论文标题
朝向反对称神经ANSATZ分离
Towards Antisymmetric Neural Ansatz Separation
论文作者
论文摘要
我们研究了反对称函数的两个基本模型（或\ emph {ansätze}）之间的分离，即表格$ f的函数$ f $（x_ {σ（1）}，\ ldots，x__ {σ（n）} $ f $置换。这些是在量子化学的背景下出现的，是费米管系统波形的基本建模工具。具体而言，我们考虑了两个流行的抗对称Ansätze：Slater表示，它利用了决定因素的交替结构，而Jastrow Ansatz则通过任意对称函数增强了使用产品的Slater决定因素。我们在$ n $尺寸中构建一种反对称功能，可以有效地以jastrow形式表达，但是，除非有很多条款（以$ n^2 $）为指数（以$ n^2 $）为指数。这代表了这两个Ansätze之间的第一个明确定量分离。
We study separations between two fundamental models (or \emph{Ansätze}) of antisymmetric functions, that is, functions $f$ of the form $f(x_{σ(1)}, \ldots, x_{σ(N)}) = \text{sign}(σ)f(x_1, \ldots, x_N)$, where $σ$ is any permutation. These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems. Specifically, we consider two popular antisymmetric Ansätze: the Slater representation, which leverages the alternating structure of determinants, and the Jastrow ansatz, which augments Slater determinants with a product by an arbitrary symmetric function. We construct an antisymmetric function in $N$ dimensions that can be efficiently expressed in Jastrow form, yet provably cannot be approximated by Slater determinants unless there are exponentially (in $N^2$) many terms. This represents the first explicit quantitative separation between these two Ansätze.
