Skip to main content
×
×
Home

Classification and lumpability in the stochastic Hopfield model

  • R. L. Paige (a1)
Abstract

Connections between classification and lumpability in the stochastic Hopfield model (SHM) are explored and developed. A simplification of the SHM's complexity based upon its inherent lumpability is derived. Contributions resulting from this reduction in complexity include: (i) computationally feasible classification time computations; (ii) a development of techniques for enumerating the stationary distribution of the SHM's energy function; and (iii) a characterization of the set of possible absorbing states of the Markov chain associated with the zero temperature SHM.

Copyright
Corresponding author
Postal address: Department of Mathematics and Statistics, Texas Technological University, Lubbock, TX 79409, USA. Email address: rpaige@math.ttu.edu
References
Hide All
Amit, D. J. (1989). Modeling Brain Function. Cambridge University Press.
Amit, D. J., Gutfreund, H. and Sompolinsky, H. (1985). Spin-glass models for neural networks. Phys. Rev. A,32, 10071018.
Butler, R. W. (2000). Reliabilities for feedback systems and their saddlepoint approximation. Statist. Sci. 15, 279298.
Daniels, H. (1954). Saddlepoint approximations in statistics. Ann. Math. Statist. 25, 631650.
Daniels, H. (1987). Tail probability approximations. Internat. Statist. Rev. 55, 3748.
Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach Intellig. 6, 720741.
Hertz, J. A., Krogh, A. S. and Palmer, R. G. (1991). Introduction to the Theory of Neural Computation. Addison-Wesley, New York.
Hoffman, R. E. (1992). Attractor neural networks and psychotic disorders. Psych. Ann. 22, 119124.
Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. USA 79, 25542558.
Kam, M. and Cheng, R. (1989). Decision-making with the Boltzmann machine. In Proc. Amer. Control Conf. (Pittsburgh, PA, June 1989) Vol. 1, pp. 902907.
Kemeny, J. and Snell, L. (1969). Finite Markov Chains. Van Nostrand, Princeton, NJ.
Kleinfield, D. and Somopolinsky, H. (1989). Associative neural models for central pattern generators. In Methods in Neuronal Modeling: From Synapses to Networks, eds Koch, C. and Segev, I., MIT Press, Cambridge, MA, pp. 195246.
Sumita, U. and Rieders, M. (1988). First passage times and lumpability of semi-Markov processes. J. Appl. Prob. 25, 675687.
Whittle, P. (1991). Neural nets and implicit inference. Ann. Appl. Prob. 1, 173188.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed