<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Carlo Baldassi</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Generalization Learning in a Perceptron with Binary Synapses</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Statistical Physics</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">biocomp</style></keyword><keyword><style  face="normal" font="default" size="100%">neuroscience</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.springerlink.com/content/r07772l167526045/</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">http://areeweb.polito.it/ricerca/cmp/sites/default/files/Baldassi09.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">136</style></volume><abstract><style face="normal" font="default" size="100%">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. </style></abstract><issue><style face="normal" font="default" size="100%">5</style></issue><section><style face="normal" font="default" size="100%">902</style></section></record></records></xml>