Storage of correlated patterns in standard and bistable Purkinje cell models.
Abstract
The cerebellum has long been considered to undergo supervised learning, with climbing
fibers acting as a 'teaching' or 'error' signal. Purkinje cells (PCs), the sole output
of the cerebellar cortex, have been considered as analogs of perceptrons storing input/output
associations. In support of this hypothesis, a recent study found that the distribution
of synaptic weights of a perceptron at maximal capacity is in striking agreement with
experimental data in adult rats. However, the calculation was performed using random
uncorrelated inputs and outputs. This is a clearly unrealistic assumption since sensory
inputs and motor outputs carry a substantial degree of temporal correlations. In this
paper, we consider a binary output neuron with a large number of inputs, which is
required to store associations between temporally correlated sequences of binary inputs
and outputs, modelled as Markov chains. Storage capacity is found to increase with
both input and output correlations, and diverges in the limit where both go to unity.
We also investigate the capacity of a bistable output unit, since PCs have been shown
to be bistable in some experimental conditions. Bistability is shown to enhance storage
capacity whenever the output correlation is stronger than the input correlation. Distribution
of synaptic weights at maximal capacity is shown to be independent on correlations,
and is also unaffected by the presence of bistability.
Type
Journal articleSubject
Action PotentialsAnimals
Computer Simulation
Humans
Information Storage and Retrieval
Memory
Models, Neurological
Pattern Recognition, Physiological
Purkinje Cells
Statistics as Topic
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https://hdl.handle.net/10161/15126Published Version (Please cite this version)
10.1371/journal.pcbi.1002448Publication Info
Clopath, Claudia; Nadal, Jean-Pierre; & Brunel, Nicolas (2012). Storage of correlated patterns in standard and bistable Purkinje cell models. PLoS Comput Biol, 8(4). pp. e1002448. 10.1371/journal.pcbi.1002448. Retrieved from https://hdl.handle.net/10161/15126.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Nicolas Brunel
Duke School of Medicine Distinguished Professor in Neuroscience
We use theoretical models of brain systems to investigate how they process and learn
information from their inputs. Our current work focuses on the mechanisms of learning
and memory, from the synapse to the network level, in collaboration with various experimental
groups. Using methods fromstatistical physics, we have shown recently that the synapticconnectivity
of a network that maximizes storage capacity reproducestwo key experimentally observed
features: low connection proba

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