Maxout Polytopes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915513928515584 |
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| author | Balakin, Andrei Cox, Shelby Loho, Georg Sturmfels, Bernd |
| author_facet | Balakin, Andrei Cox, Shelby Loho, Georg Sturmfels, Bernd |
| contents | Maxout polytopes are defined by feedforward neural networks with maxout activation function and non-negative weights after the first layer. We characterize the parameter spaces and extremal f-vectors of maxout polytopes for shallow networks, and we study the separating hypersurfaces which arise when a layer is added to the network. We also show that maxout polytopes are cubical for generic networks without bottlenecks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maxout Polytopes Balakin, Andrei Cox, Shelby Loho, Georg Sturmfels, Bernd Combinatorics Discrete Mathematics Machine Learning Maxout polytopes are defined by feedforward neural networks with maxout activation function and non-negative weights after the first layer. We characterize the parameter spaces and extremal f-vectors of maxout polytopes for shallow networks, and we study the separating hypersurfaces which arise when a layer is added to the network. We also show that maxout polytopes are cubical for generic networks without bottlenecks. |
| title | Maxout Polytopes |
| topic | Combinatorics Discrete Mathematics Machine Learning |
| url | https://arxiv.org/abs/2509.21286 |