TY - JOUR
T1 - The phase space of interactions in neural networks with definite symmetry
AU - Gardner, E.
AU - Gutfreund, H.
AU - Yekutieli, I.
PY - 1989/6/21
Y1 - 1989/6/21
N2 - We calculate the typical fraction of the phase space of interactions which solve the problemof storing a given set of p patterns represented as N-spin configurations, as a function of the storage ratio, a =p/N , of the stability parameter, K, and of the symmetry, 7, of the interaction matrices. The calculation is performed for strongly diluted networks, where the connectivityof each spin, C, is of the order of In N. For each value of K and 17, there is a maximal value of a, above which the volume of solutions vanishes. For each value of K and a, there is a typical value of 7at which this volume is maximal. The analytical studies are supplemented by numerical simulations on fully connected and diluted networks, using specific learning algorithms.
AB - We calculate the typical fraction of the phase space of interactions which solve the problemof storing a given set of p patterns represented as N-spin configurations, as a function of the storage ratio, a =p/N , of the stability parameter, K, and of the symmetry, 7, of the interaction matrices. The calculation is performed for strongly diluted networks, where the connectivityof each spin, C, is of the order of In N. For each value of K and 17, there is a maximal value of a, above which the volume of solutions vanishes. For each value of K and a, there is a typical value of 7at which this volume is maximal. The analytical studies are supplemented by numerical simulations on fully connected and diluted networks, using specific learning algorithms.
UR - http://www.scopus.com/inward/record.url?scp=2642556763&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/22/12/005
DO - 10.1088/0305-4470/22/12/005
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AN - SCOPUS:2642556763
SN - 0305-4470
VL - 22
SP - 1995
EP - 2008
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 12
ER -