The Errors of Our Ways: Understanding Error Representations in Cerebellar-Dependent Motor Learning

The cerebellum is essential for error-driven motor learning and is strongly implicated in detecting and correcting for motor errors. Therefore, elucidating how motor errors are represented in the cerebellum is essential in understanding cerebellar function, in general, and its role in motor learning, in particular. This review examines how motor errors are encoded in the cerebellar cortex in the context of a forward internal model that generates predictions about the upcoming movement and drives learning and adaptation. In this framework, sensory prediction errors, defined as the discrepancy between the predicted consequences of motor commands and the sensory feedback, are crucial for both on-line movement control and motor learning. While many studies support the dominant view that motor errors are encoded in the complex spike discharge of Purkinje cells, others have failed to relate complex spike activity with errors. Given these limitations, we review recent findings in the monkey showing that complex spike modulation is not necessarily required for motor learning or for simple spike adaptation. Also, new results demonstrate that the simple spike discharge provides continuous error signals that both lead and lag the actual movements in time, suggesting errors are encoded as both an internal prediction of motor commands and the actual sensory feedback. These dual error representations have opposing effects on simple spike discharge, consistent with the signals needed to generate sensory prediction errors used to update a forward internal model.

[1]  R. Shadmehr,et al.  Long-term adaptation to dynamics of reaching movements: a PET study , 2001, Experimental Brain Research.

[2]  T. Ebner,et al.  Hereditary cerebellar ataxia progressively impairs force adaptation during goal-directed arm movements. , 2004, Journal of neurophysiology.

[3]  Erin K Cressman,et al.  Reach adaptation and proprioceptive recalibration following exposure to misaligned sensory input. , 2010, Journal of neurophysiology.

[4]  R. F. Thompson,et al.  Classical conditioning using stimulation of the inferior olive as the unconditioned stimulus. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[5]  D. Wolpert,et al.  When Feeling Is More Important Than Seeing in Sensorimotor Adaptation , 2002, Current Biology.

[6]  C Ghez,et al.  Learning of Visuomotor Transformations for Vectorial Planning of Reaching Trajectories , 2000, The Journal of Neuroscience.

[7]  Tanaka The role of , 2000, Journal of insect physiology.

[8]  I. Kanazawa,et al.  Complex-spike activity of cerebellar Purkinje cells related to wrist tracking movement in monkey. , 1986, Journal of neurophysiology.

[9]  Timothy J Ebner,et al.  What Do Complex Spikes Signal about Limb Movements? , 2002, Annals of the New York Academy of Sciences.

[10]  D. Wolpert,et al.  Internal models in the cerebellum , 1998, Trends in Cognitive Sciences.

[11]  Mitsuo Kawato,et al.  A computational model of four regions of the cerebellum based on feedback-error learning , 2004, Biological Cybernetics.

[12]  M. Glickstein,et al.  Classical conditioning of the nictitating membrane response of the rabbit , 2004, Experimental Brain Research.

[13]  R. Ivry,et al.  Annals of the New York Academy of Sciences the Role of Strategies in Motor Learning , 2022 .

[14]  Yasmin L. Hashambhoy,et al.  Neural Correlates of Reach Errors , 2005, The Journal of Neuroscience.

[15]  A. Bastian Learning to predict the future: the cerebellum adapts feedforward movement control , 2006, Current Opinion in Neurobiology.

[16]  T. Ebner,et al.  Force field effects on cerebellar Purkinje cell discharge with implications for internal models , 2006, Nature Neuroscience.

[17]  Gary C. Sing,et al.  Primitives for Motor Adaptation Reflect Correlated Neural Tuning to Position and Velocity , 2009, Neuron.

[18]  F. A. Miles,et al.  Plasticity in the vestibulo-ocular reflex: a new hypothesis. , 1981, Annual review of neuroscience.

[19]  O. Oscasson Functional organization of olivary projection to the cerebellar anterior lobe , 1980 .

[20]  T. Ebner,et al.  Climbing fiber afferent modulation during treadmill locomotion in the cat. , 1987, Journal of neurophysiology.

[21]  M. Kawato,et al.  Temporal firing patterns of Purkinje cells in the cerebellar ventral paraflocculus during ocular following responses in monkeys II. Complex spikes. , 1998, Journal of neurophysiology.

[22]  Jochen Triesch,et al.  Spike avalanches in vivo suggest a driven, slightly subcritical brain state , 2014, Front. Syst. Neurosci..

[23]  R A Scheidt,et al.  Persistence of motor adaptation during constrained, multi-joint, arm movements. , 2000, Journal of neurophysiology.

[24]  J. Welsh,et al.  Systemic harmaline blocks associative and motor learning by the actions of the inferior olive , 1998, The European journal of neuroscience.

[25]  Richard Apps,et al.  An internal model of a moving visual target in the lateral cerebellum , 2009, The Journal of physiology.

[26]  Richard F. Thompson,et al.  The role of the cerebellum in classical conditioning of discrete behavioral responses , 2009, Neuroscience.

[27]  N. Ramnani,et al.  Cerebellar Plasticity and the Automation of First-Order Rules , 2011, The Journal of Neuroscience.

[28]  E. Boyden,et al.  Cerebellum-dependent learning: the role of multiple plasticity mechanisms. , 2004, Annual review of neuroscience.

[29]  Yoshiko Kojima,et al.  Changes in Simple Spike Activity of Some Purkinje Cells in the Oculomotor Vermis during Saccade Adaptation Are Appropriate to Participate in Motor Learning , 2010, The Journal of Neuroscience.

[30]  F. A. Miles,et al.  Long-term adaptive changes in primate vestibuloocular reflex. IV. Electrophysiological observations in flocculus of adapted monkeys. , 1980, Journal of neurophysiology.

[31]  S. M. Morton,et al.  Cerebellar Contributions to Locomotor Adaptations during Splitbelt Treadmill Walking , 2006, The Journal of Neuroscience.

[32]  Masao Ito Error detection and representation in the olivo-cerebellar system , 2013, Front. Neural Circuits.

[33]  J. Krakauer,et al.  Sensory prediction errors drive cerebellum-dependent adaptation of reaching. , 2007, Journal of neurophysiology.

[34]  E. J. Lang,et al.  Excitatory afferent modulation of complex spike synchrony , 2003, The Cerebellum.

[35]  G. Hesslow,et al.  Acquisition, Extinction, and Reacquisition of a Cerebellar Cortical Memory Trace , 2007, The Journal of Neuroscience.

[36]  Scott E. Bevans,et al.  Effect of visual error size on saccade adaptation in monkey. , 2003, Journal of neurophysiology.

[37]  J. Albus A Theory of Cerebellar Function , 1971 .

[38]  A. Fuchs,et al.  Saccadic gain modification: visual error drives motor adaptation. , 1998, Journal of neurophysiology.

[39]  Henrik Jörntell,et al.  Synaptic Memories Upside Down: Bidirectional Plasticity at Cerebellar Parallel Fiber-Purkinje Cell Synapses , 2006, Neuron.

[40]  N. Sawtell,et al.  Cerebellum-like structures and their implications for cerebellar function. , 2008, Annual review of neuroscience.

[41]  Masao Ito Cerebellar learning in the vestibulo–ocular reflex , 1998, Trends in Cognitive Sciences.

[42]  Joachim Hermsdörfer,et al.  Predictive and reactive finger force control during catching in cerebellar degeneration , 2008, The Cerebellum.

[43]  Peter Thier,et al.  The neural basis of smooth pursuit eye movements in the rhesus monkey brain , 2008, Brain and Cognition.

[44]  Robijanto Soetedjo,et al.  Complex Spike Activity of Purkinje Cells in the Oculomotor Vermis during Behavioral Adaptation of Monkey Saccades , 2006, The Journal of Neuroscience.

[45]  G. M. Redding,et al.  Adaptive spatial alignment and strategic perceptual-motor control. , 1996, Journal of experimental psychology. Human perception and performance.

[46]  S G Lisberger,et al.  Changes in the responses of Purkinje cells in the floccular complex of monkeys after motor learning in smooth pursuit eye movements. , 2000, Journal of neurophysiology.

[47]  Jessica X. Brooks,et al.  The Primate Cerebellum Selectively Encodes Unexpected Self-Motion , 2013, Current Biology.

[48]  Edward S Boyden,et al.  Active Reversal of Motor Memories Reveals Rules Governing Memory Encoding , 2003, Neuron.

[49]  John E. Schlerf,et al.  Encoding of Sensory Prediction Errors in the Human Cerebellum , 2012, The Journal of Neuroscience.

[50]  T. Ebner,et al.  Purkinje cell complex spike activity during voluntary motor learning: relationship to kinematics. , 1994, Journal of neurophysiology.

[51]  M. Kawato,et al.  Internal forward models in the cerebellum: fMRI study on grip force and load force coupling. , 2003, Progress in brain research.

[52]  S. Lisberger,et al.  Visual responses of Purkinje cells in the cerebellar flocculus during smooth-pursuit eye movements in monkeys. I. Simple spikes. , 1990, Journal of neurophysiology.

[53]  R. Shadmehr,et al.  Intact ability to learn internal models of arm dynamics in Huntington's disease but not cerebellar degeneration. , 2005, Journal of neurophysiology.

[54]  Farzaneh Najafi,et al.  Coding of stimulus strength via analog calcium signals in Purkinje cell dendrites of awake mice , 2014, eLife.

[55]  J. Krakauer,et al.  Differential cortical and subcortical activations in learning rotations and gains for reaching: a PET study. , 2004, Journal of neurophysiology.

[56]  Y. Lamarre,et al.  The Inferior olivary nucleus : anatomy and physiology , 1980 .

[57]  Masao Ito,et al.  Impulse discharge from flocculus Purkinje cells of alert rabbits during visual stimulation combined with horizontal head rotation , 1975, Brain Research.

[58]  F R Robinson,et al.  Visual error is the stimulus for saccade gain adaptation. , 2001, Brain research. Cognitive brain research.

[59]  D S Zee,et al.  Effects of lesions of the oculomotor cerebellar vermis on eye movements in primate: smooth pursuit. , 2000, Journal of neurophysiology.

[60]  Mitsuo Kawato,et al.  Internal models for motor control and trajectory planning , 1999, Current Opinion in Neurobiology.

[61]  Peter Thier,et al.  Specific vermal complex spike responses build up during the course of smooth-pursuit adaptation, paralleling the decrease of performance error , 2010, Experimental Brain Research.

[62]  J. Hore,et al.  Cerebellar participation in generation of prompt arm movements. , 1977, Journal of Neurophysiology.

[63]  Rhea R. Kimpo,et al.  Gating of neural error signals during motor learning , 2014, eLife.

[64]  Mollie K. Marko,et al.  Sensitivity to prediction error in reach adaptation. , 2012, Journal of neurophysiology.

[65]  Riccardo Zucca,et al.  Number of Spikes in Climbing Fibers Determines the Direction of Cerebellar Learning , 2013, The Journal of Neuroscience.

[66]  E. Bauswein,et al.  Simple and complex spike activity of cerebellar Purkinje cells during active and passive movements in the awake monkey. , 1983, The Journal of physiology.

[67]  M. Barrot,et al.  Clusters of cerebellar Purkinje cells control their afferent climbing fiber discharge , 2013, Proceedings of the National Academy of Sciences.

[68]  S G Lisberger,et al.  Multiple subclasses of Purkinje cells in the primate floccular complex provide similar signals to guide learning in the vestibulo-ocular reflex. , 1997, Learning & memory.

[69]  Peter Thier,et al.  A vermal Purkinje cell simple spike population response encodes the changes in eye movement kinematics due to smooth pursuit adaptation , 2013, Front. Syst. Neurosci..

[70]  Timothy J Ebner,et al.  Representation of limb kinematics in Purkinje cell simple spike discharge is conserved across multiple tasks. , 2011, Journal of neurophysiology.

[71]  Masao Ito Mechanisms of motor learning in the cerebellum 1 1 Published on the World Wide Web on 24 November 2000. , 2000, Brain Research.

[72]  Hiroshi Imamizu,et al.  Human cerebellar activity reflecting an acquired internal model of a new tool , 2000, Nature.

[73]  T. Ebner,et al.  Position, Direction of Movement, and Speed Tuning of Cerebellar Purkinje Cells during Circular Manual Tracking in Monkey , 2005, The Journal of Neuroscience.

[74]  Yan Yang,et al.  Duration of complex-spikes grades Purkinje cell plasticity and cerebellar motor learning , 2014, Nature.

[75]  P. Matthews,et al.  Learning about pain: the neural substrate of the prediction error for aversive events. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[76]  T. Ebner,et al.  Single trial coupling of Purkinje cell activity to speed and error signals during circular manual tracking , 2008, Experimental Brain Research.

[77]  Philip N. Sabes,et al.  Visual-shift adaptation is composed of separable sensory and task-dependent effects. , 2007, Journal of neurophysiology.

[78]  J. Simpson,et al.  Spatial organization of visual messages of the rabbit's cerebellar flocculus. II. Complex and simple spike responses of Purkinje cells. , 1988, Journal of neurophysiology.

[79]  Timothy J. Ebner,et al.  Cerebellum Predicts the Future Motor State , 2008, The Cerebellum.

[80]  D. Marr A theory of cerebellar cortex , 1969, The Journal of physiology.

[81]  E. D’Angelo,et al.  Beyond parallel fiber LTD: the diversity of synaptic and non-synaptic plasticity in the cerebellum , 2001, Nature Neuroscience.

[82]  Yoshiko Kojima,et al.  Complex spike activity in the oculomotor vermis of the cerebellum: a vectorial error signal for saccade motor learning? , 2008, Journal of neurophysiology.

[83]  R. Shadmehr,et al.  Cerebellar Contributions to Adaptive Control of Saccades in Humans , 2009, The Journal of Neuroscience.

[84]  Peter Thier,et al.  Cerebellar Complex Spike Firing Is Suitable to Induce as Well as to Stabilize Motor Learning , 2005, Current Biology.

[85]  S. G. Lisberger,et al.  Detection of tracking errors by visual climbing fiber inputs to monkey cerebellar flocculus during pursuit eye movements , 1986, Neuroscience Letters.

[86]  T. Kalenscher,et al.  Adaptive Motor Behavior of Cerebellar Patients During Exposure to Unfamiliar External Forces , 2004, Journal of motor behavior.

[87]  J. Krakauer,et al.  Error correction, sensory prediction, and adaptation in motor control. , 2010, Annual review of neuroscience.

[88]  Johannes Dichgans,et al.  Impairments of precision grip in two patients with acute unilateral cerebellar lesions: A simple parametric test for clinical use , 1994, Neuropsychologia.

[89]  A. M. Smith,et al.  Responses of cerebellar Purkinje cells to slip of a hand-held object. , 1992, Journal of neurophysiology.

[90]  F A Mussa-Ivaldi,et al.  Adaptive representation of dynamics during learning of a motor task , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[91]  R. Held,et al.  PLASTICITY IN HUMAN SENSORIMOTOR CONTROL. , 1963, Science.

[92]  P. Thier,et al.  Reduced saccadic resilience and impaired saccadic adaptation due to cerebellar disease , 2007, The European journal of neuroscience.

[93]  N. Daw,et al.  Reinforcement Learning Signals in the Human Striatum Distinguish Learners from Nonlearners during Reward-Based Decision Making , 2007, The Journal of Neuroscience.

[94]  Mark Shelhamer,et al.  Sensorimotor adaptation error signals are derived from realistic predictions of movement outcomes. , 2011, Journal of neurophysiology.

[95]  Daniel N. Wilson,et al.  On the specificity of antibiotics targeting the large ribosomal subunit , 2011, Annals of the New York Academy of Sciences.

[96]  P. Bach-y-Rita,et al.  Basic Mechanisms of Ocular Motility and Their Clinical Implications , 1976 .

[97]  M. Ito,et al.  Cerebellar long-term depression: characterization, signal transduction, and functional roles. , 2001, Physiological reviews.

[98]  Stephen G. Lisberger,et al.  Links from complex spikes to local plasticity and motor learning in the cerebellum of awake-behaving monkeys , 2008, Nature Neuroscience.

[99]  Yosef Yarom,et al.  Invariant phase structure of olivo-cerebellar oscillations and its putative role in temporal pattern generation , 2009, Proceedings of the National Academy of Sciences.

[100]  Romeo Chua,et al.  Reach adaptation to explicit vs. implicit target error , 2010, Experimental Brain Research.

[101]  R. Shadmehr,et al.  Neural correlates of motor memory consolidation. , 1997, Science.

[102]  D M Wolpert,et al.  Multiple paired forward and inverse models for motor control , 1998, Neural Networks.

[103]  S. Wise,et al.  The Acquisition of Motor Behavior in Vertebrates , 1996 .

[104]  John W. Krakauer,et al.  Independent learning of internal models for kinematic and dynamic control of reaching , 1999, Nature Neuroscience.

[105]  J. Raymond,et al.  Elimination of climbing fiber instructive signals during motor learning , 2009, Nature Neuroscience.

[106]  N H Barmack,et al.  Vestibular and visual climbing fiber signals evoked in the uvula-nodulus of the rabbit cerebellum by natural stimulation. , 1995, Journal of neurophysiology.

[107]  T. Ebner,et al.  Purkinje cell complex and simple spike changes during a voluntary arm movement learning task in the monkey. , 1992, Journal of neurophysiology.

[108]  L. Paninski,et al.  Spatiotemporal tuning of motor cortical neurons for hand position and velocity. , 2004, Journal of neurophysiology.

[109]  Rhea R. Kimpo,et al.  Cerebellar Purkinje cell activity drives motor learning , 2013, Nature Neuroscience.

[110]  D. Armstrong,et al.  Complex spikes in Purkinje cells in the lateral vermis (b zone) of the cat cerebellum during locomotion. , 1987, The Journal of physiology.

[111]  Erin K Cressman,et al.  Visuomotor Adaptation and Proprioceptive Recalibration , 2012, Journal of motor behavior.

[112]  Stephen G Lisberger,et al.  Interaction of plasticity and circuit organization during the acquisition of cerebellum-dependent motor learning , 2013, eLife.

[113]  J. Bower,et al.  Multiple Purkinje Cell Recording in Rodent Cerebellar Cortex , 1989, The European journal of neuroscience.

[114]  Reza Shadmehr,et al.  Learning from Sensory and Reward Prediction Errors during Motor Adaptation , 2011, PLoS Comput. Biol..

[115]  Timothy J. Ebner,et al.  The cerebellum for jocks and nerds alike , 2014, Front. Syst. Neurosci..

[116]  N. Ramnani Automatic and controlled processing in the corticocerebellar system. , 2014, Progress in brain research.

[117]  Konrad Paul Kording,et al.  Relevance of error: what drives motor adaptation? , 2009, Journal of neurophysiology.

[118]  Masao Ito,et al.  Long-lasting depression of parallel fiber-Purkinje cell transmission induced by conjunctive stimulation of parallel fibers and climbing fibers in the cerebellar cortex , 1982, Neuroscience Letters.

[119]  T. Ebner,et al.  Movement kinematics encoded in complex spike discharge of primate cerebellar Purkinje cells , 1997, Neuroreport.

[120]  C. Yeo,et al.  Time and tide in cerebellar memory formation , 2005, Current Opinion in Neurobiology.

[121]  M. Mauk,et al.  What the cerebellum computes , 2003, Trends in Neurosciences.

[122]  Laurentiu S. Popa,et al.  What Features of Limb Movements are Encoded in the Discharge of Cerebellar Neurons? , 2011, The Cerebellum.

[123]  T. Bliss,et al.  Distributed synergistic plasticity and cerebellar learning , 2012 .

[124]  Joachim Hermsdörfer,et al.  The role of the cerebellum for predictive control of grasping , 2008, The Cerebellum.

[125]  Scott R Sponheim,et al.  Prefrontal neurons transmit signals to parietal neurons that reflect executive control of cognition , 2013, Nature Neuroscience.

[126]  C. Prablanc,et al.  Automatic Drive of Limb Motor Plasticity , 2006, Journal of Cognitive Neuroscience.

[127]  Stephen G Lisberger,et al.  Encoding and decoding of learned smooth-pursuit eye movements in the floccular complex of the monkey cerebellum. , 2009, Journal of neurophysiology.

[128]  Claude Prablanc,et al.  Visuomotor adaptation needs a validation of prediction error by feedback error , 2014, Front. Hum. Neurosci..

[129]  J. Krakauer,et al.  An Implicit Plan Overrides an Explicit Strategy during Visuomotor Adaptation , 2006, The Journal of Neuroscience.

[130]  Bradley Greger,et al.  Simple spike firing in the posterior lateral cerebellar cortex of Macaque Mulatta was correlated with success–failure during a visually guided reaching task , 2005, Experimental Brain Research.

[131]  Tatsuya Kimura,et al.  Cerebellar complex spikes encode both destinations and errors in arm movements , 1998, Nature.

[132]  J. Bloedel,et al.  The responses of simultaneously recorded Purkinje cells to the perturbations of the step cycle in the walking ferret: a study using a new analytical method — the real-time postsynaptic response (RTPR) , 1986, Brain Research.

[133]  R. Llinás,et al.  Dynamic organization of motor control within the olivocerebellar system , 1995, Nature.

[134]  Daniel M. Wolpert,et al.  Forward Models for Physiological Motor Control , 1996, Neural Networks.

[135]  Tycho M. Hoogland,et al.  Strength and timing of motor responses mediated by rebound firing in the cerebellar nuclei after Purkinje cell activation , 2013, Front. Neural Circuits.

[136]  Peter Thier,et al.  Cerebellar-dependent motor learning is based on pruning a Purkinje cell population response , 2008, Proceedings of the National Academy of Sciences.

[137]  S. Lisberger,et al.  Visual responses of Purkinje cells in the cerebellar flocculus during smooth-pursuit eye movements in monkeys. II. Complex spikes. , 1990, Journal of neurophysiology.

[138]  J R Flanagan,et al.  The Role of Internal Models in Motion Planning and Control: Evidence from Grip Force Adjustments during Movements of Hand-Held Loads , 1997, The Journal of Neuroscience.

[139]  Zoubin Ghahramani,et al.  Computational principles of movement neuroscience , 2000, Nature Neuroscience.

[140]  A. Gibson,et al.  Reduction of rostral dorsal accessory olive responses during reaching. , 1996, Journal of neurophysiology.

[141]  H. C. Hulscher,et al.  Cerebellar LTD and Learning-Dependent Timing of Conditioned Eyelid Responses , 2003, Science.

[142]  F A Miles,et al.  THE “ERROR” SIGNALS SUBSERVING ADAPTIVE GAIN CONTROL IN THE PRIMATE VESTIBULO‐OCULAR REFLEX , 1981, Annals of the New York Academy of Sciences.

[143]  Javier F. Medina,et al.  Sensory-Driven Enhancement of Calcium Signals in Individual Purkinje Cell Dendrites of Awake Mice , 2014, Cell reports.

[144]  Jennifer L Raymond,et al.  Cerebellar Encoding of Multiple Candidate Error Cues in the Service of Motor Learning , 2014, The Journal of Neuroscience.

[145]  W. T. Thach,et al.  Purkinje cell activity during motor learning , 1977, Brain Research.

[146]  Timothy J Ebner,et al.  Changes in Purkinje Cell Simple Spike Encoding of Reach Kinematics during Adaption to a Mechanical Perturbation , 2015, The Journal of Neuroscience.

[147]  A. Fuchs,et al.  Role of primate flocculus during rapid behavioral modification of vestibuloocular reflex. I. Purkinje cell activity during visually guided horizontal smooth-pursuit eye movements and passive head rotation. , 1978, Journal of neurophysiology.

[148]  D. Tank,et al.  Widespread State-Dependent Shifts in Cerebellar Activity in Locomoting Mice , 2012, PloS one.

[149]  Adam Possner,et al.  Cerebellum , 2012, Neurology.

[150]  Peter Thier,et al.  The role of the cerebellum in saccadic adaptation as a window into neural mechanisms of motor learning , 2011, The European journal of neuroscience.

[151]  Michael I. Jordan,et al.  Optimal feedback control as a theory of motor coordination , 2002, Nature Neuroscience.

[152]  Soon-Lim Shin,et al.  Signals and Learning Rules Guiding Oculomotor Plasticity , 2014, The Journal of Neuroscience.

[153]  Michael I. Jordan,et al.  An internal model for sensorimotor integration. , 1995, Science.

[154]  Sarah E. Criscimagna-Hemminger,et al.  Cerebellar Contributions to Reach Adaptation and Learning Sensory Consequences of Action , 2012, The Journal of Neuroscience.

[155]  J. Bloedel,et al.  Responses of sagittally aligned Purkinje cells during perturbed locomotion: synchronous activation of climbing fiber inputs. , 1992, Journal of neurophysiology.

[156]  M. Glickstein,et al.  Classical conditioning of the nictitating membrane response of the rabbit , 2004, Experimental Brain Research.

[157]  Konrad Paul Kording,et al.  Estimating the sources of motor errors for adaptation and generalization , 2008, Nature Neuroscience.

[158]  Laurentiu S. Popa,et al.  Predictive and Feedback Performance Errors Are Signaled in the Simple Spike Discharge of Individual Purkinje Cells , 2012, The Journal of Neuroscience.

[159]  K. Doya,et al.  Chaos may enhance information transmission in the inferior olive. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[160]  E. J. Lang,et al.  Local Changes in the Excitability of the Cerebellar Cortex Produce Spatially Restricted Changes in Complex Spike Synchrony , 2009, The Journal of Neuroscience.

[161]  R. Ivry,et al.  An Explicit Strategy Prevails When the Cerebellum Fails to Compute Movement Errors , 2010, The Cerebellum.