Optimal routing to cerebellum-like structures

Abstract

The vast expansion from mossy fibers to cerebellar granule cells produces a neural representation that supports functions including associative and internal model learning. This motif is shared by other cerebellum-like structures, including the insect mushroom body, electrosensory lobe of electric fish, and mammalian dorsal cochlear nucleus, and has inspired numerous theoretical models of its functional role. Less attention has been paid to structures immediately presynaptic to granule cell layers, whose architecture can be described as a "bottleneck" and whose functional role is not understood. We therefore develop a general theory of cerebellum-like structures in conjunction with their afferent pathways. This theory predicts the role of the pontine relay to cerebellar cortex and the glomerular organization of the insect antennal lobe. It also reconciles theories of nonlinear mixing with recent observations of correlated granule cell activity. More generally, it shows that structured compression followed by random expansion is an efficient architecture for flexible computation.

Task-dependent optimal representations for cerebellar learning

“…This equivalence validates the applicability of our theory to these more realistic networks. It also argues for the importance of distributed sensorimotor representations in the cortico-cerebellar pathway, consistent with the distributed nature of representations in motor cortex (Shenoy et al, 2013;Muscinelli et al, 2022).…”

“…While dense activity has been taken as evidence against theories of combinatorial coding in cerebellar granule cells (Knogler et al, 2017; Wagner et al, 2019), our theory suggests that the two are not incompatible. Instead, the coding level of cerebellum-like regions may be determined by behavioral demands and the nature of the input to granule-like layers (Muscinelli et al, 2022). Sparse coding has also been cited as a key property of sensory representations in the cerebral cortex (Olshausen and Field, 1996).…”

Cerebellum as a kernel machine: A novel perspective on expansion recoding in granule cell layer

“…Though it is largely unknown how feature selection is guided, it is known that during motor learning, the cerebellum can modify ongoing predictive responses based on the widespread predictive feedback signal ( Giovannucci et al, 2017 ), and this feedback may help detect task-relevant inputs. In particular, one recent research suggests that projection from deep cerebellar nuclei to pontine nuclei may be taught in a supervised way by exploiting feedback signal between them to detect task-relevant components sent to GrCs ( Muscinelli et al, 2022 ). In addition, it has been discovered that reward-related signals are transmitted to the cerebellar cortex via both mossy and climbing fibers ( Kostadinov and Häusser, 2022 ), and the emergence of GrCs tuned to specific combinations of actions and reward ( Wagner et al, 2019 ) implies that they learn to associate a specific sensorimotor feature with an upcoming reward.…”

“…According to one study, when noisy clustered inputs were expanded through random synapses, response variability for inputs within the same cluster was increased, and this noise amplification effect was more pronounced as the expanded representation became sparser ( Babadi and Sompolinsky, 2014 ). A recent study, on the other hand, suggested that random expansion in GrC layers can optimally transforms representations to assist learning when compression to pontine nuclei (presynaptic layer to the granular layer) is structured ( Muscinelli et al, 2022 ). There have been also comparable discussions in other brain regions.…”

Specific connectivity optimizes learning in thalamocortical loops

“…Reciprocal CTC loops represent a departure from the labelled line view of thalamus as they feature signal compression (from cortex to thalamus) and expansion (from thalamus to cortex). 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 (Zhaoping, 2006; Druckmann, Hu, & Chklovskii, 2012), primary visual cortex (Olshausen & Field, 1996; Zhu & Rozell, 2013), olfactory bulb (Zhang & Sharpee, 2016; Qin, Li, Tang, & Tu, 2019) and the cerebellum (Litwin-Kumar, Harris, Axel, Sompolinsky, & Abbott, 2017; Muscinelli, Wagner, & Litwin-Kumar, 2022; Xie, Muscinelli, Harris, & Litwin-Kumar, 2022). 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 when inputs are strongly correlated (Ganguli & Sompolinsky, 2012).…”