Self averaging and the space of interactions in neural networks
Michel Talagrand · Random Structures and Algorithms · 1999
We prove (through a precise exponential inequality) that the logarithm of the size of the intersection of M random half spaces with the unit sphere of ℝN (resp., the discrete cube {−1, 1}N) is, as N→∞, a self averaging quantity. This provides justification for one of the first steps of a famous computation by E. Gardner [J. Phys. A 21 (1988), 257–270]. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199–213, 1999