Cerebellar granule cell axons support high-dimensional representations

Lanore, Frédéric; Cayco-Gajic, N. Alex; Gurnani, Harsha; Coyle, Diccon; Silver, R. Angus

doi:10.1038/s41593-021-00873-x

Cited by 58 publications

(47 citation statements)

References 75 publications

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“…Highly correlated activity, resulting in an apparently small dimensionality, has been widely observed in work on the cerebellar input layer [37][38][39] (but see also ref. 40 ). We found the same in our MF data, but our analysis together with the PC data suggests that enhancing small input variabilities is a fundamental information processing property of the cerebellar network.…”

Section: Discussionmentioning

confidence: 99%

Multidimensional cerebellar computations for flexible kinematic control of movements

Markanday

Hong

Inoue

et al. 2022

Preprint

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Both the environment and our body keep changing dynamically. Hence, ensuring movement precision requires adaptation to multiple demands occurring simultaneously. Here we show that the cerebellum performs the necessary multi-dimensional computations for the flexible control of different movement parameters depending on the prevailing context. This conclusion is based on the identification of a manifold-like activity in both mossy fibers (MF, network input) and Purkinje cells (PC, output), recorded from monkeys performing a saccade task. Unlike MFs, the properties of PC manifolds developed selective representations of individual movement parameters. Error feedback-driven climbing fiber input modulated the PC manifolds to predict specific, error type-dependent changes in subsequent actions. Furthermore, a feed-forward network model that simulated MF-to-PC transformations revealed that amplification and restructuring of the lesser variability in the MF activity is a pivotal circuit mechanism. Therefore, flexible control of movement by the cerebellum crucially depends on its capacity for multi-dimensional computations.

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Section: Discussionmentioning

confidence: 99%

Multidimensional cerebellar computations for flexible kinematic control of movements

Markanday

Hong

Inoue

et al. 2022

Preprint

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“…While the concept of perceptron capacity has played an essential role in the development of machine learning systems (Schölkopf & Smola, 2002; and the understanding of biological circuit computations (Brunel et al, 2004;Chapeton et al, 2012;Rigotti et al, 2013;Brunel, 2016;Rubin et al, 2017;Pehlevan & Sengupta, 2017;Lanore et al, 2021;Froudarakis et al, 2020), more work is wanting in linking it to other computational attributes of interest such as generalization. A comprehensive picture of the computational attributes of equivariant or otherwise structured representations of artificial and biological learning systems will likely combine multiple measures, including perceptron capacity.…”

Section: Discussionmentioning

confidence: 99%

Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?

Farrell¹,

Bordelon²,

Trivedi³

et al. 2021

Preprint

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Equivariance has emerged as a desirable property of representations of objects subject to identity-preserving transformations that constitute a group, such as translations and rotations. However, the expressivity of a representation constrained by group equivariance is still not fully understood. We address this gap by providing a generalization of Cover's Function Counting Theorem that quantifies the number of linearly separable and group-invariant binary dichotomies that can be assigned to equivariant representations of objects. We find that the fraction of separable dichotomies is determined by the dimension of the space that is fixed by the group action. We show how this relation extends to operations such as convolutions, element-wise nonlinearities, and global and local pooling. While other operations do not change the fraction of separable dichotomies, local pooling decreases the fraction, despite being a highly nonlinear operation. Finally, we test our theory on intermediate representations of randomly initialized and fully trained convolutional neural networks and find perfect agreement.

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“…Our model preserves mixing in granule cells, a feature thought to be crucial for the computations performed by the cerebellar cortex [3], and instead emphasizes the role of low-dimensional granule cell representations when animals are engaged in behaviors with low-dimensional structure. Such an interpretation may generally account for recordings of granule cells that exhibit low dimensionality and suggests the importance of complex behavioral tasks or multiple behaviors to probe the computations supported by these neurons [41].…”

Section: Random Mixing and Correlations In Low-dimensional Tasksmentioning

confidence: 99%

Optimal routing to cerebellum-like structures

Muscinelli

Wagner

Litwin-Kumar

2022

Preprint

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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.

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Cerebellar granule cell axons support high-dimensional representations

Cited by 58 publications

References 75 publications

Multidimensional cerebellar computations for flexible kinematic control of movements

Multidimensional cerebellar computations for flexible kinematic control of movements

Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?

Optimal routing to cerebellum-like structures

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