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We study a class of Hopfield models where the memories are represented by amixture of Gaussian and binary variables and the neurons are Ising spins. Westudy the properties of this family of models as the relative weight of the twokinds of variables in the patterns varies. We quantitatively determine how theretrieval phase squeezes towards zero as the memory patterns contain a largerfraction of mismatched variables. As the memory is purely Gaussian retrieval islost for any positive storage capacity. It is shown that this comes aboutbecause of the spherical symmetry of the free energy in the Gaussian case.Introducing two different memory pattern overlaps between spin configurationsand each contribution to the pattern from the two kinds of variables one canobserve that the Gaussian parts of the patterns act as a noise, makingretrieval more difficult. The basins of attraction of the states, the accuracyof the retrieval and the storage capacity are studied by means of Monte Carlonumerical simulations. We uncover that even in the limit where the networkcapacity shrinks to zero, the (few) retrieval states maintain a large basin ofattraction and large overlaps with the mismatched patterns. So the network canbe used for retrieval, but with a very small capacity.

A generalized Hopfield model to store and retrieve mismatched memory patterns