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Bounds on the Number of Hidden Units of Boltzmann Machines

Simon Fraser University. Centre for Systems ScienceE. Moser

出版	Simon Fraser University, Centre for Systems Science, 1990
URL	http://books.google.com.hk/books?id=mYRIHwAACAAJ&hl=&source=gbs_api

註釋

It is known that any given probability distribution of the states of the observable units of a Boltzmann machine can be realized if no limit is imposed on the number of hidden units, but very little is known about the number of hidden units necessary for such realization. This paper considers Boltzmann machines as associative memories and shows that there exist vector sets whose memorization on a Boltzmann machine requires a number of hidden units exponential in the size of the vectors. Additional results give tight bounds on the number of hidden units in terms of the vector set size. The restrictive model of auto-association in Boltzmann machines provides a construction for negation intersection, and composition of the vector sets which are memorized by Boltzmann machines.