Abstract
The first purpose of this paper is to present a class of algorithms for finding the global minimum of a continuous-variable function defined on a hypercube. These algorithms, based on both diffusion processes and simulated annealing, are implementable as analog integrated circuits. Such circuits can be viewed as generalizations of neural networks of the Hopfield type, and are called “diffusion machines.”
Our second objective is to show that “learning” in these networks can be achieved by a set of three interconnected diffusion machines: one that learns, one to model the desired behavior, and one to compute the weight changes.
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References
J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,Proc. Nat. Acad. Sci. USA,81 (1984), 3088–3092.
L. O. Chua and G. N. Lin, Nonlinear programming without computation,IEEE Trans. Circuits and Systems,31 (1984), 182–188.
J. J. Hopfield and D. W. Tank, Neural computation of decisions optimization problems,Biol. Cybernet,52 (1985), 141–152.
M. Takeda and J. W. Goodman, Neural networks for computation: number representations and programming complexity,Appl. Optics,25 (1986), 3033–3046.
D. H. Ackley, G. W. Hinton and T. J. Sejnowski, A learning algorithm for Boltzmann machines,Cognitive Sci. 9 (1985), 147–169.
S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Optimization by simulated annealing,Science,220 (1983), 671–680.
D. Mitra, F. Romeo, and A. Sangiovanni-Vincentelli, Convergence and finite-time behavior of simulated annealing,Adv. in Appl. Probab.,18 (1986), 747–771.
B. Hajek, Cooling schedules for optimal annealing,Math, Oper. Res.,13 (1988), 311–319.
S. Geman and C. R. Hwang, Diffusions for global optimization,SIAM J. Control Optim.,24 (1986), 1031–1043.
B. Guidas, Global optimization via the Langevin equation,Proc. 24th IEEE Conference on Decision and Control, 1985, pp. 774–778.
E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals,Ann. Math Statist.,36 (1965), 1560–1564.
E. Wong and B. Hajek,Stochastic Processes in Engineering Systems, Springer-Verlag, New York, 1984.
J. Alspector and R. B. Allen, A neuromorphic VLSI learning system, inAdvanced Research in VLSI, Proc. 1987 Stanford Conference, P. Losleben, ed., MIT Press, Cambridge, MA, 1987, pp. 313–349.
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Communicated by Alberto Sangiovanni-Vincentelli.
This research was supported in part by U.S. Army Research Office Grant DAAL03-89-K-0128.
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Wong, E. Stochastic neural networks. Algorithmica 6, 466–478 (1991). https://doi.org/10.1007/BF01759054
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DOI: https://doi.org/10.1007/BF01759054