Mixing times for the Swapping Algorithm on the Blume‐Emery‐Griffiths model

Ebbers, Mirko; Knöpfel, Holger; Löwe, Matthias; Vermet, Franck

doi:10.1002/rsa.20461

Cited by 14 publications

(8 citation statements)

References 28 publications

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“…The strategy is to take advantage of the large deviations estimates discussed in section 3. Recall from that section that we assume that the set of equilibrium macrostates E β , which can be expressed in the form given in (9), consists of a single point z β . Define an equilibrium configuration σ β to be a configuration such that…”

Section: Resultsmentioning

confidence: 99%

Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods

Kovchegov

Otto

2015

J Stat Phys

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Abstract. In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The parameter region for rapid mixing for the generalized Curie-Weiss-Potts model is derived as a new application of the aggregate path coupling method.

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Section: Resultsmentioning

confidence: 99%

Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods

Kovchegov

Otto

2015

J Stat Phys

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“…They prove that the Swapping Algorithm mixes slowly on the Random Energy Model, even though this model has only a third order phase transition. In the Blume-Emery-Griffiths model both, rapid or torpid mixing may occur as was shown in Ebbers et al (2014). Another idea to improve the performance of the Metropolis chain is the so called Equi-energy sampling algorithm (see e.g.…”

Section: Equi-energy Samplingmentioning

confidence: 98%

Equi-Energy sampling does not converge rapidly on the mean-field Potts model with three colors close to the critical temperature

Ebbers,

Löwe

2019

Preprint

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Equi-Energy Sampling (EES, for short) is a method to speed up the convergence of the Metropolis chain, when the latter is slow. We show that there are still models like the mean-field Potts model, where EES does not converge rapidly in certain temperature regimes. Indeed we will show that EES is slowly mixing on the mean-field Potts model, in a regime below the critical temperature. Though we will concentrate on the Potts model with three colors, our arguments remain valid for any number of colors q ≥ 3, if we adapt the temperature regime. For the situation of the mean-field Potts model this answers a question posed in Hua and Kou (2011).

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“…Proof Note that Q ∞ has its mass concentrated on the set N 0 (given by equation (12)) and the differences in the mass for the various configurations from this set stem from factor…”

Section: Fixedmentioning

confidence: 99%

“…in polynomial time), see e.g. [12,29,31], in others the convergence takes exponentially long, see [3] or [10]. The results in [11] show that equi-energy sampling typically does not overcome the problem of torpid mixing.…”

Section: Remarkmentioning

confidence: 99%

Some Remarks on Replicated Simulated Annealing

2021

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Recently authors have introduced the idea of training discrete weights neural networks using a mix between classical simulated annealing and a replica ansatz known from the statistical physics literature. Among other points, they claim their method is able to find robust configurations. In this paper, we analyze this so called “replicated simulated annealing” algorithm. In particular, we give criteria to guarantee its convergence, and study when it successfully samples from configurations. We also perform experiments using synthetic and real data bases.

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Mixing times for the Swapping Algorithm on the Blume‐Emery‐Griffiths model

Cited by 14 publications

References 28 publications

Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods

Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods

Equi-Energy sampling does not converge rapidly on the mean-field Potts model with three colors close to the critical temperature

Some Remarks on Replicated Simulated Annealing

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