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Article · UzMU xabarlari · November 27, 2025

Gibbs measures associated with the fully visible Boltzmann machine

A. Z. Xalilov, I. M. Mavlonov, Sh. A. Pardayev

Ismoil Mavlonov
Open via DOIPDF

Abstract

In this work, we have undertaken a rigorous study of Boltzmann machines and the associatedGibbs measures they induce. Beginning from the machine’s energy function, we have detailedthe construction of the corresponding Gibbs measures and derived the requisite consistency(Kolmogorov) conditions. We have further identified precise criteria under which these consistencyconditions hold and have evaluated their implications for the coherence and validity of statisticalmodels built upon Boltzmann-machine architectures.

Neural Networks and Applicationsp-Adic Analysis and Mathematical PhysicsBayesian Modeling and Causal InferenceBoltzmann machineGibbs measuresenergy function

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