyond this, we believe our
findings also demonstrate the utility of Markov categories for addressing
problems in machine learning in a conceptual yet mathematically rigorous way.
