DOI: 10.1007/bf02551274. Approximation by superpositions of a sigmoidal function

Approximation by superpositions of a sigmoidal function

10.1007/bf02551274

Crossref journal-article

Springer Science and Business Media LLC

Mathematics of Control, Signals, and Systems (297)

Bibliography

Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems, 2(4), 303â314.

Authors 1

G. Cybenko (first)

References 28 Referenced 9,970

[A] R. B. Ash,Real Analysis and Probability, Academic Press, New York, 1972. / Real Analysis and Probability by R. B. Ash (1972)
[BH] E. Baum and D. Haussler, What size net gives valid generalization?,Neural Comput. (to appear). (10.1162/neco.1989.1.1.151)
[B] B. Bavarian (ed.), Special section on neural networks for systems and control,IEEE Control Systems Mag.,8 (April 1988), 3–31. (10.1109/37.1866)
[BEHW] A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth, Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension,Proceedings of the 18th Annual ACM Symposium on Theory of Computing, Berkeley, CA, 1986, pp. 273–282. (10.1145/12130.12158)
[BST] L. Brown, B. Schreiber, and B. A. Taylor, Spectral synthesis and the Pompeiu problem,Ann. Inst. Fourier (Grenoble),23 (1973), 125–154. (10.5802/aif.474) / Ann. Inst. Fourier (Grenoble) by L. Brown (1973)
[CD] S. M. Carroll and B. W. Dickinson, Construction of neural nets using the Radon transform, preprint, 1989. (10.1109/IJCNN.1989.118639)
[C] G. Cybenko, Continuous Valued Neural Networks with Two Hidden Layers are Sufficient, Technical Report, Department of Computer Science, Tufts University, 1988.
[DS] P. Diaconis and M. Shahshahani, On nonlinear functions of linear combinations,SIAM J. Sci. Statist. Comput.,5 (1984), 175–191. (10.1137/0905013) / SIAM J. Sci. Statist. Comput. by P. Diaconis (1984)
[F] K. Funahashi, On the approximate realization of continuous mappings by neural networks,Neural Networks (to appear).
[G] L. J. Griffiths (ed.), Special section on neural networks,IEEE Trans. Acoust. Speech Signal Process.,36 (1988), 1107–1190. (10.1109/29.1651)
[HSW] K. Hornik, M. Stinchcombe, and H. White, Multi-layer feedforward networks are universal approximators, preprint, 1988. (10.1016/0893-6080(89)90020-8)
[HL1] W. Y. Huang and R. P. Lippmann, Comparisons Between Neural Net and Conventional Classifiers, Technical Report, Lincoln Laboratory, MIT, 1987.
[HL2] W. Y. Huang and R.P. Lippmann, Neural Net and Traditional Classifiers, Technical Report, Lincoln Laboratory, MIT, 1987.
[H] P. J. Huber, Projection pursuit,Ann. Statist.,13 (1985), 435–475. (10.1214/aos/1176349519) / Ann. Statist. by P. J. Huber (1985)
[J] L. K. Jones, Constructive approximations for neural networks by sigmoidal functions, Technical Report Series, No. 7, Department of Mathematics, University of Lowell, 1988.
[K] A. N. Kolmogorov, On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition,Dokl. Akad. Nauk. SSSR,114 (1957), 953–956. / Dokl. Akad. Nauk. SSSR by A. N. Kolmogorov (1957)
[LF] A. Lapedes and R. Farber, Nonlinear Signal Processing Using Neural Networks: Prediction and System Modeling, Technical Report, Theoretical Division, Los Alamos National Laboratory, 1987.
[L1] R. P. Lippmann, An introduction to computing with neural nets,IEEE ASSP Mag.,4 (April 1987), 4–22. (10.1109/MASSP.1987.1165576) / IEEE ASSP Mag. by R. P. Lippmann (1987)
[L2] G. G. Lorentz, The 13th problem of Hilbert, inMathematical Developments Arising from Hilbert’s Problems (F. Browder, ed.), vol. 2, pp. 419–430, American Mathematical Society, Providence, RI, 1976. (10.1090/pspum/028.2/0507425) / Mathematical Developments Arising from Hilbert’s Problems by G. G. Lorentz (1976)
[MSJ] J. Makhoul, R. Schwartz, and A. El-Jaroudi, Classification capabilities of two-layer neural nets.Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Glasgow, 1989 (to appear).
[MP] M. Minsky and S. Papert,Perceptrons, MIT Press, Cambridge, MA, 1969. / Perceptrons by M. Minsky (1969)
[N] N. J. Nilsson,Learning Machines, McGraw-Hill, New York, 1965. / Learning Machines by N. J. Nilsson (1965)
[P] G. Palm, On representation and approximation of nonlinear systems, Part II: Discrete systems,Biol. Cybernet.,34 (1979), 49–52. (10.1007/BF00336857) / Biol. Cybernet. by G. Palm (1979)
[R1] W. Rudin,Real and Complex Analysis, McGraw-Hill, New York, 1966. / Real and Complex Analysis by W. Rudin (1966)
[R2] W. Rudin,Functional Analysis, McGraw-Hill, New York, 1973. / Functional Analysis by W. Rudin (1973)
[RHM] D. E. Rumelhart, G. E. Hinton, and J. L. McClelland, A general framework for parallel distributed processing, inParallel Distributed Processing: Explorations in the Microstructure of Cognition (D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, eds.), vol. 1, pp. 45–76, MIT Press, Cambridge, MA, 1986. (10.7551/mitpress/5236.001.0001) / Parallel Distributed Processing: Explorations in the Microstructure of Cognition by D. E. Rumelhart (1986)
[V] L. G. Valiant, A theory of the learnable,Comm. ACM,27 (1984), 1134–1142. (10.1145/1968.1972) / Comm. ACM by L. G. Valiant (1984)
[WL] A Wieland and R. Leighton, Geometric analysis of neural network capabilities,Proceedings of IEEE First International Conference on Neural Networks, San Diego, CA, pp. III-385–III-392, 1987.

Dates

Type	When
Created	18 years, 7 months ago (Jan. 5, 2007, 6:38 a.m.)
Deposited	2 years, 3 months ago (May 10, 2023, 4:35 a.m.)
Indexed	14 minutes ago (Aug. 27, 2025, 6:48 p.m.)
Issued	35 years, 8 months ago (Dec. 1, 1989)
Published	35 years, 8 months ago (Dec. 1, 1989)
Published Print	35 years, 8 months ago (Dec. 1, 1989)

Funders 0

None

BibTeX

@article{Cybenko_1989, title={Approximation by superpositions of a sigmoidal function}, volume={2}, ISSN={1435-568X}, url={http://dx.doi.org/10.1007/bf02551274}, DOI={10.1007/bf02551274}, number={4}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Cybenko, G.}, year={1989}, month=dec, pages={303–314} }

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