Anomalous nonlinear properties of Hopfield net studied from discrete algebra and N-dimension geometry

Chia-Lun John Hu

doi:10.1117/12.461667

5 April 2002 Anomalous nonlinear properties of Hopfield net studied from discrete algebra and N-dimension geometry

Chia-Lun John Hu

Proceedings Volume 4668, Applications of Artificial Neural Networks in Image Processing VII; (2002) https://doi.org/10.1117/12.461667
Event: Electronic Imaging, 2002, San Jose, California, United States

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.

Citation Download Citation

Chia-Lun John Hu "Anomalous nonlinear properties of Hopfield net studied from discrete algebra and N-dimension geometry", Proc. SPIE 4668, Applications of Artificial Neural Networks in Image Processing VII, (5 April 2002); https://doi.org/10.1117/12.461667

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