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Some rigorous results on the Hopfield neural network model

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Abstract

We analyze the thermal equilibrium distribution of 2p mean field variables for the Hopfield model withp stored patterns, in the case where 2p is small compared to the number of spins. In particular, we give a full description of the free energy density in the thermodynamic limit, and of the so-called “symmetric solutions” for the mean field equations.

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Koch, H., Piasko, J. Some rigorous results on the Hopfield neural network model. J Stat Phys 55, 903–928 (1989). https://doi.org/10.1007/BF01041071

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