Task-dependent optimal representations for cerebellar learning

Abstract

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

Specific connectivity optimizes learning in thalamocortical loops

“…Normative models developed to clarify the role of compression and expansion in feedforward neural networks have improved our understanding of the computations in many brain areas including the retina, 15 , 16 primary visual cortex, 17 , 18 olfactory bulb, 19 , 20 and cerebellum. 21 – 24 For instance, theories of compressed sensing and efficient coding have shown that, whereas random compression can preserve the similarity structure of sparse representations, the optimal compression strategy is to extract the principal components (PCs) when inputs are strongly correlated. 25 Unfortunately, insights gained from analyzing feedforward networks cannot be directly applied to understand signal transformation in CTC loops due to their recurrent processing.…”