%0 Journal Article %1 feng-capacity-of-hopfield-1997 %A Feng, Jianfeng %A Tirozzi, Brunello %D 1997 %J Journal of Physics A: Mathematical and General %K hopfield network neural %N 10 %P 3383 %T Capacity of the Hopfield model %U http://stacks.iop.org/0305-4470/30/i=10/a=016 %V 30 %X For a given ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img5.gif if ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img6.gif neurons deviating from the memorized patterns are allowed, we constructively show that if and only if ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img7.gif all stored patterns are fixed points of the Hopfield model. If ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img8.gif neurons are allowed with ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img9.gif then ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img10.gif where ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img11.gif is the distribution function of the normal distribution. The result obtained by Amit and co-workers only formally coincides with the latter case which indicates that the replica trick approach to the capacity of the Hopfield model is only valid in the case ##IMG## http://ej.iop.org/images/0305-4470/30/10/016/img12.gif .

@article{feng-capacity-of-hopfield-1997, abstract = {For a given ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img5.gif] if ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img6.gif] neurons deviating from the memorized patterns are allowed, we constructively show that if and only if ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img7.gif] all stored patterns are fixed points of the Hopfield model. If ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img8.gif] neurons are allowed with ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img9.gif] then ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img10.gif] where ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img11.gif] is the distribution function of the normal distribution. The result obtained by Amit and co-workers only formally coincides with the latter case which indicates that the replica trick approach to the capacity of the Hopfield model is only valid in the case ##IMG## [http://ej.iop.org/images/0305-4470/30/10/016/img12.gif] .}, added-at = {2011-10-17T12:27:32.000+0200}, author = {Feng, Jianfeng and Tirozzi, Brunello}, biburl = {https://www.bibsonomy.org/bibtex/2d25c7990aed05b9accce4cb19fb79f60/mhwombat}, interhash = {b598e1674f67924495422a64a63347dc}, intrahash = {d25c7990aed05b9accce4cb19fb79f60}, journal = {Journal of Physics A: Mathematical and General}, keywords = {hopfield network neural}, number = 10, pages = 3383, timestamp = {2016-07-12T19:25:30.000+0200}, title = {Capacity of the Hopfield model}, url = {http://stacks.iop.org/0305-4470/30/i=10/a=016}, volume = 30, year = 1997 }