Abstract
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.
Abstract (translated)
近年来，机器学习技术被广泛应用于模拟难以采样的系统，这些系统的研究无法通过传统方法进行。尽管已经引入了许多不同的架构和程序，但仍然缺乏广泛的理论理解，存在次优实现的风险。作为弥补这一缺口的第一步，我们在这里对广泛应用的顺序退火（Sequential Tempering）过程进行了完整分析，该过程应用于浅层MADE（Masked Autoencoder for Distribution Estimation）架构来模拟Curie-Weiss模型。 这项工作的贡献有两方面：首先，我们描述了最优权重以及在梯度下降优化下的训练情况。其次，我们将带局部Metropolis蒙特卡罗步骤的顺序退火过程与不包含这些步骤的过程进行了比较。因此，我们可以对这种情况提供理论预测，指出最佳应用程序是什么。 这项工作为将机器学习技术融入到蒙特卡洛采样和优化中提供了明确的理论基础。
URL
https://arxiv.org/abs/2505.22598
