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Carlos Cassanello, Florian Ostendorf, Martin Rolfs; State-equation learning model for saccade adaptation. Journal of Vision 2017;17(10):1142. doi: 10.1167/17.10.1142.
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We present a theoretical assessment of a modified delta-rule based state-equation learning model intended to describe the temporal dynamics of saccade adaptation. By integrating the state equation we derive and predict functional phenomenological parameterizations that proved accurate in describing the evolution of saccade gain observed in a range of saccadic adaptation paradigms. We stress and study in detail the case of sinusoidal saccade adaptation. The introduction of richer dynamics through the trial-by-trial sine varying dependence of the disturbance avails two extra phenomenological parameters compared to those available in traditional fixed-step paradigms, namely the amplitude of the characteristic periodic component that the oculomotor response develops and the lag of this response with respect to the stimulus (Cassanello et al., J Neurophysiol, 2016). We derived the functional dependence that those phenomenological parameters should bear on the learning rates of the underlying state-equation model. We show that solving by iteration a state-equation that corrects for the last experienced error only, the response adopts the form of a convolution of the stimulus with weights that depend on the learning parameters. The relation between the learning parameters of the state-equation and the lag and amplitude of the periodic part of the oculomotor response can be obtained independently of explicitly finding the weights entering the convolution of the stimulus. Testing whether that predicted relationship holds gives an assessment of whether a single error-correcting channel suffices to explain the data, and ultimately sheds light on the quality of the learning model as a whole. We discuss generalizations of this approach as well as possible improvements in the experimental paradigms employed to understand saccadic adaptation.
Meeting abstract presented at VSS 2017
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