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Flatness of the Energy Landscape for Horn Clauses

Sathasivam, Saratha, and Wan Ahmad Tajuddin Wan Abdullah, (2007) Flatness of the Energy Landscape for Horn Clauses. Matematika, 23 (2). pp. 147-156. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/20072326.pdf

Affiliations

Universiti Sains Malaysia, School of Mathematical Sciences
University of Malaya, Faculty of Science. Dept. of Physics

Abstract

The Little-Hopfield neural network programmed with Horn clauses is studied. We argue that the energy landscape of the system, corresponding to the inconsistency function for logical interpretations of the sets of Horn clauses, has minimal ruggedness. This is supported by computer simulations.

Item Type:Journal
Keywords:Little-Hopfield neural networks, Horn clauses, energy landscape, ruggedness
Subjects:Q Science, Computer Science
ID Code:5477

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[2] W.A. Little, Math. Biosci. 19(1974), 101-120.

[3] G. Pinkas, Energy minimization and the satisfiability of propositional calculus, Neural Computation, 3(1991), pp 282-291.

[4] W.A.T. Wan Abdullah, Logic programming on a neural network, Int. J. Intelligent Sys. 7(1992), 513-519.

[5] S. Wright, The roles of mutation, inbreeding, crossbreeding, and selection in evolution, Proceedings of the Sixth International Congress on Genetics 1(1932), 356-366.

[6] S. Sathasivam, Logic Mining in Neural Networks, PhD Thesis. University of Malaya, Malaysia, 2006.

[7] J.J. Hopfield, Neural computation of decisions in optimization problems, Biol. Cybern., 52(1985), 141-152.

[8] W.A.T. Wan Abdullah, The logic of neural networks, Physics Letters A, 176(1993), 202-206.

[9] K. Iwama, CNF satisfiability test by counting and polynomial average time, SIAM, Journal of Computer, 18(1989), 385-391.

[10] A. Imada, & K. Araki, What does the landscape of a Hopfield associative memory look like? Proceedings of the 7th Annual Conference on Evolutionary Programming, Springer Verlag, Lecture notes in Computer Science (in press), 1997.

[11] B. Manderick, M.D. Weger, & P Spiessens, The Genetic Algorithm and the Structure of the Fitness Landscape, Proceedings of the 4th International Conference on Genetic Algorithms, pp 143-150, 1991.

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