Evolution of Imprints of Learning in Self-Learning Networks

Physical systems with adaptable interactions can be trained to have specific physical properties. In systems with reciprocal adaptable interactions, adaptation is a double optimization process, where a cost function penalizing deviations from the desired material property is minimized by the adaptable degrees of freedom characterizing interactions (e.g. resistances in an electrical network of nodes connected by adjustable resistors) while a physical Lyapunov function (e.g. power dissipation), is minimized by physical degrees of freedom (e.g. node voltages). This process encodes the functionality in the system’s in the system’s response to perturbations [1, 2], specifically in the physical Hessian. We build on [1,2] to develop an understanding of the evolution of the physical imprints of learning in physical networks.