Cerebellar-driven cortical dynamics can enable task acquisition, switching and consolidation

Abstract

The brain must maintain a stable world model while rapidly adapting to the environment, but the underlying mechanisms are not known. Here, we posit that cortico-cerebellar loops play a key role in this process. We introduce a computational model of cerebellar networks that learn to drive cortical networks with task-outcome predictions. First, using sensorimotor tasks, we show that cerebellar feedback in the presence of stable cortical networks is sufficient for rapid task acquisition and switching. Next, we demonstrate that, when trained in working memory tasks, the cerebellum can also underlie the maintenance of cognitive-specific dynamics in the cortex, explaining a range of optogenetic and behavioural observations. Finally, using our model, we introduce a systems consolidation theory in which task information is gradually transferred from the cerebellum to the cortex. In summary, our findings suggest that cortico-cerebellar loops are an important component of task acquisition, switching, and consolidation in the brain.

Fig. 1. Schematic of cortical recurrent networks with different types of feedback.

a Model variant with no feedback: temporal external input (x_t) is fed to a cortical RNN (grey) and a linear readout layer (blue) produces the final model output (z_t). b Model variant with readout-only feedback: in this scheme there is a feedback loop in which the RNN also receives readout predictions as extra input^,. c Model variant with cerebellar feedback: a copy of RNN activity (h_t) is sent to a (feedforward) cerebellar network $\mathcal{C}$, which feedbacks to the cortical network its own cerebellar predictions (c_t). d A key property of our cerebellar network is that it learns via behavioural timing-specific learning rules, in line with experimental observations. In this learning rule the error between the cerebellar prediction c and future behavioural outcomes y (150 ms) triggers plasticity via climbing fibers at the parallel fibre input of Purkinje cells.

Fig. 2. Cerebellum learns to drive cortical dynamics during a line drawing task.

a Given one of six possible stimuli at the first timestep the model must learn to draw a corresponding line (dotted black line) or remain still. Model output after training is shown for three model architectures with a fixed RNN. b Learning curves of models in A (same colour-coding). MSE denotes mean squared error. c Average training error across different levels of RNN internal memory (α) and plasticity (fixed RNN, input plastic and fully plastic) for the no feedback and cerebellar feedback models; arrow denotes cortical internal memory used in the other panels (α = 0.1). d Average training error of cortico-cerebellar model under varying numbers of granule cells and cerebellar temporal windows (τ). Orange arrow denotes default parameter choices. e Prediction error between cortical output and itself (gray) or cortical output and cerebellar output (orange) for different temporal delays. f Evolution of first (upper panel) and second (lower panel) principal components of cortical RNN for different stimuli, colour-coded as in a using small (τ = 0 ms) and large (τ = 250 ms) cerebellar time windows. g Variance across cues from both first and second PCs (cf. F) for different cerebellar temporal windows, τ. h Model output for different periods of cerebellar ablation (blue box represents period of ablation). i Output x and y coordinates of the lines drawn in (h). j Average model error across all inputs for ablation periods in (h, i). k Average error for different degrees of plasticity and ablation periods (left to right) as in (h–j). l Average change in task error for models with versus without cerebellar feedback during (black) and after (blue) training for different degrees of cortical plasticity. All results are averaged over 5 different initial conditions. Error bars represent standard error of the mean.

Fig. 3. Context-dependent cerebellar feedback can enable multi-task learning and switching in the cortex.

a Training error of cortico-cerebellar models originally trained for line drawing (cf. Fig. 2; α = 0.5). The models continue to execute the line-drawing task (left) before being trained on a novel curl-field variant of the task (middle) and then finally switch back to the original task (right). Data from behavioural experiments in macaque monkeys is reproduced here for comparison (bottom; ref. ). b Average training error across different levels of parallel fibre (PF) task overlap for the different tasks for the fixed RNN (top) and fully plastic (bottom) models. Task periods colour-coded as in a. Arrows denote degree of PF task overlap used in (a, c–f). c Model output for each of the three training periods defined in a for the zero-overlap condition; “zero-shot” output corresponds to the model output in the first trial when task 1 is reintroduced. d Model retention score for task 1. The retention score is computed as the error of task 1 during baseline over the error at the first trial after switching back to task 1. e, f Change in (e) activity and (f) covariance in the RNN population between task 1 (baseline) and after learning task 2. Mean changes in experimental data in F are reproduced (see Methods) from neuronal recordings obtained from premotor (PMd) and primary motor (M1) cortices in macaque monkeys. All results are averaged over 5 different initial conditions. Error bars represent standard error of the mean.

Fig. 4. Cerebellar temporal basis supports cortical dynamics of a non-linear digit drawing task.

a Schematic of cerebellar learning with a temporal basis. We consider multiple populations of Purkinje cells with different learning time windows τ. b Model output after training for different input examples of the digit drawing task (fixed RNN; α = 0.1). c Learning curves of models in b together with readout feedback model (blue). d Average training error across different levels of RNN cortical internal memory (α) and plasticity assumptions. e Performance of cerebellar feedback for different numbers of granule cells and and cerebellar time windows. Orange arrow indicates default parameter choices with a single cerebellar time window; red arrow indicates temporal basis model with multiple time-windows. f Model output under control and cerebellar ablation conditions for example inputs (digit 2 in upper panels and digit 4 in lower panels); dashed red line represents model output during and after ablation period. g Average model error across all inputs for control (left) and ablation (right) conditions. h Average error for different degrees of cortical plasticity and ablation periods (middle period illustrated in f, g). i Average change in task error for models with versus without cerebellar feedback during (black) and after (blue) training across different degrees of cortical plasticity. All results are averaged over 5 different initial conditions. Error bars represent standard error of the mean.

Fig. 5. Cortico-cerebellar model mimics mouse behaviour during evidence accumulation task.

a Schematic of evidence accumulation task: a random sequence of non-zero inputs ("air puffs'') is delivered in the leftward (−) or rightward (+) direction. The model must integrate this input and decide at the end of the task which side received more input overall. b Learning curves of models (fixed RNN; α = 0.1) without feedback (grey), with readout feedback (blue) and with cerebellar feedback (orange). c Change in average training error of the cortico-cerebellar model with respect to the no feedback model across different levels of cortical internal memory (α) and degrees of cortical plasticity. d Model beliefs over time without (orange) and with complete cerebellar ablation (purple) in model (upper panels) and data-derived behavioural model (lower panels) reproduced from Deverett et al.. Thin model lines represent one example seed. Belief P denotes model output probability. e Normalised regression weights at different periods of input presentation (cue) during control (upper) and ablation (lower) conditions for both model (orange line) and behavioural data (black line). f Model and data error under different ablation periods and degrees of cortical plasticity. g Average change in task error for models with versus without cerebellar feedback across different cue durations. h Average change in task error for models with versus without cerebellar feedback during and after training across different degrees of cortical plasticity. All model results are averaged over 5 different initial conditions. Error bars represent standard error of the mean.

Fig. 6. Cerebellar network sustains cortical dynamics during delayed association task in line with optogenetic experiments.

a Delayed association task (top); a sensory cue is presented followed by a delay and decision period. The cortico-cerebellar loop models the interactions between a working memory region and a cognitive module of the cerebellum (bottom). b Learning curves of model without feedback (grey), readout feedback (blue) or cerebellar feedback (orange) for models with an input plastic RNN (α = 0.1). c Change in average training error of the cortico-cerebellar model with respect to the no feedback model across different levels of cortical internal memory (α) and degrees of plasticity in the cortical RNN. d Cue selectivity during the delay period without (left) and with cerebellar ablation (right; blue area denotes period of ablation and thin line shows control) in the model (upper panels) and optogenetic experiments (lower panels) reproduced from Gao et al.. e First decision principal component (dPC) during the delay period without (left) and with (right) cerebellar ablation in the model (top) and in optogenetic experiments (bottom). f Cue selectivity during the delay period with cerebellar ablation when using the fully plastic RNN (cf. d). g Model error during cerebellar ablation (input plastic RNN; control error shown with dashed-dotted line). Dotted grey line denotes chance level. h Average error from cerebellar ablation at different points during the delay period and different degrees of cortical plasticity. i Average change in task error for models with versus without cerebellar feedback during and after training across different degrees of cortical plasticity. j Model error for different numbers of cerebellar granule cells (GCs) and delay period lengths in the delayed association task (fixed RNN; α = 0.1). k Signal-to-noise ratio (SNR) of RNN activities (left y-axis) and number of GCs needed to decode the stimulus from these activities (right y-axis). Results are averaged over 5 different initial conditions. Error bars represent standard error of the mean. Mouse schematic in panel a used with permission from Petrucco, L. (2020). Mouse head schema. Zenodo. 10.5281/zenodo.3925903.

Fig. 7. Cerebellum can mediate task consolidation in the cortex.

a Schematic of proposed theory of cerebellar-to-cortical task consolidation. During the initial learning phase (left), task representations are primarily driven by the cerebellum and RNN connectivity is not yet task-specialised. During the consolidation phase there is a period of cerebellar-to-cortical (CC) task information transfer (middle), whereby CC interaction drives plasticity in the cortical RNN. After consolidation (right), the RNN can operate effectively without the need for cerebellar input. The colour of the structures reflects the importance of each component throughout consolidation. b Model error in the delayed association task (Fig. 6) throughout consolidation with (purple) and without (orange) cerebellar ablation. For reference an optimal consolidation model is also given (green). Dotted black line denotes chance. c Model selectivity with and without cerebellar ablation at different stages of the consolidation process; titles colour coded according to arrows in (b). d Strength of the cerebellar-to-cortical weights (${\mathbf{W}}_{\mathcal{C}h}$; top), local cortical weights (W_hh; middle) and change in local cortical weights (ΔW_hh; bottom) over the period of consolidation. Strength and change is measured by the Euclidean norm. e Cosine similarity between cRNN (RNN and cerebellar network) activities before and during consolidation. f Cosine similarity between the learned recurrent input currents (generated locally in the cortical RNN) during consolidation and the total cortical input current (generated locally and by cerebellar-cortical input) in the pre-consolidation network. Similarity of the consolidation model is shown in orange and the optimal consolidation model in green. g Task error after the consolidation period for models with different initial degrees of performance prior to consolidation. Results are averaged over 5 different initial conditions. Error bars represent standard error of the mean.