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Finiteness results for sigmoidal “neural” networks

Authors:

Angus Macintyre,

Eduardo D. SontagAuthors Info & Claims

STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing

Pages 325 - 334

https://doi.org/10.1145/167088.167192

Published: 01 June 1993 Publication History

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References

[1]

Baum, E.B., and D. Haussler, "What size net gives valid generalization?," Neural Computation 1 (1989): 151- 160.

Digital Library

Google Scholar

[2]

Bierstone, E., and Pierre D. Milman, "Semianalytic and subanalytic sets," inst. Hautes I#tudes Sci. Publ. Math. 67(1988): 5-42.

Crossref

Google Scholar

[3]

Blum, A., and R.L. Rivest, "Training a 3-node neural network is NP-complete," in Advances in Neural Information Processing Systems 2 (D.S. Touretzky, ed), Morgan Kaufmann, San Mateo, CA, 1990, pp. 9-18.

Digital Library

Google Scholar

[4]

DasGupta, D., and G. Schnitger, "The power of approximating: a comparison of activation functions," in Advances in Neural Information Processing Systems 5 (Giles, C.L., Hanson, S.J., and Cowan, J.D., eds), Morgan Kaufmann, San Mateo, CA, 1993, to appear.

Google Scholar

[5]

Durbin, R., and D.E. Rumelhart, "Product units: a computationally powerful and biologically plausible extension to backpropagation networks, Neural Computation 1 (1989): 133-142.

Digital Library

Google Scholar

[6]

Goldberg, P., and M. Jerrum, "Bounding the Vapnlk- Chervonenkis dimension of concept classes parametrized by real numbers," submitted.

Google Scholar

[7]

Goldman, S.A., and M.J. Kearns, "On the complexity of teaching," Proc. Forth A CM Workshop on Computational Learning Theory, July 1991, pp. 303-314.

Digital Library

Google Scholar

[8]

Haussler, D., "Decision theoretic generalizations of the PAC model for neural net and other learning applications," In}orm. and Computation 100(1992): 78-150.

Digital Library

Google Scholar

[9]

Hertz, J., A. Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, Redwood City, 1991.

Digital Library

Google Scholar

[10]

Karpinski, M., and T. Werther, "VC dimension and uniform learnability of sparse polynomials and rational functions," SIAM J. Computing, to appear. (Preprint 8537-CS, Bonn, 1989.)

Digital Library

Google Scholar

[11]

Khovanskii, A.G., Fewnomials, American Mathematical Society, Providence, R.I., 1991.

Google Scholar

[12]

Laskowski, M.C., "Vapnik-Chervonenkis classes of definable sets," J. London Math. Soc. 2 45(1992): 377-384.

Google Scholar

[13]

Maass, W.G., "Bounds for the computational power and learning complexity of analog neural nets," Proc. of the 25th A CM Syrup. Theory of Computing, 1993.

Digital Library

Google Scholar

[14]

Maass W., G. Schnitger, and E.D. Sontag, "On the computational power of sigmoid versus Boolean threshold circuits," in Proc. 32nd IEEE Syrup. Foundations o} Comp. Sci., 1991: 767-776.

Digital Library

Google Scholar

[15]

Macintyre, A.J., and A.J. Wilkie, "Schanuel's conjecture implies the decidability of real exponentiation," handwritten, Oxford University, 1992.

Google Scholar

[16]

Siegelmann, H.T., and E.D. Sontag, "On the computational power of neural nets," in Proc. Fifth A CM Workshop on Computational Learning Theory, Pittsburgh, July 1992, 440-449.

Digital Library

Google Scholar

[17]

Siegelmann, H.T., and E.D. Sontag, "Analog computation, neural networks, and circuits," submitted.

Google Scholar

[18]

Sontag, E.D., "Feedforward nets for interpolation and classification," J. Comp. Syst. Sci. 45(1992): 20-48.

Digital Library

Google Scholar

[19]

Sontag, E.D., Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer, New York, 1990.

Digital Library

Google Scholar

[20]

Stengle, G. and Yukich, :I.E., "Some new Vapnik- Chervonenlds classes," The Annals of Statistics 14 (1989): 1441-1446.

Crossref

Google Scholar

[21]

Sussmann, H.J., "Uniqueness of the weights for minimal feedforward nets with a given input-output map," Neural Networks 5(1992): 589-593.

Digital Library

Google Scholar

[22]

Sussmann, H.J., "Real analytic desingularization and subanalytic sets: An elementary approach," Trans. Amer. Math. Soc. 317(1990): 417-461.

Google Scholar

[23]

Tougeron, J.C., "Sur certaines algebres de fonctions analytiques", Seminaire sur la geometrie algebrique reelle, Tome I, II Publ. Math. Univ. Paris VII 24 (1986): 35- 121.

Google Scholar

[24]

van den Dries, L., "A generalization of the Tarsld- Seidenberg theorem, and some nondefinability results," Bull. AMS 15(1986): 189-193.

Crossref

Google Scholar

[25]

van den Dries, L., " Tame topology and 0-minimal structures", preprint, University of Illinois, Urbana, 1991-2.

Google Scholar

[26]

van den Dries, L., and C. Miller, "On the real exponential field with restricted analytic functions," Israel J. Math., to appear.

Google Scholar

[27]

van den Dries, L., A. Macintyre, and D. Marker, "The elementary theory of restricted analytic fields with exponentiation," Annals o} Math., to appear.

Google Scholar

[28]

Wilkie, A.J., "Some model completeness results for expansions of the ordered field of reals by Pfaffian functions," preprint, Oxford, 1991, submitted.

Google Scholar

[29]

Wilkie, A.J., "Smooth 0-minimal theories and the model completeness of the real exponential field," preprint, Oxford, 1991, submitted.

Google Scholar

Cited By

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Ripley B(2018)Neural Networks and Related Methods for ClassificationJournal of the Royal Statistical Society Series B: Statistical Methodology10.1111/j.2517-6161.1994.tb01990.x56:3(409-437)Online publication date: 5-Dec-2018
https://doi.org/10.1111/j.2517-6161.1994.tb01990.x
Vidyasagar MKarandikar R(2008)A learning theory approach to system identification and stochastic adaptive controlJournal of Process Control10.1016/j.jprocont.2007.10.00918:3-4(421-430)Online publication date: Mar-2008
https://doi.org/10.1016/j.jprocont.2007.10.009
Boucheron SBousquet OLugosi G(2005)Theory of Classification: a Survey of Some Recent AdvancesESAIM: Probability and Statistics10.1051/ps:20050189(323-375)Online publication date: 15-Nov-2005
https://doi.org/10.1051/ps:2005018
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Finiteness results for sigmoidal “neural” networks

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Published In

STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing

June 1993

812 pages

ISBN:0897915917

DOI:10.1145/167088

Chairmen:
Rao Kosaraju
John Hopkins Univ., Baltimore, MD
,
David Johnson
AT&T Bell Lab.
,
Alok Aggarwal
IBM T. J. Watson Research Center,Yorktown Heights, NY

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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New York, NY, United States

Publication History

Published: 01 June 1993

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STOC93: 25th Annual ACM Symposium on the Theory of Computing

May 16 - 18, 1993

California, San Diego, USA

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Cited By

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Ripley B(2018)Neural Networks and Related Methods for ClassificationJournal of the Royal Statistical Society Series B: Statistical Methodology10.1111/j.2517-6161.1994.tb01990.x56:3(409-437)Online publication date: 5-Dec-2018
https://doi.org/10.1111/j.2517-6161.1994.tb01990.x
Vidyasagar MKarandikar R(2008)A learning theory approach to system identification and stochastic adaptive controlJournal of Process Control10.1016/j.jprocont.2007.10.00918:3-4(421-430)Online publication date: Mar-2008
https://doi.org/10.1016/j.jprocont.2007.10.009
Boucheron SBousquet OLugosi G(2005)Theory of Classification: a Survey of Some Recent AdvancesESAIM: Probability and Statistics10.1051/ps:20050189(323-375)Online publication date: 15-Nov-2005
https://doi.org/10.1051/ps:2005018
DasGupta BHammer B(2005)On approximate learning by multi-layered feedforward circuitsTheoretical Computer Science10.1016/j.tcs.2005.09.008348:1(95-127)Online publication date: 2-Dec-2005
https://dl.acm.org/doi/10.1016/j.tcs.2005.09.008
Karpinski MMacintyre A(2005)Approximating the volume of general Pfaffian bodiesStructures in Logic and Computer Science10.1007/3-540-63246-8_10(162-173)Online publication date: 7-Jun-2005
https://doi.org/10.1007/3-540-63246-8_10
Karpinski MMacintyre A(2005)Bounding VC-dimension for neural networks: Progress and prospectsComputational Learning Theory10.1007/3-540-59119-2_189(337-341)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-59119-2_189
Indyk P(2005)Optimal simulation of automata by neural netsSTACS 9510.1007/3-540-59042-0_85(337-348)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-59042-0_85
Sima J(2002)Training a single sigmoidal neuron is hardNeural Computation10.1162/08997660276040803514:11(2709-2728)Online publication date: 1-Nov-2002
https://dl.acm.org/doi/10.1162/089976602760408035
Vidyasagar M(2001)Randomized algorithms for robust controller synthesis using statistical learning theoryAutomatica (Journal of IFAC)10.1016/S0005-1098(01)00122-437:10(1515-1528)Online publication date: 1-Oct-2001
https://dl.acm.org/doi/10.1016/S0005-1098%2801%2900122-4
Gu HTakahashi H(2000)How Bad May Learning Curves Be?IEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/34.87979522:10(1155-1167)Online publication date: 1-Oct-2000
https://dl.acm.org/doi/10.1109/34.879795
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