Algorithms for the Optimal Loading of Recursive Neural Nets

We address the problem of choosing synaptic weights in a recursive (Hopfield) neural network so as to "optimize" the performance of the network on the recognition of binary strings. The problem has been called the net loading (or learning) problem in the literature [10]. The objective is to maximize the basins of attraction around the desired fixed points (binary strings) of the net. It is known that it is NP-hard to evaluate even the two-step radius of attraction of a recursive neural net [3]. We focus on the radius of direct (one-step) attraction and will refer to this as the loading problem. We have both theoretical and computational results on this problem, that we summarize below. ffl A proof that the net loading problem can be solved in polynomial time using linear programming techniques. This resolves a standing problem in the complexity of recursive neural networks [10]. ffl An alternate formulation of the net loading problem as a proximity problem in high-dimens..