Paralleled hardware annealing for optimal solutions on electronic neural networks

Abstract

Three basic neural network schemes have been extensively studied by researchers: the iterative networks, the backpropagation networks, and the self-organizing networks. Simulated annealing is a probabilistic hill-climbing technique that accepts, with a nonzero but gradually decreasing probability, deterioration in the cost function of the optimization problems. Hardware annealing, which combines the simulated annealing technique with continuous-time electronic neural networks by changing the voltage gain of neurons, is discussed. The initial and final voltage gains for applying hardware annealing to Hopfield data-conversion networks are presented. In hardware annealing, the voltage gain of output neurons is increased from an initial low value to a final high value in a continuous fashion which helps to achieve the optimal solution for an optimization problem in one annealing cycle. Experimental results on the transfer function and transient response of electronic neural networks achieving the global minimum are also presented.

Efficient Faulty Element Diagnostics of Large Antenna Arrays by Discrete Mean Field Neural Nets

“…{0, 1} N has been discussed in [10]. For the linear (field measurement) case, we let (see Appendix A for details):…”

“…We further prove that under suitable (sufficient) assumptions for the involved threshold function, the above Lyapounov function has a unique minimum, which coincides with the sought global minimum of the functional to be minimized on the lattice {0, 1} N . A number of critical technical issues (computation of the multilinear energy polynomial [9], optimum choice of the weights, and of the updating schedule of the threshold parameter [10]) are discussed.…”

Search of optimal solutions in multi-level neural networks

“…When the voltage gain of the neurons is sufficiently large, the sum of eigenvalues of the system matrix M of a Hopfield A/D decision network approximates to zero, and the product of eigenvalues is not equal to zero [5].…”

“…The output of the A/D decision network is not fully digital. When the voltage gain reaches only two neurons operate in the linear region [5]. When the voltage gain is slightly larger than A z , only one neuron could be in the linear region.…”

A noise annealing neural network for global optimization

“…One of the first developments in this field a stochastic learning automata called Boltzmann Machine (BM) [I], which uses SA extensively. Other generalizations of the Hopfield model based on analogies to statistical physics are also designed for avoiding local optima [15], [lo], [ I l l , [12].…”