论文标题
$ O（n^2）$ fermionic神经网络中的通用反对称性
$O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks
论文作者
论文摘要
费米文化神经网络（费梅内特）是最近提出的波函数ansatz，用于跨变异蒙特卡洛（VMC）方法来求解多电子Schrödinger方程。 Ferminet提出了置换式架构，在该体系结构上使用Slater决定因素诱导反对称性。事实证明，Ferminet具有单一决定因素具有通用近似能力，即足够代表任何反对称函数，给定足够的参数。但是，渐近计算瓶颈来自Slater的决定因素，该决定因素以$ O（n^3）$对$ n $电子进行缩放。在本文中，我们用成对的反对称结构代替Slater决定因素，该构建易于实现，并且可以将计算成本降低到$ O（n^2）$。我们正式证明，建立在置换量等架构上的成对结构可以普遍代表任何反对称功能。此外，当我们旨在代表地面波形时，可以通过连续近似值来实现这种普遍性。
Fermionic neural network (FermiNet) is a recently proposed wavefunction Ansatz, which is used in variational Monte Carlo (VMC) methods to solve the many-electron Schrödinger equation. FermiNet proposes permutation-equivariant architectures, on which a Slater determinant is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function given sufficient parameters. However, the asymptotic computational bottleneck comes from the Slater determinant, which scales with $O(N^3)$ for $N$ electrons. In this paper, we substitute the Slater determinant with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N^2)$. We formally prove that the pairwise construction built upon permutation-equivariant architectures can universally represent any antisymmetric function. Besides, this universality can be achieved via continuous approximators when we aim to represent ground-state wavefunctions.
