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For example, although in the cerebral cortex and the superior colliculus neurons display a retinotopic map that indicates the location of the visual event with respect to the fovea, and in the brainstem saccade related neurons have a motor map to translate that goal into muscle activation patterns, in the cerebellum the Purkinje cells (P-cell) associated with control of saccades are neither organized spatially to reflect a retinotopic map, nor do their firing rates encode the motor commands. Instead, P-cells are active for all saccades, producing only small time-shifts in their firing rates in response to changes in movement parameters. To understand what the P-cells are computing, we can use their climbing fiber inputs as an anatomical before assign a potent vector for each P-cell, where the potent vector is an estimate of the downstream influence of that neuron on kinematics. This spike-to-vector transformation allows for summing the activities of the P-cells, producing a time-varying resultant vector that is an estimate of the neuronal output of the population in the vector space of behavior. Here, we review the idea of using anatomical priors coupled with spike-triggered averaging to find potent vectors for P-cells, then summarize how these vectors provide insights into what the cerebellum is computing. It appears that P-cells rely on phase differences in their individual firing patterns to partially or completely cancel each other\u2019s potent vectors, conveying a resultant that, in the case of saccades, steers the eyes to the target. These patterns suggest that P-cells are akin to vector generating basis functions whose firing rates individually exhibit little relationship to behavior, but in a population can orchestrate an output critical for control of that behavior.<\/jats:p>","DOI":"10.1152\/jn.00253.2025","type":"journal-article","created":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T16:00:04Z","timestamp":1769788804000},"page":"557-578","update-policy":"https:\/\/doi.org\/10.1152\/aps-crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["A neural language for the cerebellum: control of behavior via competing populations of Purkinje cells"],"prefix":"10.1152","volume":"135","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7686-2569","authenticated-orcid":false,"given":"Reza","family":"Shadmehr","sequence":"first","affiliation":[{"name":"Johns Hopkins School of Medicine","place":["United 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