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Storing infinite numbers of patterns in a spin-glass model of neural networks

The Hopfield model for a neural network is studied in the limit when the number p of stored patterns increases with the size N of the network, as p=αN. It is shown that, despite its spin-glass features, the model exhibits associative memory for α<αc, αc≳0.14. This is a result of the existence at low temperature of 2p dynamically stable degenerate states, each of which is almost fully correlated with one of the patterns. These states become ground states at α<0.05. The phase diagram of this rich spin-glass is described.

Authors: Amit DJ, Gutfreund H, Sompolinsky H.

Year of publication: 1985

Journal: Phys Rev Lett. 1985 Sep 30;55(14):1530-1533.

Link to publication:

https://doi.org/10.1103/PhysRevLett.55.1530

Labs:

Hanoch Gutfreund

Haim Sompolinsky

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