{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T23:21:33Z","timestamp":1776813693817,"version":"3.51.2"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008497","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T00:00:00Z","timestamp":1608681600000}}],"reference-count":42,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T00:00:00Z","timestamp":1607644800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>We introduce a novel methodology for describing animal behavior as a tradeoff between value and complexity, using the Morris Water Maze navigation task as a concrete example. We develop a dynamical system model of the Water Maze navigation task, solve its optimal control under varying complexity constraints, and analyze the learning process in terms of the value and complexity of swimming trajectories. The value of a trajectory is related to its energetic cost and is correlated with swimming time. Complexity is a novel learning metric which measures how unlikely is a trajectory to be generated by a naive animal. Our model is analytically tractable, provides good fit to observed behavior and reveals that the learning process is characterized by early value optimization followed by complexity reduction. Furthermore, complexity sensitively characterizes behavioral differences between mouse strains.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008497","type":"journal-article","created":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T19:29:16Z","timestamp":1607714956000},"page":"e1008497","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Value-complexity tradeoff explains mouse navigational learning"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7207-1559","authenticated-orcid":true,"given":"Nadav","family":"Amir","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1728-8114","authenticated-orcid":true,"given":"Reut","family":"Suliman-Lavie","sequence":"additional","affiliation":[]},{"given":"Maayan","family":"Tal","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4071-5361","authenticated-orcid":true,"given":"Sagiv","family":"Shifman","sequence":"additional","affiliation":[]},{"given":"Naftali","family":"Tishby","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6645-107X","authenticated-orcid":true,"given":"Israel","family":"Nelken","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2020,12,11]]},"reference":[{"key":"pcbi.1008497.ref001","volume-title":"Reinforcement learning: An introduction","author":"RS Sutton","year":"1998"},{"issue":"2","key":"pcbi.1008497.ref002","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0023-9690(81)90020-5","article-title":"Spatial localization does not require the presence of local cues","volume":"12","author":"RGM Morris","year":"1981","journal-title":"Learning and Motivation"},{"issue":"4","key":"pcbi.1008497.ref003","first-page":"8","article-title":"Severity of Spatial Learning Impairment in Aging: Development of a Learning Index for Performance in the Morris Water Maze Measures Traditionally Used for Behavioral Analysis in the Water Maze","volume":"107","author":"M Gallagher","year":"1993","journal-title":"Behavioral Neurosctence"},{"key":"pcbi.1008497.ref004","volume-title":"Applied optimal control: optimization, estimation and control","author":"AE Bryson","year":"1975"},{"key":"pcbi.1008497.ref005","volume-title":"Elements of information theory","author":"TM Cover","year":"2012"},{"issue":"1","key":"pcbi.1008497.ref006","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"S Kullback","year":"1951","journal-title":"The annals of mathematical statistics"},{"key":"pcbi.1008497.ref007","article-title":"Statistical physics","author":"LD Landau","year":"1958","journal-title":"Pergamon"},{"issue":"14","key":"pcbi.1008497.ref008","doi-asserted-by":"crossref","first-page":"6157","DOI":"10.1523\/JNEUROSCI.19-14-06157.1999","article-title":"5-HT1B receptor knock-out mice exhibit increased exploratory activity and enhanced spatial memory performance in the Morris water maze","volume":"19","author":"G Malleret","year":"1999","journal-title":"Journal of Neuroscience"},{"issue":"12","key":"pcbi.1008497.ref009","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1111\/cns.12191","article-title":"Glia Protein Aquaporin-4 Regulates Aversive Motivation of Spatial Memory in Morris Water Maze","volume":"19","author":"J Zhang","year":"2013","journal-title":"CNS neuroscience & therapeutics"},{"key":"pcbi.1008497.ref010","article-title":"Severity of spatial learning impairment in aging: development of a learning index for performance in the Morris water maze","author":"M Gallagher","year":"2015","journal-title":"Behavioral Neuroscience"},{"issue":"3","key":"pcbi.1008497.ref011","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/37.506395","article-title":"Optimal control-1950 to 1985","volume":"16","author":"AE Bryson","year":"1996","journal-title":"IEEE Control Systems Magazine"},{"issue":"6","key":"pcbi.1008497.ref012","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/S0959-4388(99)00028-8","article-title":"Internal models for motor control and trajectory planning","volume":"9","author":"M Kawato","year":"1999","journal-title":"Current opinion in neurobiology"},{"issue":"7","key":"pcbi.1008497.ref013","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1038\/nrn1427","article-title":"Optimal feedback control and the neural basis of volitional motor control","volume":"5","author":"SH Scott","year":"2004","journal-title":"Nature Reviews Neuroscience"},{"issue":"9","key":"pcbi.1008497.ref014","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1038\/nn1309","article-title":"Optimality principles in sensorimotor control","volume":"7","author":"E Todorov","year":"2004","journal-title":"Nature Neuroscience"},{"issue":"1","key":"pcbi.1008497.ref015","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.bbr.2004.01.022","article-title":"A detailed analysis of rats\u2019 spatial memory in a probe trial of a Morris task","volume":"154","author":"A Blokland","year":"2004","journal-title":"Behavioural brain research"},{"key":"pcbi.1008497.ref016","doi-asserted-by":"crossref","first-page":"14562","DOI":"10.1038\/srep14562","article-title":"Detailed classification of swimming paths in the Morris Water Maze: multiple strategies within one trial","volume":"5","author":"TV Gehring","year":"2015","journal-title":"Scientific reports"},{"issue":"5","key":"pcbi.1008497.ref017","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1162\/0899766053491887","article-title":"Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system","volume":"17","author":"E Todorov","year":"2005","journal-title":"Neural computation"},{"issue":"1","key":"pcbi.1008497.ref018","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems","volume":"82","author":"RE Kalman","year":"1960","journal-title":"Journal of basic Engineering"},{"key":"pcbi.1008497.ref019","doi-asserted-by":"crossref","unstructured":"Foster DJ, Morris RGM, Dayan P. A Model of Hippocampally Dependent Navigation, Using the Temporal Difference Learning Rule. Hippocampus. 2000.","DOI":"10.1002\/(SICI)1098-1063(2000)10:1<1::AID-HIPO1>3.0.CO;2-1"},{"key":"pcbi.1008497.ref020","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1162\/neco.1996.8.1.85","article-title":"A Model of Spatial Map Formation in the Hippocampus of the Rat","volume":"8","author":"KI Blum","year":"1996","journal-title":"Neural Computation"},{"key":"pcbi.1008497.ref021","first-page":"11","volume-title":"Proceedings of the 1993 connectionist models summer school","author":"HS Wan","year":"1994"},{"key":"pcbi.1008497.ref022","doi-asserted-by":"crossref","unstructured":"Redish AD, Touretzky DS. The Role of the Hippocampus in Solving the Morris Water Maze. Neural Computation. 1998.","DOI":"10.1007\/978-1-4615-4831-7_17"},{"issue":"4","key":"pcbi.1008497.ref023","first-page":"79","article-title":"Learning Navigational Maps Through Potentiation and Modulation of Hippocampal Place Cells","volume":"05","author":"W Gerstner","year":"1996","journal-title":"Journal of Computational Neuroscience"},{"issue":"3","key":"pcbi.1008497.ref024","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1002\/hipo.450050304","article-title":"Simulation of spatial learning in the Morris water maze by a neural network model of the hippocampal formation and nucleus accumbens","volume":"5","author":"MA Brown","year":"1995","journal-title":"Hippocampus"},{"issue":"7","key":"pcbi.1008497.ref025","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1038\/nn.3736","article-title":"Patterns across multiple memories are identified over time","volume":"17","author":"BA Richards","year":"2014","journal-title":"Nature Neuroscience"},{"key":"pcbi.1008497.ref026","first-page":"4","article-title":"What is the Most Sensitive Measure of Water Maze Probe Test Performance?","volume":"3","author":"HR Maei","year":"2009","journal-title":"Frontiers in integrative neuroscience"},{"key":"pcbi.1008497.ref027","doi-asserted-by":"crossref","first-page":"33","DOI":"10.3389\/neuro.07.033.2009","article-title":"Development and validation of a sensitive entropy-based measure for the water maze","volume":"3","author":"H Maei","year":"2009","journal-title":"Frontiers in Integrative Neuroscience"},{"issue":"2","key":"pcbi.1008497.ref028","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.conb.2008.08.003","article-title":"Reinforcement learning: the good, the bad and the ugly","volume":"18","author":"P Dayan","year":"2008","journal-title":"Current opinion in neurobiology"},{"key":"pcbi.1008497.ref029","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1007\/978-1-4419-1452-1_19","article-title":"Information Theory of Decisions and Actions","author":"N Tishby","year":"2011","journal-title":"Perception-Action Cycle: Models, Architecture and Hardware"},{"issue":"8","key":"pcbi.1008497.ref030","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/9.1287","article-title":"Entropy formulation of optimal and adaptive control","volume":"33","author":"GN Saridis","year":"1988","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"28","key":"pcbi.1008497.ref031","doi-asserted-by":"crossref","first-page":"11478","DOI":"10.1073\/pnas.0710743106","article-title":"Efficient computation of optimal actions","volume":"106","author":"E Todorov","year":"2009","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"2","key":"pcbi.1008497.ref032","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10994-012-5278-7","article-title":"Optimal control as a graphical model inference problem","volume":"87","author":"HJ Kappen","year":"2012","journal-title":"Machine learning"},{"key":"pcbi.1008497.ref033","doi-asserted-by":"crossref","unstructured":"Piray P, Daw ND. Linear reinforcement learning: Flexible reuse of computation in planning, grid fields, and cognitive control. bioRxiv. 2020.","DOI":"10.1101\/856849"},{"key":"pcbi.1008497.ref034","unstructured":"Tishby N, Pereira FC, Bialek W. The information bottleneck method. arXiv preprint physics\/0004057. 2000."},{"key":"pcbi.1008497.ref035","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/978-3-642-24647-0_3","volume-title":"Decision Making with Imperfect Decision Makers","author":"J Rubin","year":"2012"},{"key":"pcbi.1008497.ref036","unstructured":"Shwartz-Ziv R, Tishby N. Opening the Black Box of Deep Neural Networks via Information. arXiv:170300810. 2017 04."},{"issue":"2","key":"pcbi.1008497.ref037","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1038\/nprot.2006.116","article-title":"Morris water maze: procedures for assessing spatial and related forms of learning and memory","volume":"1","author":"CV Vorhees","year":"2006","journal-title":"Nature Protocols"},{"issue":"11","key":"pcbi.1008497.ref038","doi-asserted-by":"crossref","first-page":"3236","DOI":"10.1016\/j.celrep.2018.05.043","article-title":"POGZ is required for silencing mouse embryonic \u03b2-like hemoglobin and human fetal hemoglobin expression","volume":"23","author":"B Gudmundsdottir","year":"2018","journal-title":"Cell reports"},{"key":"pcbi.1008497.ref039","doi-asserted-by":"crossref","unstructured":"Suliman R, Cohen Y, Tal M, Tal N, Gudmundsdottir B, Gudmundsson KO, et al. Pogz deficiency leads to abnormal behavior, transcription dysregulation and impaired cerebellar physiology. bioRxiv. 2018; p. 437442.","DOI":"10.1101\/437442"},{"key":"pcbi.1008497.ref040","unstructured":"Franklin GF, Powell JD, Workman ML. Digital control of dynamic systems. vol. 3. Addison-wesley Menlo Park, CA; 1998."},{"issue":"1","key":"pcbi.1008497.ref041","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1115\/1.3653115","article-title":"When Is a Linear Control System Optimal?","volume":"86","author":"RE Kalman","year":"1964","journal-title":"Journal of Basic Engineering"},{"key":"pcbi.1008497.ref042","unstructured":"Nori F, Frezza R. Linear optimal control problems and quadratic cost functions estimation. In: Mediterranean Conference on Control and Automation; 2004. p. 1099."}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1008497","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T00:00:00Z","timestamp":1608681600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008497","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T20:03:12Z","timestamp":1608753792000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008497"}},"subtitle":[],"editor":[{"given":"Blake A.","family":"Richards","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,12,11]]},"references-count":42,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12,11]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008497","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1008497","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,11]]}}}