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.

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

References in corpus (3)

• Identification of direct residue contacts in protein-protein interaction by message passing
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Mean-field message-passing equations in the Hopfield model and its generalizations

Cited by in corpus (3)

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• Gardner formula for Ising perceptron models at small densities
• Exact solution to the random sequential dynamics of a message passing algorithm