Hostname: page-component-6766d58669-wvcvf Total loading time: 0 Render date: 2026-05-25T02:22:08.559Z Has data issue: false hasContentIssue false
  • English
  • Français

A stochastic model of an artificial neuron

Published online by Cambridge University Press:  01 July 2016

P. Whittle
P. Whittle*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple model of a neuron is proposed, not intended to be biologically faithful, but to incorporate dynamic and stochastic features which seem to be realistic for both the natural and the artificial case. It is shown that the use of feedback for assemblies of such neurons can produce bistable behaviour and sharpen the discrimination of the assembly to the level of input. Particular attention is paid to bistable devices which are to serve as bit-stores (and so constitute components of a memory) and which suffer a disturbing input due to mutual interference. Approximate expressions are obtained for the equilibrium distribution of the excitation level for such assemblies and for the expected escape time of such an assembly from a metastable excitation level.

Keywords

NEURONMEMORYRELIABILITYTUNNELLINGLARGE DEVIATIONS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 809 - 822
Copyright
Copyright © Applied Probability Trust 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aleksander, I. (1989) The logic of connectionist systems. In Neural Computing Architectures, ed. Aleksander, I., pp. 133–155. MIT Press, Cambridge, MA.Google Scholar
Caianello, E. R. (1989) A study of neuronic equations. In New Developments in Neural Computing, eds. Taylor, J. G. and Mannion, C. L. T., pp. 187–199. Adam Hilger, Bristol.Google Scholar
Freidlin, M. L. and Wentzell, A. D. (1984) Random Perturbations of Dynamical Systems. Springer, New York. (Translation of Russian original published in 1979 by Nauka, Moscow.)Google Scholar
Gorse, D. (1989) A new model of the neuron. In New Developments in Neural Computing, eds. Taylor, J. G. and Mannion, C. L. T., pp. 111–118. Adam Hilger, Bristol.Google Scholar
Jack, J. J. B., Noble, D. and Tsien, R. W. (1975) Electrical Current Flow in Excitable Cells. Oxford University Press.Google Scholar
Kallianpur, G. (1983) On the diffusion approximation to a discontinuous model for a single neuron. In Contributions to Statistics, ed. Sen, P. K., pp. 247–258. North-Holland, Amsterdam.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
Mcculloch, W. S. and Pitts, W. (1943) A logical calculus of ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133.Google Scholar
Markin, V. S., Pastushenko, V. F. and Chizmadzhev, Y. A. (1987) Theory of Excitable Media. Wiley, New York. (Translation of Russian original published in 1981 by Nauka, Moscow.)Google Scholar
Von Neumann, J. (1956) Probabilistic logics and the synthesis of reliable organisms from unreliable components. In Automata Studies, pp. 43–98. Annals of Mathematics Studies No. 34, Princeton University Press.Google Scholar
Taylor, J. G. (1972) Spontaneous behaviour in neural networks. J. Theoret. Biol. 36, 513–528.Google Scholar
Taylor, J. G. (1987) Noisy neural net states and their time evolution. King's College Preprint.Google Scholar
Taylor, J. G. (1989) Living neural nets. In New Developments in Neural Computing, eds. Taylor, J. G. and Mannion, C. L. T., pp. 31–52. Adam Hilger, Bristol.Google Scholar
Walrand, J. and Varaiya, P. (1980) Interconnections of Markov chains and quasireversible queueing networks. Stoch. Proc. Appl. 10, 209–219.Google Scholar
Walsh, J. (1981) A stochastic model of neural response. Adv. Appl. Prob. 13, 231–281.Google Scholar
Whittle, P. (1990) A construction for multi-modal processes and a potential memory device. J. Appl. Prob. 27, 146–155.Google Scholar
Wong, K. Y. M. and Sherrington, D. (1989) Storage properties of Boolean neural networks. In Neural Networks from Models to Applications, Eds. Personnaz, L. and Dreyfus, G. IDSTE, Paris.Google Scholar