We investigate the optimization of neural networks governed by general objective functions. Practical formulations of such objec(cid:173) tives are notoriously difficult to solve; a common problem is the poor local extrema that result by any of the applied methods. In this paper, a novel framework is introduced for the solution oflarge(cid:173) scale optimization problems. It assumes little about the objective function and can be applied to general nonlinear, non-convex func(cid:173) tions; objectives in thousand of variables are thus efficiently min(cid:173) imized by a combination of techniques - deterministic annealing, multiscale optimization, attention mechanisms and trust region op(cid:173) timization methods.

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.

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.

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 inabilityof 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.