论文标题
通过侵犯标志问题，神经网络层的有效抗对称性
Efficient anti-symmetrization of a neural network layer by taming the sign problem
论文作者
论文摘要
神经网络的显式反对称是通用函数近似值的潜在候选者，用于通用反对称功能，这些函数在量子物理学中无处不在。但是，此过程是实施的先验成本成本高昂，因此对于大量粒子而言，它是不切实际的。该策略还遇到了标志问题。也就是说，由于取消正贡献和负有贡献，反对称功能的大小可能明显小于抗对称性之前。我们表明，可以有效地评估两层神经网络的抗对称投影，从而为使用抗对称神经网络Ansatzes中使用通用的反对称层用作构建块打开了大门。当控制符号问题时，此近似是有效的，我们表明该属性取决于标准Xavier/HE初始化方法下的激活函数的选择。结果，与标准初始化相比，使用平滑的激活函数需要重新缩放神经网络权重。
Explicit antisymmetrization of a neural network is a potential candidate for a universal function approximator for generic antisymmetric functions, which are ubiquitous in quantum physics. However, this procedure is a priori factorially costly to implement, making it impractical for large numbers of particles. The strategy also suffers from a sign problem. Namely, due to near-exact cancellation of positive and negative contributions, the magnitude of the antisymmetrized function may be significantly smaller than before anti-symmetrization. We show that the anti-symmetric projection of a two-layer neural network can be evaluated efficiently, opening the door to using a generic antisymmetric layer as a building block in anti-symmetric neural network Ansatzes. This approximation is effective when the sign problem is controlled, and we show that this property depends crucially the choice of activation function under standard Xavier/He initialization methods. As a consequence, using a smooth activation function requires re-scaling of the neural network weights compared to standard initializations.
