A fundamental question in neuroscience is how neural populations learn to control flexible behaviors. A promising region for understanding the relationship between neural circuitry, population activity, and behavior is the cerebellum, whose evolutionarily-conserved circuitry is the basis of a critical role in motor learning guided by sensory errors. In the first part of this talk, I will present our recent work attempting to understand how cerebellar supervised learning can guide motor learning and adaptation in coordination with recurrent cortical dynamics. Furthermore, testing such theories of population-level learning in data requires methods that can infer how neural dynamics evolve over slow timescales. In the second part of the talk, I will present our recent development of low tensor rank recurrent neural networks, which can identify how latent neural dynamics are reshaped over learning from high-dimensional neural data.