Abstract
Several computational approaches have been applied to studying sensorimotor adaptation. State-space models formally describe properties of adaptation but do not provide a mechanistic explanation, nor do they directly incorporate uncertainty. On the other hand, Kalman filter models, according to the Bayesian framework, view adaptation as a problem of choosing optimal actions in a noisy and uncertain environment, but they are little concerned with the structure of the physical plant of the system responsible for adaptation. In our study, we instead propose that the system can be modeled with multiple interacting states, each one described as a Kalman filter. To test our hypothesis, we measured motor error in a series of rapid reaching tasks, under different conditions of measurement uncertainty and while inserting systematic perturbations. Uncertainty was modulated by blurring the visual feedback of the endpoint location of the reaching movement. Perturbations consisted of sinusoidal offsets at different frequencies, so that the adaptation response was described in terms of amplitude ratio and phase lag of the motor error associated with each sinusoidal perturbation (i.e. the frequency response of adaptation). By applying system identification procedures, we tested which of the following architectures best fit the data: a single learning rate, two rates in series, or two rates in parallel. We found that two rates in parallel consistently provided a significantly better fit than the others. When evaluating the identified system parameters, we further discovered that both learning rates decreased under higher uncertainty. Lastly, the weight assigned to the state with the faster learning rate did not remain constant but was highest in the less uncertain condition. We propose that the identified system architecture may reflect how the perceived error is assigned to different components of the physical plant responsible for adaptation: one being dominated by vision, the other by the motor component.