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Neural Polytopes
- Publication Year :
- 2023
-
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.<br />Comment: 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
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2307.00721
- Document Type :
- Working Paper