A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices

Manfred Opper, Burak Cakmak, Ole Winther

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Resumé

We consider the problem of solving TAP mean eld equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an eective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed eld only. The TAP magnetizations are stable xed points if an AT stability criterion is fullled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
OriginalsprogEngelsk
Artikelnummer114002
TidsskriftJournal of Physics A: Mathematical and Theoretical
Vol/bind49
Udgave nummer11
Antal sider24
ISSN1751-8113
DOI
StatusUdgivet - 8 feb. 2016

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Ising model
Random Matrices
Ising Model
iteration
Magnetization
Ensemble
Memory Term
Data storage equipment
magnetization
Invariant
Stability criteria
matrices
Iteration
Cancel
Trajectories
trajectories
Thermodynamics
Thermodynamic Limit
Stability Criteria
thermodynamics

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A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices. / Opper, Manfred ; Cakmak, Burak; Winther, Ole.

I: Journal of Physics A: Mathematical and Theoretical, Bind 49, Nr. 11, 114002, 08.02.2016.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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AU - Winther, Ole

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KW - Iterative Convergent Algorithms

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