Skip to main content
NCBI home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1986 Dec;83(24):9469–9473. doi: 10.1073/pnas.83.24.9469

Sequential state generation by model neural networks.

D Kleinfeld
PMCID: PMC387161  PMID: 3467316

Abstract

Sequential patterns of neural output activity form the basis of many biological processes, such as the cyclic pattern of outputs that control locomotion. I show how such sequences can be generated by a class of model neural networks that make defined sets of transitions between selected memory states. Sequence-generating networks depend upon the interplay between two sets of synaptic connections. One set acts to stabilize the network in its current memory state, while the second set, whose action is delayed in time, causes the network to make specified transitions between the memories. The dynamic properties of these networks are described in terms of motion along an energy surface. The performance of the networks, both with intact connections and with noisy or missing connections, is illustrated by numerical examples. In addition, I present a scheme for the recognition of externally generated sequences by these networks.

Full text

PDF
9469

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Amit DJ, Gutfreund H, Sompolinsky H. Spin-glass models of neural networks. Phys Rev A Gen Phys. 1985 Aug;32(2):1007–1018. doi: 10.1103/physreva.32.1007. [DOI] [PubMed] [Google Scholar]
  2. Amit DJ, Gutfreund H, Sompolinsky H. Storing infinite numbers of patterns in a spin-glass model of neural networks. Phys Rev Lett. 1985 Sep 30;55(14):1530–1533. doi: 10.1103/PhysRevLett.55.1530. [DOI] [PubMed] [Google Scholar]
  3. Caianiello E. R. Decision equations and reverberations. Kybernetik. 1966 May;3(2):98–100. doi: 10.1007/BF00299902. [DOI] [PubMed] [Google Scholar]
  4. Fukushima K. A model of associative memory in the brain. Kybernetik. 1973 Feb;12(2):58–63. doi: 10.1007/BF00272461. [DOI] [PubMed] [Google Scholar]
  5. Getting P. A. Mechanisms of pattern generation underlying swimming in Tritonia. I. Neuronal network formed by monosynaptic connections. J Neurophysiol. 1981 Jul;46(1):65–79. doi: 10.1152/jn.1981.46.1.65. [DOI] [PubMed] [Google Scholar]
  6. Getting P. A. Mechanisms of pattern generation underlying swimming in Tritonia. III. Intrinsic and synaptic mechanisms for delayed excitation. J Neurophysiol. 1983 Apr;49(4):1036–1050. doi: 10.1152/jn.1983.49.4.1036. [DOI] [PubMed] [Google Scholar]
  7. Hopfield J. J. Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A. 1982 Apr;79(8):2554–2558. doi: 10.1073/pnas.79.8.2554. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Hopfield J. J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci U S A. 1984 May;81(10):3088–3092. doi: 10.1073/pnas.81.10.3088. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Hopfield J. J., Tank D. W. "Neural" computation of decisions in optimization problems. Biol Cybern. 1985;52(3):141–152. doi: 10.1007/BF00339943. [DOI] [PubMed] [Google Scholar]
  10. Little W. A., Shaw G. L. A statistical theory of short and long term memory. Behav Biol. 1975 Jun;14(2):115–133. doi: 10.1016/s0091-6773(75)90122-4. [DOI] [PubMed] [Google Scholar]
  11. Selverston A. I., Moulins M. Oscillatory neural networks. Annu Rev Physiol. 1985;47:29–48. doi: 10.1146/annurev.ph.47.030185.000333. [DOI] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES