Saccadic adaptation ($SA$) is a cerebellar-dependent learning of motor commands ($MC$), which aims at preserving saccade accuracy. Since $SA$ alters visual localization during fixation and even more so across saccades, it could also involve changes of target and/or saccade visuospatial representations, the latter ($CDv$) resulting from a motor-to-visual transformation (forward dynamics model) of the corollary discharge of the $MC$. In the present study, we investigated if, in addition to its established role in adaptive adjustment of $MC$, the cerebellum could contribute to the adaptation-associated perceptual changes. Transfer of backward and forward adaptation to spatial perceptual performance (during ocular fixation and trans-saccadically) was assessed in eight cerebellar patients and eight healthy volunteers. In healthy participants, both types of $SA$ altered $MC$ as well as internal representations of the saccade target and of the saccadic eye displacement. In patients, adaptation-related adjustments of $MC$ and adaptation transfer to localization were strongly reduced relative to healthy participants, unraveling abnormal adaptation-related changes of target and $CDv$. Importantly, the estimated changes of $CDv$ were totally abolished following forward session but mainly preserved in backward session, suggesting that an internal model ensuring trans-saccadic localization could be located in the adaptation-related cerebellar networks or in downstream networks, respectively.

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