On the Critical Capacity of the Hopfield Model

Abstract

We estimate the critical capacity of the zero-temperature Hopfield model by using a novel and rigorous method. The probability of having a stable fixed point is one when $\hat{I}\pm \le 0.113$ for a large number of neurons. This result is an advance on all rigorous results in the literature and the relationship between the capacity $\hat{I}\pm$ and retrieval errors obtained here for small $\hat{I}\pm$ coincides with replica calculation results.

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