Domains of solutions and replica symmetry breaking in multilayer neural networks

R. Monasson; D. O’Kane

doi:10.1209/0295-5075/27/2/002

Domains of solutions and replica symmetry breaking in multilayer neural networks

Research output: Contribution to journal › Article › peer-review

Abstract

The relationship between the geometrical structure of weight space and replica symmetry breaking (RSB) in multilayer neural networks is studied using a toy model. The distribution of sizes of the disconnected domains of solution space is computed analytically and compared to the RSB calculation of the Gardner volume. We are able to show explicity that ergodicity breaking and RSB are not equivalent. Repeating these calculations using the cavity approach allows us to interpret the geometrical meaning of a RSB ansatzd.

Original language	English
Pages (from-to)	85-90
Number of pages	6
Journal	EPL
Volume	27
Issue number	2
DOIs	https://doi.org/10.1209/0295-5075/27/2/002
Publication status	Published - 10 Jul 1994
Externally published	Yes

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title = "Domains of solutions and replica symmetry breaking in multilayer neural networks",

abstract = "The relationship between the geometrical structure of weight space and replica symmetry breaking (RSB) in multilayer neural networks is studied using a toy model. The distribution of sizes of the disconnected domains of solution space is computed analytically and compared to the RSB calculation of the Gardner volume. We are able to show explicity that ergodicity breaking and RSB are not equivalent. Repeating these calculations using the cavity approach allows us to interpret the geometrical meaning of a RSB ansatzd.",

author = "R. Monasson and D. O{\textquoteright}Kane",

year = "1994",

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AU - Monasson, R.

AU - O’Kane, D.

PY - 1994/7/10

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N2 - The relationship between the geometrical structure of weight space and replica symmetry breaking (RSB) in multilayer neural networks is studied using a toy model. The distribution of sizes of the disconnected domains of solution space is computed analytically and compared to the RSB calculation of the Gardner volume. We are able to show explicity that ergodicity breaking and RSB are not equivalent. Repeating these calculations using the cavity approach allows us to interpret the geometrical meaning of a RSB ansatzd.

AB - The relationship between the geometrical structure of weight space and replica symmetry breaking (RSB) in multilayer neural networks is studied using a toy model. The distribution of sizes of the disconnected domains of solution space is computed analytically and compared to the RSB calculation of the Gardner volume. We are able to show explicity that ergodicity breaking and RSB are not equivalent. Repeating these calculations using the cavity approach allows us to interpret the geometrical meaning of a RSB ansatzd.

U2 - 10.1209/0295-5075/27/2/002

DO - 10.1209/0295-5075/27/2/002

M3 - Article

AN - SCOPUS:84957317957

SN - 0295-5075

VL - 27

SP - 85

EP - 90

JO - EPL

JF - EPL

IS - 2

ER -

Domains of solutions and replica symmetry breaking in multilayer neural networks

Abstract

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