  Permutation equivariant neural networks are often constructed using tensor
powers of $\mathbb{R}^{n}$ as their layer spaces. We show that all of the
weight matrices that appear in these neural networks can be obtained from
Schur-Weyl duality between the symmetric group and the partition algebra. In
particular, we adapt Schur-Weyl duality to derive a simple, diagrammatic method
for calculating the weight matrices themselves.
