{"ID":2866105,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21286","arxiv_id":"2509.21286","title":"Maxout Polytopes","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.21286","url_pdf":"https://arxiv.org/pdf/2509.21286v1","authors":"[\"Andrei Balakin\",\"Shelby Cox\",\"Georg Loho\",\"Bernd Sturmfels\"]","published":"2025-09-25T15:06:10Z","proceeding":"math.CO","tasks":"[\"math.CO\",\"cs.DM\",\"cs.LG\"]","methods":"[]","has_code":false}