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Maxout Polytopes

arXiv 2509.21286 ↗First posted 25 Sep 2025math.CO cs.DM cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 20 of its 36 references that are in the map. First posted on arXiv 25 Sep 2025.

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20 of 36 references.

References · 20

  1. 2016Input Convex Neural Networkscited by 414
  2. 2014On the Number of Linear Regions of Deep Neural Networkscited by 381
  3. 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 257
  4. 2017Bounding and Counting Linear Regions of Deep Neural Networkscited by 161
  5. 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 161
  6. 2018Tropical Geometry of Deep Neural Networkscited by 95
  7. 2021Towards Lower Bounds on the Depth of ReLU Neural Networkscited by 56
  8. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  9. 2021Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sumscited by 37
  10. 2023Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopescited by 36
  11. 2024The Real Tropical Geometry of Neural Networkscited by 24
  12. 2022Algorithmic Determination of the Combinatorial Structure of the Linear Regions of ReLU Neural Networkscited by 22
8 more
  1. 2025On the Expressiveness of Rational ReLU Neural Networks With Bounded Depthcited by 18
  2. 2025Better Neural Network Expressivity: Subdividing the Simplexcited by 12
  3. 2024On Minimal Depth in Neural Networkscited by 11
  4. 2025Depth-Bounds for Neural Networks via the Braid Arrangementcited by 11
  5. 2025On the Depth of Monotone ReLU Neural Networks and ICNNscited by 11
  6. 2024Neural Networks and (Virtual) Extended Formulationscited by 9
  7. 2022A Combinatorial Perspective on the Optimization of Shallow ReLU Networkscited by 3
  8. 2023Revisiting Tropical Polynomial Division: Theory, Algorithms and Application to Neural Networkscited by 2

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