A Multiscale Attentional Framework for Relaxation Neural Networks

Many practical problems in computer vision, pattern recognition, robotics and other areas can be described in terms of constrained optimization. In the past decade, researchers have proposed means of solving such problems with the use of neural networks [Hopfield & Tank, 1985; Koch et ai., 1986], which are thus derived as relaxation dynamics for the objective functions codifying the optimization task. One disturbing aspect of the approach soon became obvious, namely the apparent inability of the methods to scale up to practical problems, the principal reason being the rapid increase in the number of local minima present in the objectives as the dimension of the problem increases. Moreover most objectives, E(v), are highly nonlinear, non-convex functions of v, and simple techniques (e.g.