The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Universal approximation bounds for superpositions of a sigmoidal function
Abstract
Approximation properties of a class of artificial neural networks are established. It is shown that feedforward networks with one layer of sigmoidal nonlinearities achieve integrated squared error of order O(1/n), where n is the number of nodes. The approximated function is assumed to have a bound on the first moment of the magnitude distribution of the Fourier transform. The nonlinear parameters associated with the sigmoidal nodes, as well as the parameters of linear combination, are adjusted in the approximation. In contrast, it is shown that for series expansions with n terms, in which only the parameters of linear combination are adjusted, the integrated squared approximation error cannot be made smaller than order 1/n/sup 2/d/ uniformly for functions satisfying the same smoothness assumption, where d is the dimension of the input to the function. For the class of functions examined, the approximation rate and the parsimony of the parameterization of the networks are shown to be advantageous in high-dimensional settings.>
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
Spline Models for Observational Data
Wahba, G. (1990) · doi:10.1137/1.9781611970128 · Cited by 4,184
Cited by
On the Continuity of Rotation Representations in Neural Networks
Zhou, Y., Barnes, C., Lu, J., Yang, J., & Li, H. (2019) · 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2019.00589 · Cited by 1,255
Universality of deep convolutional neural networks
Zhou, D.-X. (2020) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2019.06.004 · Cited by 530
Neural network with unbounded activation functions is universal approximator
Sonoda, S., & Murata, N. (2017) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2015.12.005 · Cited by 303
Deep learning for hybrid 5G services in mobile edge computing systems: learn from a digital twin
Dong, R., She, C., Hardjawana, W., Li, Y., & Vucetic, B. (2019) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2019.2927312 · Cited by 295
Theory of deep convolutional neural networks: Downsampling
Zhou, D.-X. (2020) · Neural Networks · doi:10.1016/j.neunet.2020.01.018 · Cited by 263
Deep neural network processing of DEER data
Worswick, S. G., Spencer, J. A., Jeschke, G., & Kuprov, I. (2018) · Science Advances · doi:10.1126/sciadv.aat5218 · Cited by 212
Analyzing Data Granularity Levels for Insider Threat Detection Using Machine Learning
Le, D. C., Zincir-Heywood, N., & Heywood, M. I. (2020) · IEEE Transactions on Network and Service Management · doi:10.1109/tnsm.2020.2967721 · Cited by 191
On the Expressive Power of Deep Architectures
Bengio, Y., & Delalleau, O. (2011) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-24412-4_3 · Cited by 182
Pixel-wise regression using U-Net and its application on pansharpening
Yao, W., Zeng, Z., Lian, C., & Tang, H. (2018) · Neurocomputing · doi:10.1016/j.neucom.2018.05.103 · Cited by 133
Learning Hidden Unit Contributions for Unsupervised Acoustic Model Adaptation
Swietojanski, P., Li, J., & Renals, S. (2016) · IEEE/ACM Transactions on Audio, Speech, and Language Processing · doi:10.1109/taslp.2016.2560534 · Cited by 133
Efficient probabilistic inference in generic neural networks trained with non-probabilistic feedback
Orhan, A. E., & Ma, W. J. (2017) · Nature Communications · doi:10.1038/s41467-017-00181-8 · Cited by 77
Non-invasive hypoglycemia monitoring system using extreme learning machine for Type 1 diabetes
Ling, S. H., San, P. P., & Nguyen, H. T. (2016) · ISA Transactions · doi:10.1016/j.isatra.2016.05.008 · Cited by 62
Numerical 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
Liu, C.-Y., Kuo, E.-J., Abraham Lin, C.-H., Gemsun Young, J., Chang, Y.-J., Hsieh, M.-H., & Goan, H.-S. (2025) · Quantum Machine Intelligence · doi:10.1007/s42484-025-00305-0 · Cited by 40
Mathematical Models of Overparameterized Neural Networks
Fang, C., Dong, H., & Zhang, T. (2021) · Proceedings of the IEEE · doi:10.1109/jproc.2020.3048020 · Cited by 26
Nonlocality and Nonlinearity Implies Universality in Operator Learning
Lanthaler, S., Li, Z., & Stuart, A. M. (2023) · arXiv · doi:10.48550/arxiv.2304.13221 · Cited by 25
Investigating the determinants of performance in machine learning for protein fitness prediction
Sandhu, M., Mater, A. C., Matthews, D. S., Spence, M. A., Lenskiy, A. A., & Jackson, C. (2020) · doi:10.1101/2020.09.30.319780 · Cited by 8
Investigating the determinants of performance in machine learning for protein fitness prediction
(2025) · doi:10.1002/pro.70235 · Cited by 6
Metadata
- Authors
- Barron, A. R.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1993-05
- Volume
- 39
- Issue
- 3
- Pages
- 930-945
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2166116275
- Cited by
- 2,804
- References
- 3
- FWCI
- 66.66
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
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.
