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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.08397 |
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| _version_ | 1866909684303134720 |
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| author | Van Nguyen, Bich Thang, Nguyen Cao Manh |
| author_facet | Van Nguyen, Bich Thang, Nguyen Cao Manh |
| contents | In this paper we prove theorems characterizing the decomposition of equivariant feature spaces, filters and a structural preservation theorem for invariant subspace chains in group equivariant convolutional neural networks(G-CNN). Furthermore, we give explicit matrix forms for irreducible representations of $UT_3(\F_3)$-the unitriangular matrix groups over the field with three elements. These results provide a foundation for designing new G-CNN architectures via representations of $UT_3(\F_3)$ that respect deep algebraic structure, with potential applications in symbolic visual learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation Theory of $UT_3(\mathbb{F}_3)$ and its Applications to Equivariant Decomposition in Neural Architectures Van Nguyen, Bich Thang, Nguyen Cao Manh Representation Theory 20C35 In this paper we prove theorems characterizing the decomposition of equivariant feature spaces, filters and a structural preservation theorem for invariant subspace chains in group equivariant convolutional neural networks(G-CNN). Furthermore, we give explicit matrix forms for irreducible representations of $UT_3(\F_3)$-the unitriangular matrix groups over the field with three elements. These results provide a foundation for designing new G-CNN architectures via representations of $UT_3(\F_3)$ that respect deep algebraic structure, with potential applications in symbolic visual learning. |
| title | Representation Theory of $UT_3(\mathbb{F}_3)$ and its Applications to Equivariant Decomposition in Neural Architectures |
| topic | Representation Theory 20C35 |
| url | https://arxiv.org/abs/2507.08397 |