Equivariant neural networks and piecewise linear representation theory
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915893672411136 |
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| author | Gibson, Joel Tubbenhauer, Daniel Williamson, Geordie |
| author_facet | Gibson, Joel Tubbenhauer, Daniel Williamson, Geordie |
| contents | Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead to interesting nonlinear equivariant maps between simple representations. For example, the rectified linear unit (ReLU) gives rise to piecewise linear maps. We show that these considerations lead to a filtration of equivariant neural networks, generalizing Fourier series. This observation might provide a useful tool for interpreting equivariant neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant neural networks and piecewise linear representation theory Gibson, Joel Tubbenhauer, Daniel Williamson, Geordie Machine Learning Group Theory Representation Theory Primary: 20C05, Secondary: 05E10, 68T07 Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead to interesting nonlinear equivariant maps between simple representations. For example, the rectified linear unit (ReLU) gives rise to piecewise linear maps. We show that these considerations lead to a filtration of equivariant neural networks, generalizing Fourier series. This observation might provide a useful tool for interpreting equivariant neural networks. |
| title | Equivariant neural networks and piecewise linear representation theory |
| topic | Machine Learning Group Theory Representation Theory Primary: 20C05, Secondary: 05E10, 68T07 |
| url | https://arxiv.org/abs/2408.00949 |