Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
This work establishes a theoretical basis for integrating machine learning into Monte Carlo sampling, addressing a gap in the field, but it is incremental as it focuses on a specific model and method.
The authors tackled the lack of theoretical understanding in machine-learning-assisted Monte Carlo sampling by analytically studying Sequential Tempering with a shallow MADE architecture on the Curie-Weiss model, providing optimal weights and comparing procedures with and without local Metropolis steps to predict the best approach.
Recent years have seen a rise in the application of machine learning techniques to aid the simulation of hard-to-sample systems that cannot be studied using traditional methods. Despite the introduction of many different architectures and procedures, a wide theoretical understanding is still lacking, with the risk of suboptimal implementations. As a first step to address this gap, we provide here a complete analytic study of the widely-used Sequential Tempering procedure applied to a shallow MADE architecture for the Curie-Weiss model. The contribution of this work is twofold: firstly, we give a description of the optimal weights and of the training under Gradient Descent optimization. Secondly, we compare what happens in Sequential Tempering with and without the addition of local Metropolis Monte Carlo steps. We are thus able to give theoretical predictions on the best procedure to apply in this case. This work establishes a clear theoretical basis for the integration of machine learning techniques into Monte Carlo sampling and optimization.