Hierarchical autoregressive neural networks in three-dimensional statistical system
Piotr Białas, Vaibhav Chahar, Piotr Korcyl, Tomasz Stebel, Mateusz Winiarski, Dawid Zapolski
自动回归神经网络(ANN)最近被提出作为提高蒙特卡罗算法效率的机制,用于几个自旋系统。 这个想法依赖于这样一个事实,即配置的总概率可以分解为每个自旋的条件概率,而神经网络又可以通过神经网络近似。 一旦训练,ANN 可用于从近似概率分布中采样配置,并显式评估给定配置的概率。 也有人观察到,这种有条件的概率使信息理论可观测物,如相互信息或纠缠熵。 到目前为止,这些方法已被应用于二维统计系统或一维量子系统。 在本文中,我们将分层算法的概括描述为三个空间维度,并在Ising模型的例子上研究其性能。 我们讨论了训练的效率,并通过比较具有相同数量旋转的二维和三维 Ising 模型的结果来描述缩放与系统的尺寸。 最后,我们为三维 Ising 模型提供热力学可观测值的估计值,例如在整个相变中温度范围内熵和自由能量。
Autoregressive Neural Networks (ANN) have been recently proposed as a mechanism to improve the efficiency of Monte Carlo algorithms for several spin systems. The idea relies on the fact that the total probability of a configuration can be factorized into conditional probabilities of each spin, which in turn can be approximated by a neural network. Once trained, the ANNs can be used to sample configurations from the approximated probability distribution and to explicitly evaluate this probability...