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On the Critical Capacity of the Hopfield Model

J. Feng·M. Shcherbina·B. Tirozzi
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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.

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J. Feng, M. Shcherbina, B. Tirozzi. 2000-12-21. On the Critical Capacity of the Hopfield Model. https://doi.org/10.1007/s002200000344

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