Geodesic
High-symmetry Hopfield-type neural networks
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 1, pp. 133-158

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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. 
@article{TMF_1999_118_1_a9,
     author = {L. B. Litinskii},
     title = {High-symmetry {Hopfield-type} neural networks},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {133--158},
     publisher = {mathdoc},
     volume = {118},
     number = {1},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_1_a9/}
}
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L. B. Litinskii. High-symmetry Hopfield-type neural networks. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 1, pp. 133-158. http://geodesic.mathdoc.fr/item/TMF_1999_118_1_a9/