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From: jair-ed@ptolemy.arc.nasa.gov
Subject: New Article, Improving Connectionist Energy Minimization ...
Message-ID: <1995Oct30.230620.17763@ptolemy-ethernet.arc.nasa.gov>
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Date: Mon, 30 Oct 1995 23:06:20 GMT
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JAIR is pleased to announce the publication of the following article:

Pinkas, G. and Dechter, R. (1995)
  "Improving Connectionist Energy Minimization", Volume 3, pages 223-248.
   PostScript: volume3/pinkas95a.ps (358K)
	       compressed, volume3/pinkas95a.ps.Z (138K)


   Abstract: Symmetric networks designed for energy minimization such as
   Boltzman machines and Hopfield nets are frequently investigated for
   use in optimization, constraint satisfaction and approximation of
   NP-hard problems. Nevertheless, finding a global solution (i.e., a
   global minimum for the energy function) is not guaranteed and even a
   local solution may take an exponential number of steps.  We propose an
   improvement to the standard local activation function used for such
   networks.  The improved algorithm guarantees that a global minimum is
   found in linear time for tree-like subnetworks. The algorithm, called
   activate, is uniform and does not assume that the network is
   tree-like.  It can identify tree-like subnetworks even in cyclic
   topologies (arbitrary networks) and avoid local minima along these
   trees.  For acyclic networks, the algorithm is guaranteed to converge
   to a global minimum from any initial state of the system
   (self-stabilization) and remains correct under various types of
   schedulers.  On the negative side, we show that in the presence of
   cycles, no uniform algorithm exists that guarantees optimality even
   under a sequential asynchronous scheduler.  An asynchronous scheduler
   can activate only one unit at a time while a synchronous scheduler can
   activate any number of units in a single time step.  In addition, no
   uniform algorithm exists to optimize even acyclic networks when the
   scheduler is synchronous.  Finally, we show how the algorithm can be
   improved using the cycle-cutset scheme.  The general algorithm, called
   activate-with-cutset, improves over activate and has some performance
   guarantees that are related to the size of the network's cycle-cutset.

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