Molecular modeling at the quantum level requires choosing a parameterization
of the wavefunction that both respects the required particle symmetries, and is
scalable to systems of many particles. For the simulation of fermions, valid
parameterizations must be antisymmetric with respect to the exchange of
particles. Typically, antisymmetry is enforced by leveraging the anti-symmetry
of determinants with respect to the exchange of matrix rows, but this involves
computing a full determinant each time the wavefunction is evaluated. Instead,
we introduce a new antisymmetrization layer derived from sorting, the
$\textit{sortlet}$, which scales as $O(N \log N)$ with regards to the number of
particles -- in contrast to $O(N^3)$ for the determinant. We show numerically
that applying this anti-symmeterization layer on top of an attention based
neural-network backbone yields a flexible wavefunction parameterization capable
of reaching chemical accuracy when approximating the ground state of first-row
atoms and small molecules.

分子建模在量子级别需要选择一个能够尊重所需粒子对称性并可扩展到多粒子系统的波函数参数化。本文通过引入一种基于排序的新的反对称化层（称为 sortlet），在注意力神经网络骨干上应用该反对称化层，得到了一种灵活的波函数参数化形式，能够在逼近一周期元素原子和小分子基态时达到化学精确度。