Transformations in the scale of behavior and the global optimization of constraints in adaptive networks

The natural energy minimization behavior of a dynamical system can be interpreted as a simple optimization process, finding a locally optimal resolution of problem constraints. In human problem solving, high-dimensional problems are often made much easier by inferring a low-dimensional model of the system in which search is more effective. But this is an approach that seems to require top-down domain knowledge-not one amenable to the spontaneous energy minimization behavior of a natural dynamical system. However, in this article we investigate the ability of distributed dynamical systems to improve their constraint resolution ability over time by self-organization. We use a ''self-modeling'' Hopfield network with a novel type of associative connection to illustrate how slowly changing relationships between system components can result in a transformation into a new system which is a low-dimensional caricature of the original system. The energy minimization behavior of this new system is significantly more effective at globally resolving the original system constraints. This model uses only very simple, and fully distributed, positive feedback mechanisms that are relevant to other ''active linking'' and adaptive networks. We discuss how this neural network model helps us to understand transformations and emergent collective behavior in various non-neural adaptive networks such as social, genetic and ecological networks.