The dynamics of motor learning through the formation of internal models

A medical student learning to perform a laparoscopic procedure or a recently paralyzed user of a powered wheelchair must learn to operate machinery via interfaces that translate their actions into commands for an external device. Since the user’s actions are selected from a number of alternatives that would result in the same effect in the control space of the external device, learning to use such interfaces involves dealing with redundancy. Subjects need to learn an externally chosen many-to-one map that transforms their actions into device commands. 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 the proposed model of learning dynamics and the learning performance observed in a group of subjects demonstrate a first-order exponential convergence of the learning process toward a particular state that depends only on the initial state of the inverse and forward models and on the sequence of targets supplied to the users. 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 both the skill and 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 movement goals. We test this hypothesis by taking advantage of an interface that relates the user’s actions to the position of a cursor on a computer monitor, thus allowing users to control an external device through body movements. We recorded the motions of the body and of the cursor, and used this data to estimate forward and inverse models. We followed the time evolution of these estimated models as interface users practiced and acquired a new skill. We found that the description of learning as a simple deterministic process driven by the presented sequence of targets is sufficient to capture the observed convergence to a single solution of the inverse model among an infinite variety of 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.