Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-19T23:55:13.294Z Has data issue: false hasContentIssue false
  • English
  • Français

A construction for multi-modal processes, and a potential memory device

Published online by Cambridge University Press:  14 July 2016

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

Abstract

It is shown that if parameters occurring linearly in the transition intensity of a Markov process are replaced by their respective ‘Bayesian estimates' then the new process thus generated has an equilibrium distribution which is a mixture (over parameter values) of the original parametrised equilibrium distribution.

One effectively then has an extra state dependence in that one selects from a given class of transition rules those rules which are most consistent with the value of current state. The effect of this is thus to preserve the status quo, in that unlikely transitions are made even less likely. By this means one can construct processes which show several distinct and metastable modes of behaviour, and which can serve as models for memory devices.

Keywords

MODEMETASTABILITYMEMORYNEURAL NETWORK
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 146 - 155
Copyright
Copyright © Applied Probability Trust 1990 

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.)

References

Amit, D. J., Gutfreund, H. and Sompolinsky, H. (1985) Spin-glass models of neural networks. Phys. Rev. A 32, 1007–1018.Google Scholar
Amit, D. J., Gutfreund, H. and Sompolinsky, H. (1985) Storing infinite numbers of patterns in a spin-glass model of neural networks. Phys. Rev. Letters 55, 1530–1533.CrossRefGoogle Scholar
Bartlett, M. S. (1955) An Introduction to Stochastic Processes. Cambridge University Press.Google Scholar
Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci., USA 79, 2554–2558.CrossRefGoogle ScholarPubMed
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
Mceliece, R. J., Posner, E.C., Rodemich, E. R. and Venkatesh, S. S. (1987) The capacity of the Hopfield associative memory. IEEE Trans. Inf. Theory 33, 461–482.Google Scholar
Whittle, P. (1984) Weak coupling in stochastic systems. Proc. Roy. Soc. London A 395, 141–151.Google Scholar
Whittle, P. (1986) Systems in Stochastic Equilibrium. Wiley, Chichester.Google Scholar
Whittle, P. (1989) The antiphon; a device for reliable memory from unreliable components. Proc. Roy. Soc. London A423, 201–218.Google Scholar