The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Neural Networks for Optimal Approximation of Smooth and Analytic Functions
Abstract
We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these conditions, it is also possible to construct networks that provide a geometric order of approximation for analytic target functions. The permissible activation functions include the squashing function (1 − e−x)−1 as well as a variety of radial basis functions. Our proofs are constructive. The weights and thresholds of our networks are chosen independently of the target function; we give explicit formulas for the coefficients as simple, continuous, linear functionals of the target function.
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Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Cited by
Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review
Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B., & Liao, Q. (2017) · International Journal of Automation and Computing · doi:10.1007/s11633-017-1054-2 · Cited by 559
Self-citationNumerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
Geist, M., Petersen, P., Raslan, M., Schneider, R., & Kutyniok, G. (2021) · Journal of Scientific Computing · doi:10.1007/s10915-021-01532-w · Cited by 57
Metadata
- Authors
- Mhaskar, H. N.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 1996-01
- Volume
- 8
- Issue
- 1
- Pages
- 164-177
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2079224763
- Cited by
- 321
- References
- 2
- FWCI
- 11.53
- Type
- journal article
- Language
- en
- Open access
- closed
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