Cerebellum, Predictions and Errors

Abstract

Making predictions and validating the predictions against actual sensory information is thought to be one of the most fundamental functions of the nervous system. A growing body of evidence shows that the neural mechanisms controlling behavior, both in motor and non-motor domains, rely on prediction errors, the discrepancy between predicted and actual information. The cerebellum has been viewed as a key component of the motor system providing predictions about upcoming movements and receiving feedback about motor errors. Consequentially, studies of cerebellar function have focused on the motor domain with less consideration for the wider context in which movements are generated. However, motor learning experiments show that cognition makes important contributions to motor adaptation that involves the cerebellum. One of the more successful theoretical frameworks for understanding motor control and cerebellar function is the forward internal model which states that the cerebellum predicts the sensory consequences of the motor commands and is involved in computing sensory prediction errors by comparing the predictions to the sensory feedback. The forward internal model was applied and tested mainly for effector movements, raising the question whether cerebellar encoding of behavior reflects task performance measures associated with cognitive involvement. Electrophysiological studies based on pseudo-random tracking in monkeys show that the discharge of Purkinje cell, the sole output neurons of the cerebellar cortex, encodes predictive and feedback signals not only of the effector kinematics but also of task performance. The implications are that the cerebellum implements both effector and task performance forward models and the latter are consistent with the cognitive contributions observed during motor learning. The implications of these findings include insights into recent psychophysical observations on moving with reduced feedback and motor learning. The findings also support the cerebellum's place in hierarchical generative models that work in concert to refine predictions about behavior and the world. Therefore, cerebellar representations bridge motor and non-motor domains and provide a better understanding of cerebellar function within the functional architecture of the brain.

Keywords: Purkinje cell; complex spike; forward internal model; generative model; kinematics; performance error; sensory prediction error; simple spike.

Figure 1

Implicit and explicit mechanisms of motor adaptation. (A) The canonical motor-learning curve, including baseline (period 1), adaptation to a sensorimotor perturbation (period 2), and return to baseline (period 3). (B) Following the first trial after introducing the perturbation (denoted by the black X), subjects are taught to compensate for the rotation by aiming away from the target, towards an additional marker, resulting in immediate task success. In subsequent trials, performance deteriorates due to implicit learning. (C) In an extended training period, task performance is eventually restored by strategy adjustments. An after-effect, indicative of implicit learning is revealed when the participants aim directly to the target and the perturbation is turned off. (D) Measuring strategy use during adaptation to a visuomotor rotation task. Before movement, participants explicitly report their aim. The implicit learning magnitude is the difference between aiming angle and actual end-point angle. (E) The explicit strategy (Aim) is responsible for a large immediate contribution following the perturbation that declines with time. Implicit learning (Adaptation) is slower and monotonic and matches the magnitude of the initial aftereffect. Adapted with permission from McDougle et al. (2016). (F) Schematics of the forward internal model hypothesis. Based on inputs from the motor cortex (Motor Command) and sensory system (Sensory Feedback), the cerebellar cortex (symbolized by the blue box) implements two independent forward models, an implicit one for the effector (coded in black) and an explicit one for the task strategy (coded in red). These models provide sensory predictions in two different spaces: one effector-related (kinematic predictions) and one task-related (task performance predictions). These sensory predictions are compared with the correspondent sensory feedback to compute sensory prediction errors in both spaces. Sensory prediction errors are used to independently update each internal model. The cerebellar output, integrating all sensory prediction errors, is used to update the Motor Controller.

Figure 2

Time course of the simple spike (SS) modulation with behavioral parameters during pseudo-random tracking. (A) Color coded maps of the SS firing, relative to the overall mean, for an example Purkinje cell in the velocity space (V_x, V_y) at different lead/lags (τ). Negative τ represents the firing leading velocity. (B) For the cell in (A), the R² for V_x as a function of lead/lag (τ) reveals modulation at both feedforward and feedback timing. The red trace shows the mean of the control regressions computed on trial shuffled data (100 repetitions). The dashed red trace is the mean +3 SD of the control regressions. On the R² temporal profiles asterisks (*) indicate the leads/lags of the corresponding SS firing maps in (A). (C) For the same neuron, the regression coefficients for V_x (${\text{β}}_{{\text{V}}_{\text{X}}}$) are plotted as a function of τ. The sign change in ${\text{β}}_{{\text{V}}_{\text{X}}}$ represents the reversal in the firing sensitivity at feedforward lead compared to feedback lag. (D) SS firing maps of another example Purkinje cell with position error (XE, YE) at different leads/lags (τ). Target depicted by black circles. Same conventions as in (A). (E,F) For the cell in (D), the temporal profiles for the R² (E) and regression coefficients (β_XE) for XE (F) exhibit predictive and feedback local maxima. β_XE shows the reversal in the SS firing sensitivity at lead compared to lag timings (F). Conventions for red lines as in (B). Adapted with permission from Popa et al. (2016a).

Figure 3

Effects of feedback manipulations on behavioral parameters encoding by SS discharge. (A) R² temporal profiles for an example Purkinje cell SS firing regressed with position error during delay cursor delay (baseline—black trace, 200 ms delay—green trace). The predictive encoding shifts to more negative τ-values while the timing of the feedback modulation does not change. (B) R² temporal profiles for an example Purkinje cell SS firing regressed with position error during the hidden cursor condition (baseline—black trace, hidden cursor—red trace). The reduction in visual feedback decreases the strength of the feedback encoding of position error but not the predictive encoding. (C) R² temporal profiles for an example Purkinje cell SS firing regressed with velocity during cursor delay (baseline—black trace, 100 ms delay—green trace). (D) R² temporal profiles for an example Purkinje cell SS firing regressed with velocity during the hidden cursor condition (baseline—black trace, hidden cursor—red trace). The kinematic representations are not changed by either manipulation of the visual feedback. Adapted with permission from Streng et al. (2018b).

Figure 4

During hold periods SS firing correlates with movement parameters during track period. (A) SS firing (inset) during the initial hold period prior to tracking (gray shadow) from an example trial matched to position (specifically X-position) at τ values spanning 0 to −2,000 ms illustrated by the sliding window. Note that the window length is equal in duration to the initial hold period. Colored traces illustrate the X sliding window at different times: black (0 ms), pink (−500 ms), blue (−1,000 ms), green (−1,500 ms), and red (−2,000 ms). (B) For the SS discharge of this neuron, the R² obtained from correlating firing rate with X-position across all trials is shown as a function of time (τ). The key observation is that the SS firing in the hold period encodes information about the upcoming position. (C) SS discharge rate (inset) during the final hold period (gray shadow) matched to position error (specifically YE) recorded in both track (gray) and final hold (black) periods using a sliding window of the same duration as the final hold period spanning from 0 to 2,000 ms. Colored traces illustrate the YE sliding window at different times: black (0 ms), pink (500 ms), blue (1,000 ms), green (1,500 ms), and red (2,000 ms). (D) For this Purkinje cell, plot of the R² as a function of time (τ) from regressing SS with YE across all trials. Here the critical observation is that the firing in the hold period contains position error information about the just completed track period. Direction of recording time is indicated by bottom arrows in (A,C). For (B,D), conventions for the colored dots conventions are as in (A,C), respectively. Chance encoding (red traces) and conventions for τ values, as in Figure 2. Adapted with permission from Popa et al. (2017).