Anomalous nonlinear properties of Hopfield net 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
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.