Weight Space Structure and the Storage Capacity of a Fully-connected Committee Machine Typeset Using Revt E X
نویسندگان
چکیده
We study the storage capacity of a fully-connected committee machine with a large number K of hidden nodes. The storage capacity is obtained by analyzing the geometrical structure of the weight space related to the internal representation. By examining the asymptotic behavior of order parameters in the limit of large K, the storage capacity c is found to be proportional to K p ln K up to the leading order. This result satisses the mathematical bound given by Mitchison and Durbin, whereas the replica-symmetric solution in a conventional Gardner's approach violates this bound.
منابع مشابه
The Storage Capacity of a Fully-Connected Committee Machine
We study the storage capacity of a fully-connected committee machine with a large number K of hidden nodes. The storage capacity is obtained by analyzing the geometrical structure of the weight space related to the internal representation . By examining the asymptotic behavior of order parameters in the limit of large K, the storage capacity Q c is found to be proportional to ]{ Jln ]{ up to th...
متن کاملStorage Capacity of a fully - connected parity machine
We study a fully-connected parity machine with K hidden units for continuous weights. The geometrical structure of the weight space of this model is analyzed in terms of the volumes associated with the internal representations of training set. By examining the asymptotic behavior of order parameters in the large K limit, we nd the maximum number c , the storage capacity, of patterns per input u...
متن کاملPeriodic Orbits of the Integrable Swinging Atwood's Machine Typeset Using Revt E X
(a) (b) (c) (d) Abstract We identify all the periodic orbits of the integrable swinging Atwood's machine by calculating the rotation number of each orbit on its invariant tori in phase space, and also providing explicit formulas for the initial conditions needed to generate each orbit.
متن کاملHilbert Space of Wormholes Typeset Using Revt E X
Wormhole boundary conditions for the Wheeler–DeWitt equation can be derived from the path integral formulation. It is proposed that the wormhole wave function must be square integrable in the maximal analytic extension of minisuperspace. Quantum wormholes can be invested with a Hilbert space structure, the inner product being naturally induced by the minisuperspace metric, in which the Wheeler–...
متن کاملA COVERING PROPERTY IN PRINCIPAL BUNDLES
Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...
متن کامل