Applying The INN Model to the MaxClique Problem

A neural network model, the INN (Inverted Neurons Network), is applied to the Maximum Clique problem. First, I describe the INN model and how it implements a given graph instance. The model has a threshold parameter t, which determines the character of the network stable states. As shown in an earlier work 5], the stable states of the network correspond to the t-codegree sets of its underlying graph, and, in the case of t < 1, to its maximal cliques. These results are brieey reviewed. In this work I concentrate on improving the deterministic dynamics called t-annealing. The main issue is the initialization procedure and the choice of parameters. Adaptive procedures for choosing the initial state of the network and setting the threshold are presented. The result is the \Adaptive t-Annealing" algorithm (AtA). This algorithm is tested on many benchmark problems and found to be more eecient than steepest descent or the simple t-annealing procedure.