English

On the Critical Capacity of the Hopfield Model

Mathematical Physics 2009-10-31 v1 math.MP q-bio

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 α0.113\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 α\alpha and retrieval errors obtained here for small α\alpha coincides with replica calculation results.

Keywords

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}
}

Comments

Latex 36 page macros: http://www.springer.de/author/tex/help-journals.html