This project will attempt to advance our fundamental understanding of Hopfield neural networks - - a class of artificial neural network designed to minimize complicated functions of a large number of variables. Hopfield networks solve these problems very quickly, and have been applied to problems like the traveling salesman problem (i.e., efficient routing systems), the N-queen problem, bearing estimation, robot path finding, robot arm positioning, content addressable memory, and others. Unfortunately, Hopefield nets are only guaranteed to converge to a local minimum. Other techniques have been developed to explore the solution space stochastically, to look for better solutions far away from this local minimum; however, these techniques may be expensive. The P.I. here will be extending his recent work on a different approach - - to find conditions which insure that the Hopfield net will in fact find a global minimum, and exploit these conditions in applications such as radar and sonar detection.
