Learning in large neural networks requires solving the credit assignment problem: how can individual synapses be updated to improve global performance? Normative theories assert that synaptic weights should be adjusted proportionally to a local gradient estimate to descend a global objective function. Recent years have seen various proposals for biologically plausible learning rules that approximate gradient descent in neural networks. However, this view is difficult to reconcile with the diversity of plasticity rules observed experimentally. This diversity means that weight updates may not always align with a global gradient, introducing fundamentally non-gradient components into the learning dynamics. This problem is often overlooked when training artificial neural network models, raising our central question: Can networks still learn effectively when their dynamics include non-gradient terms?

The cerebellum plays a key role in motor adaptation by driving trial-to-trial recalibration of movements based on previous errors. In primates, this adaptive response is achieved by cerebellar modulation of motor cortical signals, but the nature and timing of this process are unknown. Specifically, cortical correlates of adaptation are encoded already in the pre-movement motor plan, but these early cortical signals could be driven by a cerebellar-to-cortical information flow or evolve independently through intracortical mechanisms. To address this question, we trained monkeys to reach against a viscous force field while blocking cerebellar outflow. During the force field trials, the cerebellar block led to impaired adaptation and a compensatory, re-aiming-like shift in motor cortical preparatory activity. In the null-field conditions, the cerebellar block altered neural preparatory activity by increasing task-representation dimensionality and impeding generalization. A computational model indicated that low-dimensional (cerebellar-like) feedback is sufficient to replicate these findings. We conclude that cerebellar signals carry task structure information that constrains the dimensionality of the cortical preparatory manifold and promotes generalization. In the absence of these signals, cortical mechanisms are harnessed to partially restore adaptation.