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Cited by 17Neural Networks and ApplicationsNeural dynamics and brain functionNeural Networks and Reservoir Computing

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On the Storage Capacity of Nonlinear Neural Networks

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Mazza, Christian·1997·Neural Networks
DOI 10.1016/s0893-6080(97)00017-8
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Abstract

We consider the Hopfield associative memory for storing m patterns xi(r) in { - 1, + 1}(n), r = 1, em leader,m. The weights are given by the scalar product model w(ij)=(m/n)G,i not equal j,w(ii) identical with 0, where G:R --> R is some nonlinear function, like G(x) z.tbnd6; Sgn(x), which is used in hardware implementation of associative memories. We give a rigorous lower bound for the memory size of this (ANN) by using large deviations estimates. Our main results states that retrieval without errors occurs when m(n) --> infinity as n --> infinity in such a way that m(n) < (n/2log(n))q(G), where 0 < q(G): = E(NG)N))(2)/E(G(N)(2))) </= 1, N denotes a standard normal random variable, and E(.) is the expectation operator. Copyright 1997 Elsevier Science Ltd.

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Citations

Cites

Research works printed but not linked: 14

  1. Amit, D.J. (1992). Modeling brain function. The world of attractor neural networks. Cambridge: Cambridge University Press.
  2. Billingsley, P. (1968). Convergence of probability measures. New York: Wiley.
  3. Feller, W. (1971). An introduction to probability theory and its applications, Vols I and II. New York: Wiley.
  4. Kamp, Y., & Hasler, M. (1990). Recursive neural networks for associative memory. New York: Wiley.
  5. Hebb, D. (1949). The organization of behavior. New York: Wiley.
  6. van Hemmen, 1987, Nonlinear neural networks near saturation, Physical Review A, 35, 1959, 10.1103/PhysRevA.36.1959 · DOI
  7. van Hemmen, J.L., & Kühn, R. (1991). Collective phenomena in neural networks. In E. Domany, J.L. van Hemmen & K. Schulten (Eds.), Models of neural networks (pp. 1–101). New York: Springer-Verlag. · DOI
  8. Loukianova, 1994, Capacité de mémoire dans le modèle de Hopfield, Comptes Rendus de l'Académie des Sciences de Paris Série I, 318, 157
  9. Mazza, C. (1994). On the storage capacity of nonlinear neural networks. Institute for Mathematics and its Applications, Preprint Series (p. 1266). MN: University of Minnesota.
  10. Mazza, C. (1996). Neural net inference and content addressable memory. IEEE Transactions on Neural Networks, to appear.
  11. McEliece, 1987, The capacity of the Hopfield associative memory, IEEE Transactions on Information Theory, 33, 461, 10.1109/TIT.1987.1057328 · DOI · Paper page
  12. Newman, 1988, Memory capacity in neural network models: rigorous lower bounds, Neural Networks, 1, 223, 10.1016/0893-6080(88)90028-7 · DOI
  13. Piret, 1990, Analysis of a modified Hebbian rule, IEEE Transactions on Information Theory, 36, 1391, 10.1109/18.59934 · DOI
  14. Sompolinsky, 1986, Neural networks with nonlinear synapses and a static noise, Physical Review A, 34, 2571, 10.1103/PhysRevA.34.2571 · DOI

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Metadata

Authors
Mazza, C.
Corresponding author
Mazza, Christian
ORCID
Mazza, Christian
Venue
Neural Networks
Publisher
Elsevier BV
Published
1997-06
Volume
10
Issue
4
Pages
593-597
ISSN
0893-6080 (ISSN-L)
DOI
10.1016/s0893-6080(97)00017-8
OpenAlex
W2050270536
Cited by
17
References
1
Citations by year
2024: 1 · 2020: 1 · 2016: 1
FWCI
2.36
Type
journal article
Language
en
Open access
Licence
Locations
  • Neural Networks (publishedVersion)
  • PubMed (publishedVersion)
  • Archive ouverte UNIGE (University of Geneva) (submittedVersion, cc-by)
  • University of Minnesota Digital Conservancy (University of Minnesota) (submittedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Reservoir Computing
Keywords
Hopfield associative memory, storage capacity, nonlinear neural networks, sign function, large deviations, lower bounds, pattern retrieval, binary patterns, memory capacity

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