Golden, R. M. (1993). Stability and optimization analyses of the
generalized brain-state-in-a-box neural network model.
Journal of Mathematical Psychology, 37,
282--298.
ABSTRACT
Anderson's brain-state-in-a-box (BSB) neural network model may be viewed
as a version of Hopfield's two-state neural model with continuous
rather than discrete states and synchronous updating. A generalization
of the BSB model which allows each model neuron in the system to have a
bias and its own maximum and minimum firing rate is considered. Moreover,
the generalization does not require that the matrix of connection weights
be symmetric. A method of choosing the step constant of the algorithm is
then described which guarantees that the generalized
discrete-time BSB model: (i) approaches the largest set of system equilibrium
points, and (ii) minimizes the Boltzmann machine quadratic energy function.
A simple test (essentially a vector by matrix multiplication) for checking for
asymptotically stable equilbrium points is also provided. Finally, a special
case of the generalized BSB model is shown to be applicable to a particular
type of optimal control problem.
Semi-final post script draft (possibly missing figures)
Golden's Neural Network Publications List