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

Autor: Manfred Opper, Burak Çakmak, Ole Winther
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Statistics and Probability
FOS: Computer and information sciences
Stability criterion
Gaussian
Computer Science - Information Theory
General Physics and Astronomy
FOS: Physical sciences
02 engineering and technology
Fixed point
Iterative Convergent Algorithms
01 natural sciences
symbols.namesake
Ising models
0103 physical sciences
0202 electrical engineering
electronic engineering
information engineering
Applied mathematics
Free Probability
010306 general physics
Mathematical Physics
Mathematics
Information Theory (cs.IT)
TAP Equations
020206 networking & telecommunications
Statistical and Nonlinear Physics
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Invariant (physics)
Condensed Matter - Disordered Systems and Neural Networks
Free probability
Modeling and Simulation
Thermodynamic limit
symbols
Ising model
Dynamical Functional Theory
Random matrix
Random Matrices
Zdroj: Opper, M, Cakmak, B & Winther, O 2016, ' A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices ', Journal of Physics A: Mathematical and Theoretical, vol. 49, no. 11, 114002 . https://doi.org/10.1088/1751-8113/49/11/114002
Opper, M, Çakmak, B & Winther, O 2016, ' A theory of solving TAP equations for Ising models with general invariant random matrices ', Journal of Physics A: Mathematical and Theoretical, vol. 49, no. 11, 114002 . https://doi.org/10.1088/1751-8113/49/11/114002
Popis: We consider the problem of solving TAP mean field equations by iteration for Ising model 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 effective 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 field only. The TAP magnetizations are stable fixed points if an AT stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
27 pages, 6 Figures Published in Journal of Physics A: Mathematical and Theoretical, Volume 49, Number 11, 2016
Databáze: OpenAIRE
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