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Classification and lumpability in the stochastic Hopfield model

Part of: Special processes Distribution theory Artificial intelligence (68Txx)

Published online by Cambridge University Press:  19 February 2016

R. L. Paige
R. L. Paige*
Affiliation:
Texas Technological University
*
∗ Postal address: Department of Mathematics and Statistics, Texas Technological University, Lubbock, TX 79409, USA. Email address: [email protected]
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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.

Keywords

Classification timesneural networks

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 62E17: Approximations to distributions (nonasymptotic) 68T01: General
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 4 , December 2001 , pp. 930 - 943
Copyright
Copyright © Applied Probability Trust 2001 

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