论文标题
使用复杂值的神经网络来缓解哈伯德标志问题
Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
论文作者
论文摘要
蒙特卡洛模拟远离半填充的符号问题，可以通过变形集成轮廓来减少符号问题。这种转换可以使用神经网络实施，从而诱导鲍尔茨曼重量的雅各布决定因素。通用神经网络的这种额外的决定因素成本与体积立方缩放，以防止大规模模拟。我们基于复杂值的仿射耦合层实现了一个新的体系结构，从而将其降低到线性缩放。我们通过成功将其应用于不同尺寸的系统来证明该方法的功效，由于其严重的符号问题，其他蒙特卡洛方法最大的是最大的。
Monte Carlo simulations away from half-filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented using neural networks. This additional determinant cost for a generic neural network scales cubically with the volume, preventing large-scale simulations. We implement a new architecture, based on complex-valued affine coupling layers, which reduces this to linear scaling. We demonstrate the efficacy of this method by successfully applying it to systems of different size, the largest of which is intractable by other Monte Carlo methods due to its severe sign problem.
