论文标题
机器学习在有保守数量的情况下生成的配置：一个警示的故事
Machine learning generated configurations in presence of a conserved quantity: a cautionary tale
论文作者
论文摘要
我们研究了一家专门训练的机器学习算法的性能，该算法是从重要性采样的蒙特卡洛模拟中获得的二维ISING模型，并具有保守的磁化。对于监督的机器学习，我们使用卷积神经网络，发现相应的输出不仅允许以高精度定位相变点，还显示出由ISING关键指数特征的有限尺寸缩放。对于无监督的学习，训练有限制的Boltzmann机器（RBM），以生成新的配置，然后将其用于计算各种数量。我们发现RBM无法识别保守数量并生成具有原始物理系统中禁止的磁化和能量的配置。 RBM生成的配置会导致能量密度概率分布，而权重和错误的空间相关性。我们表明，当训练RBM的配置从非保守的ISING模型获得时，也会遇到缺点。
We investigate the performance of machine learning algorithms trained exclusively with configurations obtained from importance sampling Monte Carlo simulations of the two-dimensional Ising model with conserved magnetization. For supervised machine learning, we use convolutional neural networks and find that the corresponding output not only allows to locate the phase transition point with high precision, it also displays a finite-size scaling characterized by an Ising critical exponent. For unsupervised learning, restricted Boltzmann machines (RBM) are trained to generate new configurations that are then used to compute various quantities. We find that RBM is incapable of recognizing the conserved quantity and generates configurations with magnetizations and energies forbidden in the original physical system. The RBM generated configurations result in energy density probability distributions with incorrect weights as well as in wrong spatial correlations. We show that shortcomings are also encountered when training RBM with configurations obtained from the non-conserved Ising model.
