Neural Polytopes
Machine Learning
2023-07-13 v2 Graphics
High Energy Physics - Theory
Geometric Topology
Abstract
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.
Cite
@article{arxiv.2307.00721,
title = {Neural Polytopes},
author = {Koji Hashimoto and Tomoya Naito and Hisashi Naito},
journal= {arXiv preprint arXiv:2307.00721},
year = {2023}
}
Comments
5 pages, 9 figures. v2: References added. Accepted at the 1st Workshop on the Synergy of Scientific and Machine Learning Modeling at International Conference on Machine Learning (ICML), Honolulu, Hawaii, USA. 2023