# Neural Polytopes

arXiv: https://arxiv.org/abs/2307.00721 · HTML: https://mlsanity.com/paper/2307.00721/

## Key facts

- Cited by 1 papers 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 (most cited first, 12 of 12)

- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [On the number of response regions of deep feed forward networks with piece-wise linear activations](https://mlsanity.com/paper/1312.6098/) (2013)
- [Reverse-Engineering Deep ReLU Networks](https://mlsanity.com/paper/1910.00744/) (2019)
- [Mad Max: Affine Spline Insights into Deep Learning](https://mlsanity.com/paper/1805.06576/) (2018)
- [Provable Robustness of ReLU networks via Maximization of Linear Regions](https://mlsanity.com/paper/1810.07481/) (2018)
- [Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes](https://mlsanity.com/paper/2302.12553/) (2023)
- [Interpreting Neural Networks through the Polytope Lens](https://mlsanity.com/paper/2211.12312/) (2022)
- [Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verification](https://mlsanity.com/paper/2111.08922/) (2021)
- [Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds](https://mlsanity.com/paper/2112.09117/) (2021)

## Built on by (most cited first, 1 of 1)

- [Neural Bounding](https://mlsanity.com/paper/2310.06822/) (2023)

## 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.