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NJIT Mathematical Biology Seminar

Tuesday, September 20, 2005, 4:00 pm
Cullimore Hall 611
New Jersey Institute of Technology

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Optimal information storage and the distribution of synaptic weights: experiment vs theory

Nicolas Brunel

CNRS, Laboratory of Neurophysics and Physiology
Université Paris 5 René Descartes

It is widely believed that synaptic modifications are one of the factors underlying learning and memory. However, few studies have examined what can be deduced about the learning process from the distribution of synaptic weights. To gain insight about how learning shapes the distribution of synaptic weights, we analyzed the perceptron, a prototypical feedforward neural network. We obtained the synaptic weight distribution for a perceptron with excitatory synapses at its optimal storage capacity. It contains more than 50% `silent' synapses (synapses with zero weight) and this fraction increases with storage reliability: silent synapses are therefore a necessary byproduct of optimising learning and reliability. Exploiting the classical analogy between the perceptron and the cerebellar Purkinje cell, we fitted the optimal weight distribution to that measured for granule-cell---Purkinje-cell synapses. The two distributions agree well, suggesting that a single Purkinje cell can learn up to 5Kbytes of information, in the form of 40,000 input-output associations.