Deterministic annealing techniques for a discrete-time neural-network updating in a block-sequential mode

A global stability criterion for two constituent parameters of the discrete-time neural network updating in a block-sequential mode is derived, and two deterministic annealing techniques incorporating its stability condition are studied. One technique concerns reducing the decay rate of the membrane potential gradually toward zero; the other relates to increasing the neuron gain gradually toward infinity while updating the neuron states iteratively. It is shown that the deterministic annealing for parallel or partial-parallel updating can be successfully accomplished without falling into sustained oscillations by properly controlling the decay rate of the membrane potential as well as the neuron gain. It is also demonstrated that near optimal solutions are obtained for parallel, partial-parallel, and sequential updating by the suitable selection of the two constituent parameters.