33 The Predicting Machine
The Cerebellum, Coordination, and Predictive Control
33.1 A familiar syndrome and an unfinished explanation
The previous chapter (Chapter 32) followed a hand toward a visible target. The action required a continuing relation among the object, the eyes, the hand, and the body’s changing posture. Cerebellar damage can disrupt that action even when the person sees the target, understands the task, and has enough strength to move. The hand approaches inaccurately, passes beyond its destination, and returns through a succession of corrections. What was ordinarily fluent becomes laborious.
The cerebellum presents an unusual scientific problem. We know a great deal about its cells, connections, and forms of plasticity. We can record its activity during behavior, perturb individual pathways, and relate lesions to recognizable clinical syndromes. Yet there is no settled answer to what its primary function is. There may not be one primary function at the level at which we ordinarily describe behavior.
I regard the patient findings as the most important starting point. They establish what an explanation must account for: the loss of accurate coordination, stable gaze and posture, appropriate timing, and the capacity to recalibrate movement through experience. Circuit knowledge then constrains how those abilities could be produced. A wiring diagram becomes an explanation when it connects the operation of the circuit to the organization of behavior and to the particular ways that behavior fails.
The organizing proposal of this chapter is that cerebellar learning helps controllers anticipate consequences and adjust their output before delayed feedback can complete the correction.
This proposal is appealing because it connects several otherwise separate observations. Braking a reach, compensating for motion at another joint, stabilizing an image during head movement, and learning the timing of a blink all require activity appropriate to an event that has not yet fully unfolded. Forward models provide one explicit account of how such prediction can be accomplished. The chapter develops that account, examines the experiments that support it, and then considers how much of cerebellar function it explains.
The evolutionary perspective remains essential. Cerebellar circuits became coupled to different sensory systems, bodies, and forebrain networks across vertebrate history. Their recurring architecture invites a common explanation, while their varied connections make it important to identify what each loop actually contributes.
33.2 What cerebellar damage reveals
Cerebellar damage does not ordinarily resemble interruption of the corticospinal tract, a ventral root, or a peripheral motor nerve. A patient may still generate substantial force and initiate the intended action. What deteriorates is the organization of that force across joints and time.
The broad clinical term is ataxia. A reach can overshoot or undershoot its target, a failure called dysmetria. As the finger approaches the target, corrections may alternate around it, producing an intention tremor that becomes most visible when precision is required. A movement that should combine shoulder, elbow, wrist, and hand can break into a sequence of partially isolated components. Rapid alternation of opposing movements becomes irregular, a deficit called dysdiadochokinesia. Gait widens and becomes unstable. Speech can become poorly timed and variably stressed. Eye movements can show dysmetria, impaired holding, or nystagmus.
These signs expose several demands hidden within a successful movement. Reaching requires acceleration followed by braking at an appropriate time. Moving the shoulder changes the forces acting at the elbow. Alternating movements require transitions between opposing muscle groups. Standing requires continual adjustment to small departures from a stable relation to gravity. The patient’s difficulty extends across these demands even though the muscles retain the capacity to contract.
The motor syndrome is therefore more informative than the statement that the cerebellum coordinates movement. It identifies the relations that coordination must preserve. Force must be scaled to the load; activity at one joint must be appropriate to movement at another; and correction must occur soon enough to improve the action rather than disturb its next phase.
Cerebellar syndromes differ with anatomy. Damage near the midline often affects stance, gait, and axial control. More lateral lesions can produce ipsilateral limb dysmetria and impaired multijoint coordination. Vestibulocerebellar damage disrupts gaze stabilization and balance. The distribution of these signs points toward several interacting loops rather than one undifferentiated motor organ [@stoodley2016lesion].
The distinction from weakness is especially useful when the chapters of this unit are read together. In Chapter 31, damage to descending or peripheral pathways impaired access to force and fractionated movement. In Chapter 32, optic ataxia exposed difficulty relating a visual target to the moving hand, often under particular combinations of gaze, visual field, and effector. Cerebellar ataxia affects the calibration and coordination of actions across visual and nonvisual conditions. These profiles identify different failures within the same embodied controller.
Cerebellar disease can also reduce muscle tone, alter force scaling, and make an action functionally impossible. Relatively preserved strength is a useful clinical contrast, not a requirement that every affected muscle behave normally. The important observation is that loss of effective coordination can be much greater than loss of elementary activation.
I take this clinical pattern to be a demanding constraint on theory. An account of the cerebellum must explain why a person who knows what to do and retains much of the machinery for doing it nevertheless loses fluent control. Prediction offers a way to connect these failures. If the controller misjudges where a limb will be when a correction takes effect, braking can begin too late. If it fails to anticipate interaction forces, multijoint movement can decompose. The appeal of this account lies in the relation it establishes among the deficits. Whether the same computation explains them all remains an experimental question.
33.3 Prediction in a delayed controller
Negative feedback is indispensable because disturbances cannot all be known in advance. A foot can land on a loose stone, a cup can be heavier than expected, and another person can move the object being reached for. Feedback reveals those departures. Delay determines whether the correction will stabilize the action or chase it.
Several delays accumulate within an ordinary movement. Receptors and peripheral axons require time to signal a change. Spinal, brainstem, thalamic, and cortical pathways add synaptic and conduction delays. Vision requires retinal and cortical processing. A new descending command then requires additional time to reach motor neurons, activate muscle, develop force, and accelerate the body. The relevant interval differs across pathways, but even a short delay matters when the limb is moving rapidly.
Body dynamics add a second problem. Moving the shoulder produces interaction torques at the elbow and wrist. Muscle force depends on length, velocity, activation history, and load. A command that worked a moment ago may no longer produce the same consequence after fatigue, growth, injury, a change of tool, or a change in the environment. The controller must know not only where the body was but how its present command is likely to change it.
A forward model supplies a prediction of that relation. It takes an estimate of the current state together with information about the intended or ongoing action and predicts a later state or sensory consequence. The prediction can be generated before the real consequence returns through afferent pathways. A state estimator then combines that phase-advanced prediction with delayed and noisy sensory evidence to infer the body’s current condition.
The logic can be followed through a reach. A descending command begins to accelerate the arm. A motor-related signal informs the forward model that the command has been issued. The model predicts the emerging joint velocities, interaction torques, and sensory consequences. That prediction allows braking and interjoint compensation to begin before visual or proprioceptive evidence could report the complete result. When the actual evidence arrives, it is compared with the predicted evidence. The discrepancy helps correct the current estimate and, with experience, recalibrate the learned relation.
In this architecture, predictive and feedback control form one recurrent process. The forward model supplies an internal, rapidly available consequence of the action. External feedback later supplies the measured consequence. Their difference is a sensory prediction error: the discrepancy between the sensory consequence expected from an action and the consequence observed. That discrepancy can update the state estimate and help recalibrate future control.
An engineering Smith predictor stabilizes a delayed system by placing a model of the controlled plant and its delay inside the controller. The model predicts how the plant should respond to a command before the delayed measurement returns. A delayed copy of that prediction can then be compared in temporal register with the real feedback. The controller acts immediately on the model’s current estimate while using the later mismatch to correct both performance and the model [@miall1993smith].
The biological analogy is not that the cerebellum contains a literal block diagram. The useful point is the division of labor. A learned model of body dynamics advances the controller beyond delayed sensory evidence. A learned model of the delay allows predicted and observed consequences to be compared at the appropriate time. The external sensory loop remains essential, but it no longer has to carry the entire burden of rapid control.
This idea makes a testable prediction about cerebellar damage. The controller could retain sensitivity to visual feedback while its response falls farther behind the movement being tracked. Experiments later in the chapter separate the strength of that response from its timing.
A forward model answers a different question from an inverse model. Given a state and a command, the forward model predicts a consequence. Given a desired consequence and the current state, an inverse model estimates a command that could produce it. A control policy specifies what action to issue under the present conditions. These operations can cooperate: prediction helps estimate the situation on which a policy acts, and experience improves both the estimate and the response [@wolpert1998internal].
For a familiar lift, a useful command may be learned well enough to be issued directly from the context. Such anticipatory control does not require a fresh, detailed simulation of the arm on every trial. The important biological capacity is to prepare appropriate activity before its consequences are fully available through feedback. The distinction between learning that activity and learning an explicit prediction of its consequences will return when we compare cerebellar theories.
33.4 A map of recurrent loops
The cerebellum contains roughly four-fifths of the neurons in the human brain, most of them small granule cells. Its cortex is folded so tightly that an unfolded human cerebellar surface would form a strip nearly a meter long and would approach four-fifths of the surface area of the neocortex [@azevedo2009neurons; @sereno2020surface]. A large cortical sheet is compressed into a structure whose external size gives little indication of its cellular scale.
The cerebellar cortex surrounds white matter and the cerebellar nuclei. Three pairs of peduncles connect it to the brainstem. The middle peduncle carries the enormous input from pontine nuclei; the superior peduncle carries much of the nuclear output; and the inferior peduncle carries several spinal, vestibular, and olivary pathways together with some outgoing connections. The input and output routes place cerebellar circuitry within the ongoing traffic among body, brainstem, and cerebrum.
The cerebellum can be divided by lobules, fissures, molecular zones, afferent pathways, output nuclei, and patterns of activity. No single map serves every purpose. Three broad families of connections provide a useful starting map.
Vestibular and ocular-motor loops include the flocculus, nodulus, nearby vermis, vestibular inputs, and vestibular nuclei. They contribute to gaze stabilization, balance, orientation relative to gravity, and the prediction of sensory consequences produced by head and eye movement.
Spinal, brainstem, and somatic sensorimotor loops occupy much of the anterior lobe and intermediate cerebellum. They receive information related to limb and trunk state, spinal interneuronal activity, brainstem commands, and cerebral motor output. Their projections return through cerebellar nuclei to brainstem and thalamocortical motor systems. These loops are positioned to predict changing body state, compensate for interaction forces, and recalibrate posture and movement.
Cerebral association and motor loops are especially extensive in the lateral hemispheres and posterior cerebellum. Cerebral cortex reaches the cerebellum principally through the pontine nuclei, while cerebellar nuclear output returns through thalamus to motor, premotor, parietal, prefrontal, and other association territories. Viral tracing in nonhuman primates has demonstrated closed-loop organization linking different cerebellar territories with motor and prefrontal cortex [@kellystrick2003loops].
Cortical output also has a broad medial-to-lateral organization. Vermal Purkinje cells project mainly to the fastigial nucleus and to vestibular targets; intermediate cortex projects mainly to the interposed nuclei; and lateral hemispheric cortex projects mainly to the dentate nucleus. Those relations are useful first approximations, not sharply sealed channels. Nuclear territories contain several projection-cell classes, and each participates in recurrent networks with brainstem, thalamic, and cerebral targets [@dezeeuw2021diversity].
These families overlap. Vestibular signals influence limb and postural control. Somatic signals enter territories engaged during apparently cognitive tasks. Cerebral association cortex can alter eye movements, posture, and action selection. Functional imaging also reveals more than one body representation and broad maps related to distinct cerebral networks. The human cerebellum is therefore not arranged as one anterior motor region followed by one posterior cognitive region. It contains repeated, interleaved gradients of sensorimotor and association-related organization [@buckner2011organization; @king2019boundaries].
The traditional names archicerebellum, paleocerebellum, and neocerebellum encouraged the idea that vestibular, spinal, and cerebral territories were added in a simple old-to-new sequence. That evolutionary ladder is misleading. The terms describe useful anatomical biases only imperfectly, and living vertebrates do not preserve successive historical stages. Cerebellar evolution altered the relative size, geometry, inputs, outputs, and behavioral use of related cerebellar circuits in different lineages.
33.5 Why cerebellar signs are often ipsilateral
A lesion of the left cerebral motor cortex commonly weakens the right side of the body because the corticospinal pathway crosses. A lesion of the left cerebellar hemisphere more commonly produces ataxia of the left limbs. This apparent exception follows from the crossings within the larger loop.
Cerebral input reaches the opposite cerebellar hemisphere mainly through crossed pontocerebellar fibers. Cerebellar nuclear output then crosses in the superior cerebellar peduncle to influence thalamus and motor cortex. Descending corticospinal output crosses again before reaching the limb. Two crossings restore the cerebellar hemisphere’s predominant relation to the ipsilateral body. Several spinocerebellar pathways also preserve or recover an ipsilateral relation through uncrossed or double-crossed routes.
The rule is most useful for lateralized appendicular signs. Damage to the vermis commonly produces truncal and gait ataxia rather than a clean unilateral limb syndrome. Vestibular and ocular-motor effects can be bilateral or direction-specific. Diffuse disease and lesions that interrupt cerebellar peduncles can produce more complicated patterns.
The bedside distinction remains valuable. Contralateral weakness suggests damage along a cerebral corticospinal system; ipsilateral dysmetria with relatively preserved strength suggests a cerebellar hemisphere or its connections. As throughout this unit, the kind of failure and the side on which it appears jointly constrain lesion localization.
33.6 The canonical circuit
The whole-loop view in Figure 33.5 connects the descending and sensory pathways already introduced in this unit with the internal circuitry developed below.
The canonical cerebellar diagram begins with two afferent systems. Mossy fibers arise from many precerebellar sources, including pontine, vestibular, reticular, spinal, and external cuneate pathways. They terminate in the granule-cell layer and also send excitatory collaterals to cerebellar output neurons. Depending on the pathway and territory, they carry proprioceptive input, cutaneous input, vestibular information, spinal interneuronal activity, motor-cortical and association-cortical signals, task context, and mixtures of these variables.
That mixture gives the circuit access to the conditions that make one action differ from another. To predict the consequence of an action, the circuit needs information about the state from which the action begins, the command or intention that will alter that state, and the context that changes the relation between command and consequence. A cup, a hammer, and an empty hand impose different dynamics on the same arm. A head turn generated voluntarily has different implications from the same motion imposed externally. Mossy-fiber pathways provide the ingredients from which such distinctions can be learned.
Each mossy fiber contacts granule cells within cerebellar glomeruli. A granule cell receives only a small number of mossy-fiber inputs, but the population is enormous. In mice, pontine motor-related input and proprioceptive input can converge on individual granule cells [@huang2013convergence]. The axon of each granule cell ascends and bifurcates into a long parallel fiber that crosses many Purkinje-cell dendritic trees. This expansion creates a high-dimensional basis in which combinations of state, command, context, and time can be separated and assigned different learned weights. Population imaging confirms that parallel-fiber activity can occupy a high-dimensional space during behavior [@lanore2021highdimensional].
Purkinje cells form the sole output of the cerebellar cortex. They fire frequent simple spikes shaped by parallel-fiber input, interneurons, intrinsic conductances, and recurrent network state. Their axons inhibit neurons in the deep cerebellar and vestibular nuclei. Because Purkinje cells fire tonically, prediction can be expressed through increases, decreases, pauses, synchrony, and changes in population pattern rather than through a simple on–off code.
Purkinje simple-spike activity provides a learned transformation of this input. Its relationship to behavior can be expressed in several ways: an estimate of limb state, a signal related to impending motion, or a timed change that prepares a downstream response. The circuit’s connectivity determines which variables are available and which motor or cerebral system receives the result. Identifying that transformation is one of the central tasks of cerebellar physiology.
The cerebellar and vestibular nuclei are not passive relays released whenever Purkinje inhibition falls. They receive direct excitatory collaterals from mossy and climbing fibers, inhibitory Purkinje input, and additional local and nucleocortical influences. Their projection neurons provide most of the cerebellum’s output to thalamic and brainstem targets. Synchronized changes across Purkinje cells can produce precisely timed nuclear spiking, showing how the temporal organization of cortical inhibition can shape cerebellar output [@personraman2012synchrony].
The second afferent system originates in the inferior olive. Each Purkinje cell receives one climbing fiber in the adult mammalian cerebellum, but that fiber forms many synapses across the dendritic tree and evokes a distinctive complex spike. Olivary neurons are electrically coupled and organized with Purkinje cells and nuclear targets into narrow modules or microzones. Climbing-fiber events can signal a mismatch, an unexpected outcome, or another behaviorally important event and can powerfully change the mapping from parallel-fiber context to Purkinje output.
The combination of diverse contextual input, modifiable synapses, and instructive signals gives this circuit considerable learning capacity. A common arrangement can be trained differently according to the information entering it and the systems reached by its output.
The familiar sequence—mossy fiber, granule cell, parallel fiber, Purkinje cell, nucleus—is still a first approximation. The actual cerebellum contains molecular stripes, several interneuron classes, unipolar brush cells, recurrent pathways, nucleo-olivary and nucleocortical projections, and lineage-specific variants. These features organize local modules within the larger sheet and provide additional ways to regulate their timing, gain, and plasticity.
33.7 An ancient circuit with changing connections
The evolutionary history of the cerebellum begins before the appearance of the large, layered structure familiar in mammals. Comparative evidence suggests that vertebrate evolution assembled the cerebellar circuit from older developmental and sensory-motor components, then repeatedly coupled that circuit to new effectors, sensory systems, and forebrain loops.
Jawless vertebrates reveal an early part of that history. Developmental studies in lamprey and hagfish have identified ancestral gene-expression programs associated in jawed vertebrates with the rhombic lip, ventricular zone, granule-cell lineage, and inhibitory cerebellar neurons [@sugahara2021cerebellum]. An adult sea-lamprey cell atlas, however, did not identify the full canonical ensemble of granule cells, Purkinje cells, and cerebellar nuclear neurons that defines the mature cerebellum of jawed vertebrates [@lamanna2023lamprey]. The most useful conclusion is not that lamprey possesses a tiny mammalian cerebellum or no relevant ancestry at all. Developmental territories and regulatory programs preceded the fully differentiated adult circuit.
A recognizable cerebellar organization is established across jawed vertebrates, but evolution did not preserve one fixed geometry. Amniotes concentrate many output neurons in deep cerebellar nuclei. Teleost fish instead place eurydendroid cells within the cerebellar tissue near Purkinje cells, where they can receive both Purkinje-cell and parallel-fiber input. The bichir Polypterus, an early-diverging ray-finned fish, shows an intermediate output arrangement rather than either the standard teleost pattern or an amniote deep nucleus [@ikenaga2022polypterus]. Major cell classes and circuit relations were conserved while their physical arrangement and projection routes changed.
Fish also possess cerebellum-like structures associated with electrosensory, mechanosensory, and related systems. These structures are not displaced pieces of the true cerebellum, but they share the same informative conjunction: peripheral sensory input, contextual parallel-fiber input, and plasticity that learns which sensory events follow the animal’s own behavior. In several species, the circuit constructs a negative image of predictable reafference. These living circuits make it possible to study how a cerebellar-type architecture learns the sensory consequences of behavior.
Larval zebrafish show how that predictive contribution fits inside recurrent control. When visual feedback during the optomotor response was perturbed unpredictably, fish made rapid compensatory changes that could be described by an acute feedback controller. Disrupting the cerebellum did not abolish that immediate correction. When the altered relation between swimming and visual feedback persisted, however, the controller was recalibrated, and that longer-term adaptation required an intact cerebellum [@markov2021zebrafish]. The cerebellum did not replace feedback. It learned the changed action–consequence relation that allowed the feedback controller to work properly on subsequent movements.
Forebrain–cerebellar interactions expanded independently in several lineages. Mammals route extensive cortical input through the pontine nuclei. Birds possess pontine pathways but also a telencephalon-to-cerebellum relay through the medial spiriform nucleus. Comparative measurements show that this nucleus is especially enlarged in parrots and covaries with telencephalic size, indicating convergent expansion of forebrain–cerebellar communication through an anatomical route different from the mammalian cortico-ponto-cerebellar system [@gutierrezibanez2018parrots].
Within primates, the cerebellum and cerebrum scale largely together. Comparative analysis does not support a simple claim that apes acquired a wholly disproportionate cerebellum. It does support primate-wide relative expansion of particular lateral territories, especially crura I and II, as brains become larger [@magielse2023primate]. Regional reorganization is more informative than one ratio of total cerebellar to cerebral volume.
The evolutionary pattern is therefore one of conservation, duplication, and reassignment. Related circuits were embedded in vestibular, electrosensory, postural, locomotor, ocular, manipulative, vocal, and forebrain systems. The variables available to each circuit changed with the body and ecological niche. The conserved architecture provided a substrate for learning relations among context, activity, and consequence.
This view fits the larger argument of the book. Evolution did not replace older feedback controllers with an abstract forebrain planner. It elaborated cerebellar loops alongside spinal, brainstem, sensory, and cerebral systems. Their history is part of the larger evolution of coordinated action, not a succession of three independent organs called archi-, paleo-, and neocerebellum.
33.8 Learning to cancel a sensory consequence
I was introduced to electric fish as a graduate student, when I was assigned to host Ted Bullock during a several-day visit to my university. Before his visit began, I had to research his work and present a talk to the faculty and graduate students. My responsibilities also included playing tennis with him, and he humiliated me on the court. It was from Bullock that I first learned about electric fish, forward models and prediction. Electric fish gave those ideas a concrete biological setting: an animal’s own actions help determine what its sensory systems will encounter next.
33.8.1 An electric field as a sensory probe
Weakly electric mormyrid fish emit brief electric-organ discharges, or EODs, from an organ near the tail. Each pulse establishes an electric field in the surrounding water. The intervals between pulses change with behavior, allowing the fish to sample at different rates as it rests, explores, or searches for food [@dempsey2019generalization].
During active electrolocation, nearby objects alter the fish’s self-generated field. A prey item that conducts electricity differently from the surrounding water changes the pattern of voltage across the skin. Mormyromast electroreceptors sample that pattern, producing an electric image of the object. In the elephantnose fish, Gnathonemus petersii, receptor-rich regions around the head and flexible chin appendage support close inspection [@pusch2008active]. The comparison in Figure 33.8 makes the sequence visible: the object changes the field, and the changed field alters the input available at the sensory surface.
The fish also has a passive electrosensory system. Its ampullary receptors detect weak external electrical fields, including those produced by other animals. The fish’s own discharge strongly activates these receptors, creating interference that can obscure much smaller external signals. The same pulse that supplies the active system with a useful probe therefore creates a problem for the passive system. This second problem provides a particularly clear demonstration of learned prediction [@kennedy2014temporal; @dempsey2019generalization].
33.8.2 Learning a negative image
The electrosensory lateral line lobe, or ELL, contains a cerebellum-like circuit that learns to cancel predictable sensory input. Peripheral afferents convey the response to the electric discharge. A separate pathway carries a corollary discharge, activity associated with the motor command that produces the pulse. Granule cells distribute this command-related activity across time. Their parallel fibers contact ELL neurons through synapses whose weights change with experience. Learning shapes an opposite-signed response that counteracts the sensory pattern normally produced by the fish’s own discharge. This learned response is called a negative image [@bell1997plasticity; @kennedy2014temporal].
The prediction is expressed as a timed pattern of neural influence. It can be exposed experimentally by separating the command from its expected sensory consequence. In a preparation where the electric discharge is blocked, an artificial electrical stimulus can be paired with the continuing motor command. After repeated pairing, the response to the paired stimulus is reduced. Presenting the command without the stimulus then reveals a response opposed to the sensory response that had been paired with it [@dempsey2019generalization]. The experiment separates the consequence being predicted from the internal activity that predicts it.
The cancellation has a measurable behavioral benefit. Enikolopov, Abbott, and Sawtell presented weak electrical stimuli resembling signals from prey. Learned negative images improved both neural coding and behavioral detection of those stimuli despite self-generated interference. Manipulating synaptic plasticity altered circuit output and disrupted detection [@enikolopov2018predictions]. This connects the cellular learning mechanism to the animal’s ability to detect an external event.
The active electrosensory system also encounters predictable interference. Moving the tail changes the position of the electric organ relative to receptors on the head and body, altering the sensory consequences of each pulse. Requarth and Sawtell showed that ELL neurons can learn negative images of movement-related sensory input using corollary-discharge signals ascending from the spinal cord [@requarth2014corollary]. Prediction can therefore account for consequences of the fish’s movements as well as consequences of the discharge command itself.
These experiments make the forward-model idea unusually tangible. An internal signal related to action acquires a learned relation to a subsequent sensory event. The resulting prediction can be measured separately, altered through experience, and linked to improved detection. Suppressing predictable input allows externally generated changes to have greater influence on the circuit’s output.
The comparison with the cerebellum requires an anatomical distinction. The ELL is a cerebellum-like hindbrain structure, distinct from the cerebellum proper and its valvula. Alviña and Sawtell examined Purkinje cells in the posterior caudal lobe of the true cerebellum, which shares important inputs and targets with ELL. Protocols that produced rapid associative plasticity in ELL did not produce the same effect in those Purkinje cells [@alvinasawtell2014caudal]. Related circuit arrangements can have different learning properties. ELL supplies cerebellar theories with a concrete mechanism to examine and a standard of experimental evidence to meet.
33.9 Prediction can be tested
The forward-model account becomes most informative when it predicts a particular pattern of error. Increased variability alone can follow many disturbances. A systematic relation between an error and the limb’s earlier state, or between tracking performance and feedback delay, places a stronger constraint on explanation.
33.9.1 Reaching from an estimate of the moving hand
Miall and colleagues asked healthy participants to move a hand slowly sideways and, following a cue, interrupt that motion with a rapid reach to a remembered target. Vision was blocked during the movement. Planning the reach therefore required an estimate of where the hand had arrived when the new action began.
Transcranial magnetic stimulation over the ipsilateral lateral cerebellum increased reaching errors. Their direction was consistent with planning from a hand position approximately 138 milliseconds behind the actual position. Stimulation and other control conditions helped distinguish this pattern from nonspecific effects on movement initiation [@miall2007state].
The lag was inferred from the geometry of the errors, not recorded from a neural representation. Its importance is the specificity of the prediction: disrupting cerebellar processing made the reach behave as though it began from an obsolete estimate. That result supports a contribution to updating limb state during movement.
33.9.2 Separating the strength of feedback from its timing
Zimmet and colleagues studied people with cerebellar ataxia and controls tracking a moving visual target with an arm-supported apparatus. The task distinguished feedback gain, the strength of the response, from phase lag, how far the response fell behind the target. Patients showed broadly preserved gain but greater lag. A model with a Smith-predictor-like component reproduced control performance; removing that component captured important features of patient performance [@zimmet2020feedback].
The investigators then altered the cursor representing the patient’s hand. An acceleration-dependent adjustment provided a phase advance in the visual feedback and reduced dysmetria in a reaching task. The apparatus computed the altered display from the current movement; it did not have access to future hand position.
This intervention is valuable because it follows from the proposed mechanism. A patient who can use feedback should benefit if some of its temporal disadvantage is reduced. The improvement supports that account under the tested conditions without establishing a literal Smith predictor in cerebellar tissue.
33.9.3 Separating self-generated from imposed motion
Vestibular experiments provide another separation. A head can rotate because an animal generated a command or because an apparatus moved it. Vestibular receptors respond in both conditions. The nervous system must distinguish the consequences of its own action from an imposed disturbance while retaining the ability to respond to both.
In macaques, Brooks and colleagues altered the normal relation between a voluntary head command and its mechanical consequence. Cerebellar nuclear neurons initially responded strongly to the unexpected motion. As behavior adapted, neuronal sensitivity changed with the learning. The responses were consistent with an evolving mismatch between the expected and actual sensory consequence [@brooks2015updating].
Zobeiri and Cullen subsequently recorded Purkinje cells in the anterior vermis under passive, active, and attempted-but-prevented head movements. Passive motion exposed sensory responses; prevented attempts exposed motor-related activity without the expected motion. During active movement, the components combined in a manner consistent with predicting self-generated sensory input. A population model using roughly 40 Purkinje cells accounted for the suppression measured in downstream cerebellar and vestibular neurons [@zobeiri2024purkinje].
The vestibular system also reveals a different internal-model problem. Otolith organs respond to both linear acceleration and head orientation relative to gravity. Cerebellar Purkinje and nuclear activity can reflect estimates that separate those ambiguous inputs. Under artificial motion conditions that induce an erroneous percept, neurons followed the model-derived interpretation rather than simply reproducing the peripheral signal [@laurens2013internal].
These experiments give predictive accounts biological substance. They link a proposed variable to behavior, perturbation, and neural activity. Their strength comes from the particular distinctions each experiment makes, and those distinctions should be preserved as the explanation is extended to other cerebellar systems.
33.10 How the circuit learns
The regular architecture of the cerebellum encouraged unusually explicit theories of learning. Marr proposed that mossy-fiber information would be expanded into many granule-cell combinations, allowing Purkinje cells to learn which patterns mattered. Albus developed a related account in which climbing-fiber activity altered the efficacy of active parallel-fiber synapses [@marr1969theory; @albus1971theory]. Ito and colleagues then demonstrated long-lasting depression of parallel-fiber influence on Purkinje cells when parallel-fiber and climbing-fiber activity were paired [@itokano1982longlasting].
This parallel-fiber–Purkinje-cell long-term depression, or LTD, gave the theory a concrete cellular mechanism. Parallel-fiber activity identifies a particular combination of input. A climbing-fiber event produces powerful dendritic activity. When the required conditions coincide, the effectiveness of the active parallel-fiber synapses can decrease. The same input pattern will then have a different influence on Purkinje firing during a later encounter.
The consequences depend on the sign of the next connection. Purkinje cells inhibit cerebellar nuclear neurons. Reducing Purkinje activity can therefore release nuclear output from some of that inhibition. This provides a way for experience to alter a future response, including an anticipatory response timed to an expected event. An increase in learned motor output can emerge from a decrease in activity at an inhibitory stage.
33.10.1 The instructive pathway belongs to a loop
The inferior olive receives sensory and other inputs together with feedback from the cerebellum. The classical nucleo-olivary pathway is inhibitory: GABAergic neurons in the cerebellar nuclei project back to the olive. These are distinct from the excitatory nuclear populations that send output toward thalamus and other targets. Climbing fibers return olivary activity to Purkinje cells within organized modules.
This arrangement makes a comparator interpretation appealing. Incoming information can report a consequence, while cerebellar feedback can modify the response to an expected event. Learning can then reduce an instructive response as the event becomes better anticipated. The loop places the teaching signal under the influence of what the cerebellar system has already learned.
The simple subtraction in a comparator model is an interpretation of that arrangement. Olivary neurons have intrinsic dynamics and electrical coupling, and the relative timing of excitation and inhibition strongly affects their output [@loyola2023olive]. Climbing-fiber events also convey different information across tasks: movement error, retinal slip, unexpected reward or reward omission, salience, and learned expectation can all be relevant [@kitazawa1998complexspikes; @ohmae2015temporaldifference; @kostadinov2019reward]. Identifying the teaching variable is part of explaining a particular module.
33.10.2 Learning is distributed across the circuit
Parallel-fiber transmission can potentiate as well as depress. Inhibitory synapses, mossy-fiber pathways, intrinsic excitability, and cerebellar nuclear circuits also change with experience. Experiments that disrupt a canonical LTD pathway can leave substantial vestibulo-ocular, eyeblink, or locomotor learning intact [@schonewille2011ltd]. The learning capacity of the system therefore extends beyond one synaptic mechanism.
Practice can also change where a learned response is expressed. Cerebellar cortical plasticity, nuclear plasticity, and changes in connected brainstem or cerebral systems can make different contributions during acquisition, retention, and subsequent adjustment. A familiar action may be executed efficiently while a change of context again places demands on cerebellar learning [@dezeeuw2021diversity].
Marr, Albus, and Ito established a productive research program by connecting a recognizable circuit with an explicit learning problem. Their legacy is the possibility of following experience into changes in neural influence and then into behavior. Which transformations are learned, and how they are distributed among sites, can be examined experimentally.
33.11 Three preparations for studying cerebellar learning
Three preparations reveal different uses of cerebellar learning. Vestibulo-ocular adaptation changes the calibration of a rapid response. Reaching adaptation changes how an action is adjusted after an unexpected sensory consequence. Eyeblink conditioning establishes a response to an event that has not yet occurred. Together they make it possible to relate behavior to the input, output, and plasticity of particular circuits.
33.11.1 Vestibulo-ocular adaptation calibrates a rapid controller
When the head turns, the vestibulo-ocular reflex, or VOR, rotates the eyes in the opposite direction. The immediate drive begins with vestibular evidence that the head is moving. This short-latency response helps stabilize an image before slower visual pathways could calculate and correct retinal motion.
The reflex must be calibrated. If eye rotation is too small or too large for the head movement, the image slips across the retina. Magnifying or minifying lenses change the eye movement required for stability. Repeated exposure gradually changes VOR gain so that the eyes again compensate appropriately. The floccular cerebellum and vestibular nuclei are central to this adaptation. Climbing-fiber activity can convey retinal-slip information that helps alter the relation between head motion and eye motion [@boydenraymond2003vor; @dezeeuw2021diversity].
The VOR illustrates control across several timescales. Vestibular pathways supply a rapid response to actual head movement. Cerebellar and vestibular plasticity calibrate that response to the current visual and mechanical conditions. Visual feedback reports the residual slip and helps shape later performance. The learned adjustment allows a fast controller to remain useful when its operating conditions change.
33.11.2 Reaching adaptation separates success from expectation
In a visuomotor-rotation task, a participant moves a hand while a cursor is rotated away from the true hand direction. Early reaches miss the target. With practice, the hand direction changes to compensate. When the rotation is removed, an aftereffect can appear: the hand initially moves in the compensatory direction even though it is no longer needed. The altered relation has changed subsequent output.
Two discrepancies must be distinguished. Task error is the difference between the achieved result and the goal, such as the cursor missing the target. Sensory prediction error is the difference between the sensory consequence expected from an action and the consequence observed. A successful action can still produce a sensory prediction error.
Mazzoni and Krakauer made that distinction concrete by teaching participants an aiming strategy that compensated for a visual rotation. Aiming toward a neighboring location initially brought the cursor onto the required target. Task success was restored. Nevertheless, implicit adaptation continued and eventually drove performance away from the target. The strategy solved one problem while the altered relation between aim and cursor continued to drive another learning process [@mazzonikrakauer2006implicit].
This experiment explains why reduced target error is not a sufficient measure of adaptation. A person can improve by changing strategy, while automatic recalibration continues under different constraints. Conversely, impaired recalibration can be partly concealed by a useful explicit strategy.
Tseng and colleagues tested people with cerebellar degeneration in reaching tasks that separated sensory prediction error from online motor correction. Cerebellar damage reduced adaptation, and permitting online corrections did not restore it. The results implicated sensory prediction error in cerebellum-dependent learning rather than the corrective movement itself [@tseng2007cerebellum].
The distinction also connects this chapter with the later discussion of action value. A sensory consequence can be unexpected without being bad, and an expected consequence can still fail to achieve the goal. Sensory prediction error, task error, and reward prediction error answer different questions. Their interactions allow the nervous system to learn both how an action works and whether it is worth pursuing.
33.11.3 Eyeblink conditioning links a cue to a timed response
In delay eyeblink conditioning, a neutral cue such as a tone begins before an air puff near the eye and overlaps with it. After repeated pairings, the cue evokes a blink that peaks near the expected time of the puff. Cerebellar lesions can prevent acquisition even when the unconditioned blink remains available. The failure concerns learning the anticipatory response, rather than loss of all ability to close the eye [@lincoln1982eyeblink; @mccormickthompson1984eyeblink].
The task gives the canonical circuit a concrete interpretation. Information about the tone reaches cerebellar mossy-fiber pathways through pontine relays. Information associated with the air puff reaches the inferior olive through somatosensory pathways and enters cerebellar cortex through climbing fibers. The cue and the event to be anticipated therefore enter through different routes.
Learning changes activity between cue onset and the expected puff. In blink-related microzones, a learned reduction in Purkinje simple-spike firing releases interposed nuclear neurons from inhibition. Nuclear activity, shaped also by its excitatory inputs and local plasticity, recruits brainstem pathways that produce eyelid closure. The developing response is thus expressed through a timed change in inhibition and the resulting nuclear output [@tenbrinke2017eyeblink].
This is why the timing of the learned response matters. A blink that begins at cue onset and ends before the puff would offer little protection. The circuit must relate a present cue to the interval over which the useful response should develop. Climbing-fiber responses can also change with expectation, including responses to an unexpectedly delivered puff and reduced activity when an expected puff is omitted [@ohmae2015temporaldifference].
When a gap separates the cue from the puff in trace conditioning, forebrain contributions become more important. The ability to maintain information across that gap places the cerebellar learning circuit within a broader memory system. Delay conditioning provides the more direct example of how contextual input, instruction, and modifiable output can establish a timed anticipatory action.
33.12 What the models explain, and what remains open
Forward models give a coherent account of several findings developed in this chapter. They predict why delayed sensory evidence benefits from information about ongoing commands, why disrupting a state estimate can produce systematic reaching errors, and how a learned prediction can cancel self-generated sensory input. These are substantial explanatory achievements.
The proposal also suggests a route from the clinical syndrome to the underlying failure. Inaccurate forecasts of limb state and interaction forces could impair braking, interjoint coordination, and stable correction. A model that learns the relation between command and consequence could account for both successful adaptation and its loss after cerebellar damage. This is why I find predictive control an effective organizing perspective for the chapter.
The open question is how specifically the circuitry implements that perspective. Predicting a sensory consequence and learning a command that acts before a consequence occurs are different computations. Eyeblink conditioning demonstrates the latter particularly clearly. A timed response to a cue does not by itself establish an internal simulation of the sensory consequences of an outgoing motor command. Similarly, VOR adaptation establishes a changed controller without uniquely identifying every intermediate representation.
| Account | What is learned or computed | What it helps explain |
|---|---|---|
| Forward model | A relation from state, action, and context to a predicted consequence | State estimation, expected sensory input, and compensation for delay |
| Inverse model or learned control policy | Commands appropriate to a desired result or recurring situation | Anticipatory motor output and practiced responses |
| Adaptive filter | A weighted combination of contextual signals that approximates another signal | Learning a negative image or an adjustment from distributed input |
| Timing account | The temporal relations needed to organize a response | The interval and temporal precision of conditioned and voluntary actions |
An adaptive filter specifies a possible implementation and can be incorporated into more than one control architecture [@fujita1982adaptive]. Timing is necessary for both a useful prediction and a useful command. These perspectives therefore overlap, but the overlap does not make them interchangeable. Recent work explicitly compares learned feedforward policies with forward internal models, asking which interpretation better explains the signals and causal effects observed in particular cerebellar circuits [@nguyenperson2025predictive].
A repeated anatomical motif likewise does not require a single behavioral purpose. Related circuit operations can be applied to different inputs and targets. A vestibular loop, a blink-related microzone, and a lateral cerebellar loop linked to cerebral association cortex may share learning mechanisms while contributing differently to behavior.
The title The Predicting Machine expresses a productive commitment about what to investigate: anticipatory control, learned consequences, and temporal organization. Establishing one primary cerebellar function would require showing how a particular computation accounts for the range of patient findings and experimental dissociations. Detailed knowledge of the circuit makes that question tractable; it does not answer it in advance.
33.13 How far does the account extend beyond movement?
The cerebellum has extensive connections with cerebral association systems. Cortical input reaches it through pontine relays, and nuclear output returns through thalamus to territories that include premotor, prefrontal, and posterior parietal cortex. Tracing and human imaging establish organized loops extending well beyond primary motor systems. Large posterior cerebellar territories are engaged during tasks involving language, working memory, and other cognitive demands [@kellystrick2003loops; @buckner2011organization; @guell2018triple].
The anatomical expansion of lateral cerebellar territories and their forebrain relationships gives these connections evolutionary importance. Flexible behavior places demands on sequences extending beyond an immediate limb movement: preparing a tool action, organizing a vocal exchange, or maintaining the relations among successive steps. Cerebellar learning could improve the timing and adjustment of such sequences. This is an appealing extension of the control perspective because the relevant loops are anatomically real and the behavioral demands unfold through time.
Patient findings show that these connections have consequences. Schmahmann and Sherman described executive, visuospatial, linguistic, and affective changes after cerebellar disease, calling the pattern the cerebellar cognitive affective syndrome. Later lesion work related different motor and cognitive profiles to lesion location [@schmahmannsherman1998ccas; @stoodley2016lesion]. These findings include disturbances beyond motor speech. Dysarthria, the impaired coordination of speech musculature, is a motor sign; it does not by itself establish a disorder of language or thought.
A meta-analysis of 129 studies also found cognitive impairment across several domains in cerebellar disorders, with greater overall impairment in degenerative than focal conditions [@reumers2025cognition]. Such findings support careful assessment of cognition in affected patients. They do not by themselves identify the operation whose disruption produces the measured differences.
My assessment of this evidence is more reserved than my assessment of the motor syndrome. The cognitive findings have not, to my mind, yielded an equally compelling link between a distinctive loss of function and a particular cerebellar computation. Some cortical lesions can produce striking failures of language comprehension, object recognition, or the representation of space. Those dissociations give theories a relatively specific target. Reduced fluency, slower processing, or difficulty with executive tasks can be important to the patient while admitting several explanations about the contribution that has been lost.
The distinction is between the presence of a deficit and its explanatory specificity. Cognitive tasks require combinations of attention, memory, language, response selection, and often speech or manual output. Focal injury, degenerative disease, and developmental disruption also provide different kinds of evidence. A convincing computational account must relate the affected component to lesion location and to performance under conditions that separate it from accompanying demands.
The phrase dysmetria of thought captures one proposed continuity with motor dysfunction [@schmahmann1998dysmetria]. Cerebellar participation might help cerebral activity unfold with appropriate timing, scale, and sensitivity to context. The analogy suggests useful tests, especially of sequencing and adjustment. It becomes explanatory only when those tests identify the relevant operation and distinguish its failure from a more general disruption of the connected network.
I therefore give the nonmotor findings a place in the chapter without treating them as the resolution of the cerebellar problem. Expanded anatomy and measurable cognitive effects justify the investigation. They have not yet made the cerebellum’s contribution to cognition as clear as its contribution to coordinated movement. The strongest next step is a task that connects a well-characterized patient deficit to a specific computation and to the circuit that could perform it.
33.14 From patient findings to circuit explanations
The most informative research connects the clinical failure with a task that separates possible causes. A patient who reaches inaccurately may have a poor estimate of starting position, impaired anticipation of interaction forces, delayed correction, or difficulty learning from repeated error. Measuring the endpoint alone leaves these possibilities entangled. Manipulating the initial state, load, sensory evidence, and opportunity for correction helps distinguish them.
Lesions and degenerative disease establish the consequences of losing cerebellar tissue or its connections. Lesion location, time since onset, and associated sensory and motor findings constrain the interpretation. Focal lesions and progressive disease should be considered separately because they interrupt the system in different ways and allow different forms of compensation.
Perturbation and adaptation tasks change the relation between action and consequence. A visual rotation, altered head-motion load, or shifted timing of an expected event can expose the variable that learning tracks. Aftereffects, retention, and transfer to a new context distinguish a change in the learned controller from success produced by an immediate strategy.
Recording and causal intervention connect those behavioral distinctions to circuitry. Simple spikes, complex spikes, granule-cell activity, and nuclear output can be measured during carefully separated sensory and motor conditions. Stimulation, inactivation, and genetic manipulation test whether a pathway contributes to acquisition, expression, or adjustment of the response.
Comparative anatomy, development, and imaging identify the circuits available to perform those operations and the systems with which they interact. They reveal conserved cell types, reorganized output routes, and the expansion of particular loops. The functional meaning of a connection becomes clearer when the comparison also identifies what information travels through it and how its loss changes behavior.
Computational models bring these levels together by stating what a proposed mechanism should do under a new condition. A model earns explanatory force when it predicts a particular failure or a useful intervention. The clinical syndrome remains the biological problem; the experiment and model make its components precise enough to test.
33.15 Coda: coordination requires more than force
The cerebellar patient can reveal how much successful action depends on relations that ordinary movement conceals. Preserved strength does not ensure a stable reach. Seeing the target does not ensure that braking begins at the right moment. Repeated attempts do not ensure that the next command will be calibrated more accurately. These failures establish the demands that cerebellar circuitry normally helps the motor system meet.
Predictive control offers a powerful way to organize those demands. Learned relations among state, context, action, and consequence allow a controller to prepare useful output while sensory evidence is still arriving. Cerebellar and cerebellum-like experiments show that such relations can be learned, expressed in neural activity, and disrupted in ways that alter behavior.
The evidence supports a substantial role for the cerebellum in prediction, timing, coordination, and adaptation. The larger question is how these contributions are related. A forward model, a learned policy, an adaptive filter, and a timed response describe different aspects of a possible solution. Determining which circuits implement which operations remains part of the explanation we are seeking.
The next chapter turns to the basal ganglia and the problem of selecting among available actions. The distinction is useful within the framework of this book: cerebellar loops help calibrate the unfolding action, while basal-ganglia loops influence access, vigor, persistence, and switching. Both act through recurrent networks with cortex and brainstem, and both depend on the body whose behavior they help organize.
Established findings. Cerebellar damage can profoundly disturb coordination, balance, eye movements, timing, and motor adaptation while leaving substantial strength and the capacity to initiate action. Cerebellar circuitry contains organized sensory and motor-related inputs, inhibitory Purkinje output, powerful climbing-fiber instruction, and plasticity at several sites. Experiments support cerebellar contributions to state estimation and learned anticipatory control. Cerebellar lesions can also produce cognitive and affective changes.
The organizing interpretation. Predictive control connects many of these findings by asking how experience prepares an appropriate response before delayed feedback can complete the correction. Forward models make this proposal explicit and generate useful experimental predictions. Learned policies, adaptive filtering, and timing mechanisms provide related accounts whose contributions must be distinguished.
The open question. We do not yet have a settled account of a primary cerebellar function, or agreement that one computation will explain the full range of cerebellar contributions. Patient findings remain central because they specify the failures that such an account must explain. The extension from motor control to cognition is biologically plausible and supported by clinical effects, but its computational basis is less clearly established.