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A. Caveretta, W. Dahmen, C. Micchelli
1991
Earlier work this paper cites.
I. Daubechies, J. Lagarias
1991
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A. Cohen, I, Daubechies, J. C. Feauveau
1992
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I. Daubechies
1992
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Then

N. Dym, B. Sober, I. Daubechies
2020
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R. DeVore, B. Hanin, G. Petrova
2021
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D. Elbrac̈hter, D. Perekrestenko, P. Grohs, H. Bȯlcskei
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2021

Neural Network Approximation of Refinable Functions

Daubechies, Ingrid, DeVore, Ronald, Dym, Nadav et al.

Understand

In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks.

By now, there exists a variety of results which show that a wide range of functions can be approximated with sometimes surprising accuracy by these outputs.
For example, it is known that the set of functions that can be approximated with exponential accuracy (in terms of the number of parameters used) includes, on one hand, very smooth functions such as polynomials and analytic functions (see e.g.
\cite{E,S,Y}) and, on the other hand, very rough functions such as the Weierstrass function (see e.g.