## Generalization Learning in a Perceptron with Binary Synapses

 Title Generalization Learning in a Perceptron with Binary Synapses Publication Type Journal Article Year of Publication 2009 Authors Baldassi C Journal Journal of Statistical Physics Volume 136 Issue 5 Start Page 902 Date Published 09/2009 ISSN 0022-4715 (Print) 1572-9613 (Online) Abstract We consider the generalization problem for a perceptron with binary synapses, implementing the Stochastic Belief-Propagation-Inspired (SBPI) learning algorithm which we proposed earlier, and perform a mean-field calculation to obtain a differential equation which describes the behaviour of the device in the limit of a large number of synapses N. We show that the solving time of SBPI is of order $N\sqrt{\log N}$ , while the similar, well-known clipped perceptron (CP) algorithm does not converge to a solution at all in the time frame we considered. The analysis gives some insight into the ongoing process and shows that, in this context, the SBPI algorithm is equivalent to a new, simpler algorithm, which only differs from the CP algorithm by the addition of a stochastic, unsupervised meta-plastic reinforcement process, whose rate of application must be less than $\sqrt{2/(\pi N)}$ for the learning to be achieved effectively. The analytical results are confirmed by simulations. URL http://www.springerlink.com/content/r07772l167526045/ DOI 10.1007/s10955-009-9822-1
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