神经网络中的自平均与交互空间

Random Struct. Algorithms Pub Date : 1999-05-01 DOI:10.1002/(SICI)1098-2418(199905)14:3%3C199::AID-RSA1%3E3.0.CO;2-6

M. Talagrand

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引用次数: 10

摘要

Ž。摘要:我们通过一个精确的指数不等式证明了M个随机半空间与R的单位球相交的N Ž大小的对数。4N。离散立方y1，作为Na '，是一个自平均量。这为w Ž提供了理由。这是E. Gardner J. Phys著名计算的第一步。[21] [j]。John Wiley & Sons, Inc.;随机结构。Alg。[j]中国科学:地球科学，1994,13 (2)，1999

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Self averaging and the space of interactions in neural networks

Ž . ABSTRACT: We prove through a precise exponential inequality that the logarithm of the N Ž size of the intersection of M random half spaces with the unit sphere of R resp., the 4N . discrete cube y1, 1 is, as Na`, a self averaging quantity. This provides justification for w Ž . x one of the first steps of a famous computation by E. Gardner J. Phys. A 21 1988 , 257]270 . Q 1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199]213, 1999

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Random Struct. Algorithms

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