Connecting Permutation Equivariant Neural Networks and Partition Diagrams
Connecting Permutation Equivariant Neural Networks and Partition Diagrams
Permutation equivariant neural networks are often constructed using tensor powers of Rn 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 …