Related papers: Approximation with Neural Networks in Variable Lebesgue Spaces

Approximation with Neural Networks in Variable Lebesgue Spaces

URL: http://arxiv.org/abs/2007.04166v1
Date: Wed, 8 Jul 2020 14:52:48 GMT
Title: Approximation with Neural Networks in Variable Lebesgue Spaces
Authors: \'Angela Capel and Jes\'us Oc\'ariz
Abstract summary: This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks with any desired accuracy.
Score: 1.0152838128195465
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks with any desired accuracy. This result subsequently leads to determine the universality of the approximation depending on the boundedness of the exponent function. Furthermore, whenever the exponent is unbounded, we obtain some characterization results for the subspace of functions that can be approximated.

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