Hopfield, J. J. (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences of the United States of America, 81 (10). pp. 3088-3092. ISSN 0027-8424 http://resolver.caltech.edu/CaltechAUTHORS:HOPpnas84
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A model for a large network of "neurons" with a graded response (or sigmoid input--output relation) is studied. This deterministic system has collective properties in very close correspondence with the earlier stochastic model based on McCulloch--Pitts neurons. The content-addressable memory and other emergent collective properties of the original model also are present in the graded response model. The idea that such collective properties are used in biological systems is given added credence by the continued presence of such properties for more nearly biological "neurons." Collective analog electrical circuits of the kind described will certainly function. The collective states of the two models have a simple correspondence. The original model will continue to be useful for simulations, because its connection to graded response systems is established. Equations that include the effect of action potentials in the graded response system are also developed.
|Additional Information:||© 1984 by the National Academy of Sciences. Contributed by J. J. Hopfield, February 13, 1984. The author thanks David Feinstein, John Lambe, Carver Mead, and John Platt for discussions and permission to mention unpublished work. The work at California Institute of Technology was supported in part by National Science Foundation Grant DMR-8107494. This is contribution no. 6975 from the Division of Chemistry and Chemical Engineering, California Institute of Technology. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.|
|Subject Keywords:||associative memory; neural network; stability; action potentials|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||31 Jul 2007|
|Last Modified:||26 Dec 2012 09:34|
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