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 $\alpha\le 0.113$ for a large number of neurons. This result is an advance on all rigorous results in the literature and the relationship between the capacity $\alpha$ and retrieval errors obtained here for small $\alpha$ coincides with replica calculation results.Comment: Latex 36 page macros: http://www.springer.de/author/tex/help-journals.htm