AI 中文总结
研究将自回归生成神经网络模型用于反铁磁伊辛模型，在模型低温相平衡构型上训练网络并用于蒙特卡罗模拟，发现其弛豫时间随训练数据集规模增加而下降，动力学指数降低，但大系统规模下训练成本阻碍方法实际应用。
AI 中文摘要
我们通过将自回归生成神经网络模型应用于随机正则图上的反铁磁伊辛模型来严格评估其性能。我们在该模型低温自旋玻璃相的平衡构型上训练网络，并使用网络生成的自旋构型进行蒙特卡罗模拟。随着训练数据集规模的增加，蒙特卡罗模拟的弛豫时间急剧下降并收敛到一个最优值。与局部蒙特卡罗动力学相比，表征最优弛豫时间随系统规模增长的动力学指数略有降低。然而，我们发现实现最优性能所需的训练数据集规模随系统规模增长得比弛豫时间快得多，这意味着在大系统规模下，总训练成本最终会阻碍该方法的实际应用。
英文摘要
We critically assess the performance of an autoregressive generative neural network model by applying it to an antiferromagnetic Ising model on a random regular graph. We train the network on equilibrium configurations in the low-temperature spin-glass phase of the model and perform Monte Carlo simulations using spin configurations generated by the network. The relaxation time of the Monte Carlo simulations drastically decreases with increasing the size of the training dataset and converges to an optimal value. The dynamical exponent characterizing the growth of the optimal relaxation time as a function of the system size is slightly reduced compared to the local Monte Carlo dynamics. However, we find that the size of the training dataset to achieve the optimal performance grows much faster with the system size than the relaxation time, implying that the total training cost eventually hinders a practical use of the method at large system sizes.
CommentsSubmission to SciPost
