The DOI matches its Crossref record; 86 of the 86 references it cites were found in a registry or an index.
Approximation theory of the MLP model in neural networks
Abstract
In this survey we discuss various approximation-theoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. The MLP model is one of the more popular and practical of the many neural network models. Mathematically it is also one of the simpler models. Nonetheless the mathematics of this model is not well understood, and many of these problems are approximation-theoretic in character. Most of the research we will discuss is of very recent vintage. We will report on what has been done and on various unanswered questions. We will not be presenting practical (algorithmic) methods. We will, however, be exploring the capabilities and limitations of this model.
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Cites
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Jagtap, A. D., Kharazmi, E., & Karniadakis, G. E. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113028 · Cited by 1,208
Error bounds for approximations with deep ReLU networks
Yarotsky, D. (2017) · Neural Networks · doi:10.1016/j.neunet.2017.07.002 · Cited by 1,085
Universal Differential Equations for Scientific Machine Learning
Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A., & Edelman, A. (2020) · doi:10.21203/rs.3.rs-55125/v1 · Cited by 643
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
Universality of deep convolutional neural networks
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Metadata
- Authors
- Pinkus, A.
- Venue
- Acta Numerica
- Publisher
- Cambridge University Press (CUP)
- Published
- 1999-01
- Volume
- 8
- Pages
- 143-195
- ISSN
- 0962-4929 (ISSN-L)
- 1474-0508
- OpenAlex
- W2158581396
- Cited by
- 1,529
- References
- 86
- FWCI
- 5.29
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
