Properties of feedback neural networks studied from discrete algebra and N-dimension geometry
Chia-Lun John Hu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2002
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.