Reza Shadmehr

Neurons in the brain are often many synapses away from motoneurons, yet if a movement results in error, each distant neuron needs a teacher that considers its specific contribution to production of that movement. This credit assignment problem is solved in machine learning via gradient descent of a loss function, where the loss defines the subjective cost incurred by error. Does the brain use gradient descent to teach individual neurons? We trained marmosets to make saccades to visual targets and then varied the loss by assigning reward value to each target. The climbing fibers, which are the teachers of Purkinje cells (P-cells) in the cerebellum, used a multiplicative encoding to scale the spatial properties of the error vector with its reward properties, incorporating reward prediction errors. Using spike-triggered suppression of P-cells, we quantified the potent vector that mapped each P-cell’s output to eye movements and discovered that the climbing fibers were not merely transmitting errors. Rather, they were providing a signal that was, on average, proportional to the dot product of the reward dependent error vector upon the P-cell’s potent vector. Thus, the climbing fibers solved the credit assignment problem by providing the gradient of a loss function with respect to the output of their individual P-cells.

The language with which the neurons of the cerebellum encode information appears distinct from the rest of the brain. For example, although in the cerebral cortex and the superior colliculus neurons display a retinotopic map that indicates the location of the visual event with respect to the fovea, and in the brainstem saccade related neurons have a motor map to translate that goal into muscle activation patterns, in the cerebellum the Purkinje cells (P-cell) associated with control of saccades are neither organized spatially to reflect a retinotopic map, nor do their firing rates encode the motor commands. Instead, P-cells are active for all saccades, producing only small time-shifts in their firing rates in response to changes in movement parameters. To understand what the P-cells are computing, we can use their climbing fiber inputs as an anatomical before assign a potent vector for each P-cell, where the potent vector is an estimate of the downstream influence of that neuron on kinematics. This spike-to-vector transformation allows for summing the activities of the P-cells, producing a time-varying resultant vector that is an estimate of the neuronal output of the population in the vector space of behavior. Here, we review the idea of using anatomical priors coupled with spike-triggered averaging to find potent vectors for P-cells, then summarize how these vectors provide insights into what the cerebellum is computing. It appears that P-cells rely on phase differences in their individual firing patterns to partially or completely cancel each other’s potent vectors, conveying a resultant that, in the case of saccades, steers the eyes to the target. These patterns suggest that P-cells are akin to vector generating basis functions whose firing rates individually exhibit little relationship to behavior, but in a population can orchestrate an output critical for control of that behavior.

We tend to think of neurons as either excitatory or inhibitory, but certain neurons chemically inhibit their downstream targets while electrically exciting their neighbors. For example, in the cerebellum, molecular layer interneurons (MLIs) inhibit Purkinje cells (P-cells) via release of GABA but promote spiking in each other via gap junctions. What is gained by having an inhibitory neuron excite its neighbor? Here, we recorded activities of P-cells and MLIs as marmosets performed saccadic eye movements and found that spike timing in pairs of neighboring neurons of the same type exhibited a mathematical regularity: as firing rates increased, rate of spikes that were within 1ms of each other grew disproportionately while 2-4ms intervals were suppressed. To uncover the purpose of this coordination, during saccades we recorded thousands of neuron triplets in which two MLIs converged onto a single target P-cell. When the MLIs spiked within 1ms of each other, they produced superposition of their individual effects on their target; a deep inhibition followed by a post-inhibitory rebound. However, when the MLIs spiked 2-4ms apart, the two spikes interfered with each other, producing partial cancellation. Thus, electrical coupling between inhibitory neurons orchestrated their spike timing so that as firing rates increased, the temporal intervals that induced constructive superposition were promoted while the intervals that caused destructive competition were suppressed.

Implicit adaptation depends not only on feedback uncertainty but also on goal uncertainty. In a large-scale online visuomotor rotation study ( n = 180), increasing spatial ambiguity in the target midpoint—while keeping visual input constant—systematically attenuated implicit adaptation. These results call for a revision of standard models of motor adaptation, positioning the precision of the motor goal as a fundamental component in modulating motor learning.

Moving and holding-still ( holding ) have been posited to be separately controlled. The paretic arm after stroke exhibits different abnormalities during rest vs. movement, providing an opportunity to ask whether control of these behaviors is independently affected in stroke. We quantified resting postural abnormalities in human stroke patients by measuring their biases in force production as they held their hand still in various locations in a planar workspace and then assessed whether these resting force biases influenced reaching in the same workspace. Patients displayed marked resting force biases at each location, even when the arm was supported. However, these biases did not transfer to arm-supported planar reaching movements; rather, abnormal resting forces only appeared to switch on after a movement had fully stopped. These findings suggest that moving and holding are functionally separable modes of control. At the same time, resting biases mirrored characteristics of abnormal movement synergies, in line with a shared mechanism. This appears to contradict the functional separation of moving and holding observed in the same patients. To resolve this paradox, we propose a conceptual model that predicts a breakdown in this functional separation when patients move without weight support. This conceptual model posits that synergies are the manifestation of a spillover of posture into movement. Mapping these functional systems onto anatomical and physiological details of lesioned substrate after stroke may provide implementation-level insight into how normal arm motor control is assembled.

We tend to think of neurons as either excitatory or inhibitory, but certain neurons chemically inhibit their downstream targets while electrically exciting each other. For example, in the cerebellum, molecular layer interneurons type 1 (MLI1s) inhibit Purkinje cells (P-cells) via release of GABA but promote spiking in each other via gap junctions. P-cells inhibit nucleus neurons while exciting each other via ephaptic coupling. What is gained by excitatory interactions among inhibitory neurons? We recorded from the marmoset cerebellum during saccadic eye movements and found that spike timing in electrically coupled P-cell pairs, as well as MLI1 pairs, exhibited a mathematical regularity: as firing rates increased, the rate of spikes that were within 1ms of each other grew disproportionately while 2-4ms intervals were suppressed. We isolated triplets in which two MLI1s converged onto a single P-cell and found that if the MLI1s spiked within 1ms of each other, they produced superposition of their individual effects on their target; a deep inhibition followed by a post-inhibitory rebound. This enhanced the temporal precision in the downstream P-cell’s next spike. However, when the MLI1s spiked 2-4ms apart, the two spikes interfered with each other, producing partial cancellation. Thus, electrical coupling of inhibitory neurons promoted production of spike intervals that induced constructive superposition. This reduced the variance of spike timing in the downstream neuron.

Moving and holding-still (holding) have been posited to be under separate control regimes for both eye and arm movements. The paretic arm after stroke exhibits different abnormalities during rest vs. movement, providing an opportunity to ask whether control of these behaviors is independently affected in stroke. Here, we quantified resting postural abnormalities in stroke patients by measuring their biases in force production as they held their hand still in various locations in a planar workspace, and then assessed the influence of these resting force biases on reaching in the same workspace. We found that patients had marked resting force biases at each location, even when the arm was supported. However, these biases did not transfer to arm-supported planar reaching movements: not during initial acceleration, not in response to mid-trajectory perturbations, and not during deceleration to a stop. Rather, the abnormal resting forces only appeared to switch on after a movement had fully stopped. These findings suggest that moving and holding are functionally separable modes of control. At the same time, we found that the resting biases mirrored characteristics of abnormal synergies during movement: they markedly decreased when arm support was provided; they were higher in more distant positions that require breaking out of flexion; and they scaled with the Fugl-Meyer score for the upper extremity (a measure of intrusion of abnormal synergies during active movement). These three shared features suggest a common mechanism for resting biases and abnormal synergies, which appears to be a contradiction given the functional separation of moving and holding observed in the same patients. To resolve this paradox, we propose a conceptual model that predicts a breakdown in the functional separation between reaching and holding when patients move in the absence of weight support. This conceptual model posits that synergies are the behavioral manifestation of a spillover of posture into movement. Mapping these functional systems onto anatomical and physiological details of lesioned substrate after stroke may provide implementation-level insight into how normal arm motor control is assembled.

Implicit sensorimotor adaptation—the automatic correction of movement errors through feedback and practice—is driven by a perceptual prediction error, the mismatch between the perceived movement outcome and its intended goal. While perceptual uncertainty is known to attenuate adaptation, the impact of goal uncertainty on adaptation remains unknown. We employed a visuomotor adaptation task that isolates implicit adaptation (N = 180), manipulating goal uncertainty by varying how precisely the goal’s midpoint could be identified. Display format was varied independently to control for the objective size of visual features, and targets were hidden at movement onset, ensuring identical visual input at the moment the error was experienced. We found that goal uncertainty significantly attenuated implicit adaptation, independent of low-level visual and kinematic features. Together, these results demonstrate that a precise internal representation of the goal is essential for supporting implicit sensorimotor adaptation.

Null space theory predicts that neurons generate spikes not only to produce behavior but also to prevent the undesirable effect of other neurons on behavior. In this work, we show that this competitive cancellation is essential for understanding computation in the cerebellum. In marmosets, we identified a vector for each Purkinje cell (P cell) along which its spikes displaced the eyes. Two spikes in two different P cells produced superposition of their vectors. In the resulting population activity, the spikes were canceled if their contributions were perpendicular to the intended movement. Mossy fibers provided a copy of the motor commands and the goal of the movement. Molecular layer interneurons transformed these inputs so that the P cell population predicted when the movement had reached the goal and should be stopped.

We use our tongue much like our hands: to interact with objects and transport them. For example, we use our hands to sense properties of objects and transport them in the nearby space, and we use our tongue to sense properties of food morsels and transport them through the oral cavity. But what does the cerebellum contribute to control of tongue movements? Here, we trained head-fixed marmosets to make skillful tongue movements to harvest food from small tubes that were placed at sharp angles to their mouth. We identified the lingual regions of the cerebellar vermis and then measured the contribution of each Purkinje cell (P-cell) to control of the tongue by relying on the brief but complete suppression that they experienced following an input from the inferior olive. When a P-cell was suppressed during protraction, the tongue’s trajectory became hypermetric, and when the suppression took place during retraction, the tongue’s return to the mouth was slowed. Both effects were amplified when two P-cells were simultaneously suppressed. Moreover, these effects were present even when the pauses were not due to the climbing fiber input. Therefore, suppression of P-cells in the lingual vermis disrupted the forces that would normally decelerate the tongue as it approached the target. Notably, the population simple spike activity peaked near deceleration onset when the movement required precision (aiming for a tube), but not when the movement was for the purpose of grooming. Thus, the P-cells appeared to signal when to stop protrusion as the tongue approached its target.