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.

翻译：显式反对称化神经网络是一种通用的反对称函数逼近器，在量子物理学中具有广泛应用。然而，该方法先验地具有阶乘级别的计算代价，使得其在处理大量粒子时难以实际应用。该策略还面临符号问题：由于正负贡献几乎完全抵消，反对称化后函数的幅值可能远小于反对称化前的幅值。我们证明了双层神经网络的反对称投影可以高效计算，为将通用反对称层作为反对称神经网络安萨茨的基本构建模块开辟了可能性。当符号问题得到控制时，该近似方法有效，且我们发现该性质关键取决于在标准Xavier/He初始化方法下激活函数的选择。由此，使用光滑激活函数时，需对神经网络权重进行相较于标准初始化的重新缩放。