Fig. 1: Cerebro-cerebellar networks as feedback prediction machines.

a A recurrent cerebral cortical network A learns through external sensory feedback given by a task-specific prediction error module E_Task computed at the end of a task fb_T (top red arrow). The cerebellum aims to continuously predict the feedback expected by the cerebral network \({\hat{fb}}_{t}\) (blue) given current cerebral activity a_t (black). The cerebellar network (i.e. granule cells; GC and Purkinje cells; PC) learns through prediction errors (bottom red arrow) computed at the inferior olive (diamond) by comparing predicted cerebral feedback \({\hat{fb}}_{t}\) with actual cerebral feedback fb_t (light blue). Shaded boxes represent multiple cerebral areas and cerebellar modules that may be interacting in parallel (see Fig. S1 for the same framework applied to decoupling across multiple brain areas). b Example of cerebro-cerebellar model unfolded in time in which the cerebral network learns to associate a cue given at t₁ (x₁, green) with feedback received at the end of the task, t_T (cf. Fig. 2). At the end of the task the cerebral network A receives external sensory feedback fb_T (red), which is transmitted to the cerebellar network as cerebral feedback fb_T (light blue). Here we highlight a case of cerebral feedback horizon stopping at the end of the task T, but feedback may also be available earlier in the task (dashed red arrows). The cerebellum generates cerebral feedback predictions \({\hat{fb}}_{T}\) (blue) given cerebral activity a_T (black) and learns using inferior olive (diamond) error signals (red arrow). Before t_T cerebral feedback may not be readily available, thus the cerebellum learns through self-predictions. In this case the inferior olive (diamond) compares old cerebellar predictions (e.g. \({\hat{fb}}_{i}\)) with the new one (e.g. \({\hat{fb}}_{T}\)) to generate cerebellar learning signals (red arrow; see main text and “Methods” section for details).