Connecting Permutation Equivariant Neural Networks and Partition Diagrams

• URL: http://arxiv.org/abs/2212.08648v3
• Date: Thu, 8 Aug 2024 13:09:51 GMT
• Title: Connecting Permutation Equivariant Neural Networks and Partition Diagrams
• Authors: Edward Pearce-Crump,
• Abstract summary: We show that all of the weight matrices that appear in Permutation equivariant neural networks can be obtained from Schur-Weyl duality. In particular, we adapt Schur-Weyl duality to derive a simple, diagrammatic method for calculating the weight matrices themselves.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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