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In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.<\/jats:p>","DOI":"10.7554\/elife.82914","type":"journal-article","created":{"date-parts":[[2023,9,6]],"date-time":"2023-09-06T07:30:18Z","timestamp":1693985418000},"update-policy":"https:\/\/doi.org\/10.7554\/elife.82914","source":"Crossref","is-referenced-by-count":17,"title":["Task-dependent optimal representations for cerebellar learning"],"prefix":"10.7554","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1456-4811","authenticated-orcid":true,"given":"Marjorie","family":"Xie","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hj8s172","id-type":"ROR","asserted-by":"publisher"}],"name":"Zuckerman Mind Brain Behavior Institute, Columbia University","place":["New York, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5256-2289","authenticated-orcid":true,"given":"Samuel P","family":"Muscinelli","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hj8s172","id-type":"ROR","asserted-by":"publisher"}],"name":"Zuckerman Mind Brain Behavior Institute, Columbia University","place":["New York, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3716-6173","authenticated-orcid":true,"given":"Kameron","family":"Decker Harris","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05wn7r715","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Computer Science, Western Washington University","place":["Bellingham, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2422-6576","authenticated-orcid":true,"given":"Ashok","family":"Litwin-Kumar","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hj8s172","id-type":"ROR","asserted-by":"publisher"}],"name":"Zuckerman Mind Brain Behavior Institute, Columbia University","place":["New York, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"4374","published-online":{"date-parts":[[2023,9,6]]},"reference":[{"key":"bib1","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1093\/acprof:oso\/9780195393798.001.0001","volume-title":"The Dynamic Brain: An Exploration of Neuronal Variability and Its Functional Significance","author":"Abbott","year":"2011"},{"key":"bib2","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0025-5564(71)90051-4","article-title":"A theory of cerebellar function","volume":"10","author":"Albus","year":"1971","journal-title":"Mathematical Biosciences"},{"key":"bib3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.7551\/mitpress\/8996.001.0001","volume-title":"Optimization for Machine Learning","author":"Andersen","year":"2011"},{"key":"bib4","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1007\/s12311-018-0952-3","article-title":"Cerebellar modules and their role as operational cerebellar processing units: a consensus paper","volume":"17","author":"Apps","year":"2018","journal-title":"Cerebellum"},{"key":"bib5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25983-8","volume-title":"Spherical Harmonics and Approximations on the Unit Sphere: An Introduction","author":"Atkinson","year":"2012"},{"key":"bib6","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1016\/j.neuron.2014.07.035","article-title":"Sparseness and expansion in sensory representations","volume":"83","author":"Babadi","year":"2014","journal-title":"Neuron"},{"key":"bib7","article-title":"Sharp Analysis of Low-Rank Kernel Matrix Approximations","volume-title":"arXiv","author":"Bach","year":"2012","unstructured":"Bach F. 2012. 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