机器学习阶段的通用训练方案和由此产生的通用性
A universal training scheme and the resulting universality for machine learning phases
摘要：
自动编码器（AE）和生成对抗网络（GANs）仅在200个站点的一维（1D）网格上训练一次。此外，AE仅包含一个由两个神经元组成的隐藏层，并且GANs的生成器和消隐器也由两个神经元组成。用于训练所考虑的无监督神经网络（NN）的训练集由两种人工配置组成。值得注意的是，尽管架构简单，但构建的AE和GANs都精确地确定了多个模型的临界点，包括三维（3D）经典$O(3)$模型、二维（2D）广义经典XY模型、2D两态Potts模型和1D Bose-哈伯德模型。本文给出的结果以及{ \it Eur. Phys. J. Plus { \bf 136}，1116（2021）}建议，当考虑相变时，可以容易地构造出非常有效并且适用于广泛物理系统的优雅的通用神经网络。特别地，由于用两种配置训练的NN可以应用于许多模型，所以当涉及机器学习时，很可能大多数相变属于具有两个元素的类，即伊辛类。
英文摘要：
An autoencoder (AE) and a generative adversarial networks (GANs) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons and both the generator and the discriminator of the GANs are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NN) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GANs have precisely determined the critical points of several models, including the three-dimensional (3D) classical $O(3)$ model, the two-dimensional (2D) generalized classical XY model, the 2D two-state Potts model, and the 1D Bose-Hubbard model. The results presented here as well as that shown in {\it Eur. Phys. J. Plus {\bf 136}, 1116 (2021)} suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since a NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
