Fig. 3: Cerebro-cerebellar model improves learning in online complex sensorimotor and sensory discrimination tasks.

a Model behaviour across three tasks using a dataset of handwritten digits, each presented sequentially to the network (Methods and main text). Online line drawing (LD) visuomotor task: given temporally varying visual input the model is trained with sparse feedback (red dots) to draw a straight line (top left). Online digit drawing (DD) visuomotor task: given temporally varying visual input the model is trained to draw a digit following a template (top middle); target trajectories are in dotted grey and model input/output is coloured by digit. Online visual discrimination task: pattern recognition variant in which the model is trained to discriminate between 10 different digits given as sequential input. A representation of the structure of the input (green), output (green; target in grey) and feedback (red) for each task is also given (bottom of each task). b Learning curves for the three tasks for both cerebral RNN (gray, cRNN), cerebro-cerebellar RNN (orange, ccRNN). The cerebral network in all tasks uses approximately cerebral feedback horizon of 10% (cf. d). c The dysmetria score quantifies the irregularity in movement during the testing phase of the model (online LD and DD visuomotor tasks) or the uncertainty in the sensory discrimination (online visual discrimination task). d ccRNN model performance relative to cRNN across different degrees of cerebral feedback horizon (ns denotes not significant: p = 0.921 in the online LD visuomotor and p = 0.567 in the online DD visuomotor). Arrow indicates the feedback horizon used in (b, c). **p < 0.001 ***p < 0.0001, ****p < 0.0001 (two-sided paired t-test between cRNN and ccRNN). Error bars represent mean ± SEM across 10 different initial conditions. Source data are provided as a Source Data file.