The dynamics of motor learning through the formation of internal models

Abstract A medical student learning to perform a laparoscopic procedure as well as a recently paralyzed user of a powered wheelchair must learn to operate machinery via interfaces that translate their actions into commands for the external device. Mathematically, we describe this type of learning as a deterministic dynamical process, whose state is the evolving forward and inverse internal models of the interface. The forward model predicts the outcomes of actions while the inverse model generates actions designed to attain desired outcomes. Both the mathematical analysis of learning dynamics and the performance observed in a group of subjects demonstrate first-order exponential convergence of the learning process toward a particular state that depends only on the initial inverse and forward models and on the supplied sequence of targets. Noise is not only present but necessary for the convergence of learning through the minimization of the difference between actual and predicted outcomes. Author summary Several studies have suggested that as we learn a new skill our brain forms representations, or “internal models”, of the skill and of the environment in which we operate. Theories of motor learning postulate that the brain builds forward models that predict the sensory consequences of motor commands, and inverse models that generate successful commands from planned movements. We test this hypothesis taking advantage of a special interface that generates a novel relation between the subject’s actions and the position of a cursor on a computer monitor, thus allowing subjects to control an external device by movements of their body. We recorded the motions of the body and of the cursor, and obtained estimates of both forward and inverse models. We followed how these estimates evolved in time as subjects practiced and acquired a new skill. We found that the description of learning as a simple deterministic process driven by the sequence of targets is sufficient to capture the observed convergence to a single solution of the inverse model among an infinite variety of alternative possibilities. This work is relevant to the study of fundamental learning mechanisms as well as to the design of intelligent interfaces for people with paralysis.