Storage of correlated patterns in standard and bistable Purkinje cell models.
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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.
Information Storage and Retrieval
Pattern Recognition, Physiological
Statistics as Topic
Published Version (Please cite this version)10.1371/journal.pcbi.1002448
Publication InfoClopath, C; Nadal, J-P; & 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.
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Professor of Neurobiology
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