Energy-Decreasing Dynamics in Mean-Field Spin Models

TL;DR

This paper compares energy-decreasing algorithms in mean-field spin models, analyzing their efficiency and basin attraction properties, and finds that greedy algorithms relax faster but reluctant algorithms can perform better in fixed trial scenarios.

Contribution

It introduces a comparative analysis of greedy and reluctant dynamics in mean-field spin models, including new metrics like attraction basin wideness and interpolation between algorithms.

Findings

Reluctant algorithms perform better for a fixed number of trials.

Greedy algorithms have shorter relaxation times scaling linearly with system size.

Both algorithms become similar when considering fixed elapsed time due to different relaxation scalings.

Abstract

We perform a statistical analysis of deterministic energy-decreasing algorithms on mean-field spin models with complex energy landscape like the Sine model and the Sherrington Kirkpatrick model. We specifically address the following question: in the search of low energy configurations is it convenient (and in which sense) a quick decrease along the gradient (greedy dynamics) or a slow decrease close to the level curves (reluctant dynamics)? Average time and wideness of the attraction basins are introduced for each algorithm together with an interpolation among the two and experimental results are presented for different system sizes. We found that while the reluctant algorithm performs better for a fixed number of trials, the two algorithms become basically equivalent for a given elapsed time due to the fact that the greedy has a shorter relaxation time which scales linearly with the system size compared to a quadratic dependence for the reluctant.