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Proceedings Paper

Anomalous nonlinear properties of Hopfield net studied from discrete algebra and N-dimension geometry
Author(s): Chia-Lun John Hu
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Paper Abstract

For a one-layered-feedback neural network, e.g., a Hopfield net, containing discrete sign-function neurons, the nonlinear properties of this network can be studied very efficiently using simple discrete mathematics. This paper summarizes the discrete-formulation of the problem as a matrix difference equation, the simple iterative method of solving this difference equation and the derivation of the major anomalous properties of the system from the solutions. These anomalous properties include, eigen-state storage, associative storage, domain of attraction, content- addressable recall, fault-tolerant recall, capacity of storage, binary oscillating states, limit-cycles in the state space, and noise-sensitive input states. The physical origin and the systematic trend of the derivation of these properties are easily seen in the numerical examples given.

Paper Details

Date Published: 5 April 2002
PDF: 7 pages
Proc. SPIE 4668, Applications of Artificial Neural Networks in Image Processing VII, (5 April 2002); doi: 10.1117/12.461667
Show Author Affiliations
Chia-Lun John Hu, Southern Illinois Univ./Carbondale (United States)

Published in SPIE Proceedings Vol. 4668:
Applications of Artificial Neural Networks in Image Processing VII
Nasser M. Nasrabadi; Aggelos K. Katsaggelos, Editor(s)

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