Abstract
The effect of damage on the pattern recognition in the Hopfield-model of neural networks is studied. It is assumed that in a damaged network the synaptic efficaciesJ i,j=Jj,i, between pairs of neuronsS i andS j follow the Hebb rule with probability (1−p) and are equal to zero with probabilityp. Numerical simulations are performed for a net consisting of 400 neurons. It is investigated in detail how the retrieval of noisy patterns and the storage capacity of the net depends, for varying initial noise, on the concentrationp of the damaged synaptic efficacies.
References
J. A. Anderson and E. Rosenfeld, eds.,Neurocomputing (MIT Press, Cambridge, Massachusetts, 1988).
R. Eckmiller and Ch. v. Malsburg, eds.,Neural Computers (Springer-Verlag, Berlin, 1988).
S. I. Amari, S. Grossberg, and T. Kohonen, eds.,Neural Networks I (Pergamon Press, New York, 1988).
H. Sompolinsky,Phys. Today 1988 (December):70 (1988).
J. J. Hopfield,Proc. Natl. Acad. Sci. USA 79:2554 (1982).
W. S. McCulloch and W. Pitts,Bull. Math. Biophys. 5:127 (1943).
D. O. Hebb,The Organization of Behavior (Wiley, New York, 1949).
W. A. Little,Math. Biosci. 19:101 (1974); W. A. Little and G. L. Shaw,Math. Biosci. 39:281 (1978).
D. J. Amit, H. Gutfreund, and H. Sompolinsky,Ann. Phys. 173:30 (1987).
M. A. Sivilotti, M. A. Mahowald, and C. A. Mead, inProceedings of the 1987 Stanford Conference, (MIT Press, Cambridge, Massachusetts, 1988), p. 295.
W. Kinzel,Z. Phys. B 60:205 (1985).
K. E. Kürten,Phys. Lett. 129:157 (1988).
D. Stauffer,Introduction to Percolation Theory (Taylor and Francis, London, 1985).
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Koscielny-Bunde, E. Effect of damage in neural networks. J Stat Phys 58, 1257–1266 (1990). https://doi.org/10.1007/BF01026576
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DOI: https://doi.org/10.1007/BF01026576