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 $α\le 0.113$ for a large number of neurons. This result is an advance on all rigorous results in the literature and the relationship between the capacity $α$ and retrieval errors obtained here for small $α$ coincides with replica calculation results.