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High-symmetry Hopfield-type neural networks

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Abstract

We study the set of fixed points of a Hopfield-type neural network with a connection matrix constructed from a high-symmetry set of memorized patterns using the Hebb rule. The memorized patterns depending on an external parameter are interpreted as distorted copies of a vector standard to be learned by the network. The dependence of the fixed-point set of the network on the distortion parameter is described analytically. The investigation results are interpreted in terms of neural networks and the Ising model.

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Authors and Affiliations

  1. Institute for High-Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow Oblast, Russia

    L. B. Litinskii

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  1. L. B. Litinskii
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 1, pp. 133–158, January, 1999.

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Litinskii, L.B. High-symmetry Hopfield-type neural networks. Theor Math Phys 118, 107–127 (1999). https://doi.org/10.1007/BF02557200

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  • DOI: https://doi.org/10.1007/BF02557200

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