Properties of feedback neural networks studied from discrete algebra and N-dimension geometry

Chia-Lun John Hu

doi:10.1117/12.458409

6 March 2002 Properties of feedback neural networks studied from discrete algebra and N-dimension geometry

Chia-Lun John Hu

Proceedings Volume 4734, Optical Pattern Recognition XIII; (2002) https://doi.org/10.1117/12.458409
Event: AeroSense 2002, 2002, Orlando, FL, United States

Abstract

Hopfield net is a typical example of a one-layer, feed-back neural network containing a layer of binary neurons and a linear feed-back matrix - the connection matrix. It was first formulated by Hopfield using nonlinear-differential equations and later by Grossberg using differential-integral equations. The nonlinear properties of the network derived form these formulations are scarce and non-systematic because of the difficulty of obtaining the complete solutions form these formulations. We use a simple discrete- algebra formulation which contains only one nonlinear operator - the threshold-logic operator, or the SGN operator. Many interesting and systematic anomalous nonlinear properties can then be derived. These 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. This paper will describe the physical origins of these anomalous nonlinear properties and the simplified mathematical analysis that leads to the derivation of these properties.

Citation Download Citation

Chia-Lun John Hu "Properties of feedback neural networks studied from discrete algebra and N-dimension geometry", Proc. SPIE 4734, Optical Pattern Recognition XIII, (6 March 2002); https://doi.org/10.1117/12.458409

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