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Connecting Permutation Equivariant Neural Networks and Partition Diagrams
Edward Pearce-Crump
1511 - 1518
10.3233/FAIA240655
Research Article
Frontiers in Artificial Intelligence and Applications
Volume 392: ECAI 2024
Abstract

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 to derive a simple, diagrammatic method for calculating the weight matrices themselves.

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