Article ; Online: Low dimensional approximation and generalization of multivariate functions on smooth manifolds using deep ReLU neural networks.
Neural networks : the official journal of the International Neural Network Society
2024 Volume 174, Page(s) 106223
Abstract: The expressive power of deep neural networks is manifested by their remarkable ability to approximate multivariate functions in a way that appears to overcome the curse of dimensionality. This ability is exemplified by their success in solving high- ... ...
Abstract | The expressive power of deep neural networks is manifested by their remarkable ability to approximate multivariate functions in a way that appears to overcome the curse of dimensionality. This ability is exemplified by their success in solving high-dimensional problems where traditional numerical solvers fail due to their limitations in accurately representing high-dimensional structures. To provide a theoretical framework for explaining this phenomenon, we analyze the approximation of Hölder functions defined on a d-dimensional smooth manifold M embedded in R |
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MeSH term(s) | Neural Networks, Computer |
Language | English |
Publishing date | 2024-03-01 |
Publishing country | United States |
Document type | Journal Article |
ZDB-ID | 740542-x |
ISSN | 1879-2782 ; 0893-6080 |
ISSN (online) | 1879-2782 |
ISSN | 0893-6080 |
DOI | 10.1016/j.neunet.2024.106223 |
Database | MEDical Literature Analysis and Retrieval System OnLINE |
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