Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices

Abstract

We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical functional method that the proposed algorithm converges when the so-called de Almeida Thouless (AT) criterion is fulfilled. Moreover, we give exact analytical expressions for the rate of the convergence.

arXiv comment14 pages, 6 figures, the extended version of the previous preprint arXiv:1901.08583v1, both authors are co-first authors

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• The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
• Gardner formula for Ising perceptron models at small densities
• Exact solution to the random sequential dynamics of a message passing algorithm
• Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
• Semi-analytic approximate stability selection for correlated data in generalized linear models
• Analysis of Random Sequential Message Passing Algorithms for Approximate Inference