mlsanityData to 14 Oct 2026

Neural Polytopes

arXiv 2307.00721 ↗First posted 3 Jul 2023cs.LG cs.GR hep-thcited by 1

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Abstract (arXiv)

We find that simple neural networks with ReLU activation generate polytopes as an approximation of a unit sphere in various dimensions. The species of polytopes are regulated by the network architecture, such as the number of units and layers. For a variety of activation functions, generalization of polytopes is obtained, which we call neural polytopes. They are a smooth analogue of polytopes, exhibiting geometric duality. This finding initiates research of generative discrete geometry to approximate surfaces by machine learning.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 12 of its 21 references that are in the map. First posted on arXiv 3 Jul 2023.

Builds on

12 of 21 references.

References · 12

  1. 2014On the Number of Linear Regions of Deep Neural Networkscited by 381
  2. 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 257
  3. 2019Complexity of Linear Regions in Deep Networkscited by 167
  4. 2017Bounding and Counting Linear Regions of Deep Neural Networkscited by 161
  5. 2013On the number of response regions of deep feed forward networks with piece-wise linear activationscited by 94
  6. 2019Reverse-Engineering Deep ReLU Networkscited by 83
  7. 2018Mad Max: Affine Spline Insights into Deep Learningcited by 55
  8. 2018Provable Robustness of ReLU networks via Maximization of Linear Regionscited by 51
  9. 2023Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopescited by 36
  10. 2022Interpreting Neural Networks through the Polytope Lenscited by 33
  11. 2021Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verificationcited by 13
  12. 2021Machine Learning Kreuzer--Skarke Calabi--Yau Threefoldscited by 8

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Cited by year

Citing papers per year: 2023: 1.

1 paper.

  1. 2023Neural Boundingcited by 0