A generative learning model for saccade adaptation

Plasticity in the oculomotor system ensures that saccadic eye movements reliably meet their visual goals—to bring regions of interest into foveal, high-acuity vision. Here, we present a comprehensive description of sensorimotor learning in saccades. We induced continuous adaptation of saccade amplitudes using a double-step paradigm, in which participants saccade to a peripheral target stimulus, which then undergoes a surreptitious, intra-saccadic shift (ISS) as the eyes are in flight. In our experiments, the ISS followed a systematic variation, increasing or decreasing from one saccade to the next as a sinusoidal function of the trial number. Over a large range of frequencies, we confirm that adaptation gain shows (1) a periodic response, reflecting the frequency of the ISS with a delay of a number of trials, and (2) a simultaneous drift towards lower saccade gains. We then show that state-space-based linear time-invariant systems (LTIS) represent suitable generative models for this evolution of saccade gain over time. This state-equation algorithm computes the prediction of an internal (or hidden state-) variable by learning from recent feedback errors, and it can be compared to experimentally observed adaptation gain. The algorithm also includes a forgetting rate that quantifies per-trial leaks in the adaptation gain, as well as a systematic, non-error-based bias. Finally, we study how the parameters of the generative models depend on features of the ISS. Driven by a sinusoidal disturbance, the state-equation admits an exact analytical solution that expresses the parameters of the phenomenological description as functions of those of the generative model. Together with statistical model selection criteria, we use these correspondences to characterize and refine the structure of compatible state-equation models. We discuss the relation of these findings to established results and suggest that they may guide further design of experimental research across domains of sensorimotor adaptation. Author Summary Constant adjustments of saccade metrics maintain oculomotor accuracy under changing environments. This error-driven learning can be induced experimentally by manipulating the targeting error of eye movements. Here, we investigate oculomotor learning in healthy participants in response to a sinusoidally evolving error. We then fit a class of generative models to the observed dynamics of oculomotor adaptation under this new learning regime. Formal model comparison suggests a richer model parameterization for such a sinusoidal error variation than proposed so far in the context of classical, step-like disturbances. We identify and fit the parameters of a generative model as underlying those of a phenomenological description of adaptation dynamics and provide an explicit link of this generative model to more established state equations for motor learning. The joint use of the sinusoidal adaption regime and consecutive model fit may provide a powerful approach to assess interindividual differences in adaptation across healthy individuals and to evaluate changes in learning dynamics in altered brain states, such as sustained by injuries, diseases, or aging.