Gardner and Derrida have introduced a natural version of the problem
of the capacity of the binary perceptron “with temperature,”and
they proposed (based on “physical” methods) remarkable formulas
for this model. We give a complete rigorous proof that these formulas are
correct at sufficiently high temperature for a much larger class of models.
@article{1019160259,
author = {Talagrand, Michel},
title = {Intersecting random half-spaces: toward the Gardner-Derrida
formula},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 725-758},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160259}
}
Talagrand, Michel. Intersecting random half-spaces: toward the Gardner-Derrida
formula. Ann. Probab., Tome 28 (2000) no. 1, pp. 725-758. http://gdmltest.u-ga.fr/item/1019160259/