eas@utcsrgv.UUCP (Ann Struthers) (11/19/84)
Subject: Computation in Networks of Stochastic Computing Elements
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COMPUTATION IN NETWORKS OF STOCHASTIC COMPUTING ELEMENTS
Tuesday, November 20, 1984
11:00 A.M
Sandford Fleming Building 1105
Professor Geoffrey Hinton
Computer Science Department
Carnegie Mellon University
Computer vision systems need to be able to perform best-fit searches
rapidly. Given a large set of candidate hypotheses about how to
interpret parts or aspects of an image, and a set of plausible
constraints between pairs of local hypotheses, truth-values must be
assigned to the hypotheses so as too minimize the total violation of
the plausible constraints. This is a combinatorial optimization
problem. It can be solved by allowing a network of simple computing
elements to settle into a stable state. Each element represents a
hypothesis, and the interactions between the elements implement the
constraints.
Until recently it has been very difficult to analyze this kind of
cooperative computation, because the elements must be non-linear and
cross-compiled. If, however, the elements adopt discrete states
according to a particular stochastic function of their inputs, it is
possible to use statistical mechanics to describe the behaviour of the
whole system. An unexpected result of this analysis is that there is
a very simple relationship between the probability of settling into a
particular global state and the strengths of the local couplings
between the individual computing elements. This relationship allows
a cooperative system to learn the implicit constraints in any domain
simply by being told whether the state it settles into is correct. The
learning algorithm converges on a set of weights which is optimal, i.e.
a set of weights which minimizes the difference between the probabilities
with which the system settles on particular interpretations and the
probabilities that these interpretations are correct.