Connecting Permutation Equivariant Neural Networks and Partition Diagrams
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908008926150656 |
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| author | Pearce-Crump, Edward |
| author_facet | Pearce-Crump, Edward |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08648 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Connecting Permutation Equivariant Neural Networks and Partition Diagrams Pearce-Crump, Edward Machine Learning Combinatorics Representation Theory 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. |
| title | Connecting Permutation Equivariant Neural Networks and Partition Diagrams |
| topic | Machine Learning Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2212.08648 |