Parisi Phase in a Neuron
Disordered Systems and Neural Networks
2009-10-30 v1 q-bio
Abstract
Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses we obtain a variational free energy functional for the neuron. The solution is demonstrated at high temperature and large relative number of examples, where several phases are identified by thermodynamical stability analysis, two of them exhibiting spontaneous full replica symmetry breaking. We give analytically the curved segments of the order parameter function and in representative cases compute the free energy, the storage error, and the entropy.
Keywords
Cite
@article{arxiv.cond-mat/9708188,
title = {Parisi Phase in a Neuron},
author = {G. Györgyi and P. Reimann},
journal= {arXiv preprint arXiv:cond-mat/9708188},
year = {2009}
}
Comments
4 pages in prl twocolumn format + 3 Postscript figures. Submitted to Physical Review Letters