✦ LIBER ✦

Bounds on the number of hidden units of boltzmann machines

✍ Scribed by Eduard Moser; Tiko Kameda

Book ID: 104348557
Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 911 KB
Volume: 5
Category: Article
ISSN: 0893-6080
DOI: 10.1016/s0893-6080(05)80087-5

No coin nor oath required. For personal study only.

✦ Synopsis

lt is known that any given probability distribution ~?f the states of the observable units of a Boltzmann machine can be realized f no limit is imposed on the number of hidden units. But veo, little is known about the number of hidden units necessao, for such realization. We consider Boltzmann machines as associative memories and show that there exist vector sets whose memorization on a Boltzmann machine requires a number of hidden units which is t;xponential in the size of the vectors (i.e., the number qf componous in each vector). Additional results give tight bounds on the number of hidden units needed in terms o.f the vector set size (i.e.. the number of vectors in the set). Furthermore. we show how to construct Boltzmann ma~qfines which realize negation, intersection, and composition of the vector sets memorized by given Boltzmann machines.

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