A long-memory model of motor learning in the saccadic system: a regime-switching approach

Maintenance of movement accuracy relies on motor learning, by which prior errors guide future behavior. One aspect of this learning process involves the accurate generation of predictions of movement outcome. These predictions can, for example, drive anticipatory movements during a predictive-saccade task. Predictive saccades are rapid eye movements made to anticipated future targets based on error information from prior movements. This predictive process exhibits long-memory (fractal) behavior, as suggested by inter-trial fluctuations. Here, we model this learning process using a regime-switching approach, which avoids the computational complexities associated with true long-memory processes. The resulting model demonstrates two fundamental characteristics. First, long-memory behavior can be mimicked by a system possessing no true long-term memory, producing model outputs consistent with human-subjects performance. In contrast, the popular two-state model, which is frequently used in motor learning, cannot replicate these findings. Second, our model suggests that apparent long-term memory arises from the trade-off between correcting for the most recent movement error and maintaining consistent long-term behavior. Thus, the model surprisingly predicts that stronger long-memory behavior correlates to faster learning during adaptation (in which systematic errors drive large behavioral changes); greater apparent long-term memory indicates more effective incorporation of error from the cumulative history across trials.