On the Critical Capacity of the Hopfield Model
Mathematical Physics
2009-10-31 v1 math.MP
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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 for a large number of neurons. This result is an advance on all rigorous results in the literature and the relationship between the capacity and retrieval errors obtained here for small coincides with replica calculation results.
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Cite
@article{arxiv.math-ph/0012038,
title = {On the Critical Capacity of the Hopfield Model},
author = {J. Feng and M. Shcherbina and B. Tirozzi},
journal= {arXiv preprint arXiv:math-ph/0012038},
year = {2009}
}
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