Crisanti–Sommers Formula and Simultaneous Symmetry Breaking in Multi-species Spherical Spin Glasses

Bates, Erik; Youngtak, Sohn,

doi:10.1007/s00220-022-04421-x

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2022

2024

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Cited by 8 publications

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“…By adding some extra terms to the perturbations, we can regularize our posterior probability by introducing the Ghirlanda-Guerra identities while preserving the Nishimori identities and the concentration of the overlaps. The synchronization of spin glasses was also recently adapted in other contexts [27,10,9,1,3] to compute the free energy of various models. A different point of view to study multispecies models using the TAP approach was also applied recently in [41,42].…”

Section: Introductionmentioning

confidence: 99%

Low-rank Matrix Estimation with Inhomogeneous Noise

Guionnet¹,

Ko²,

Krząkała³

et al. 2022

Preprint

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We study low-rank matrix estimation for a generic inhomogeneous output channel through which the matrix is observed. This generalizes the commonly considered spiked matrix model with homogeneous noise to include for instance the dense degree-corrected stochastic block model. We adapt techniques used to study multispecies spin glasses to derive and rigorously prove an expression for the free energy of the problem in the large size limit, providing a framework to study the signal detection thresholds. We discuss an application of this framework to the degree corrected stochastic block models.

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