The combination of neural networks and quantum Monte Carlo methods has arisen
as a path forward for highly accurate electronic structure calculations.
Previous proposals have combined equivariant neural network layers with an
antisymmetric layer to satisfy the antisymmetry requirements of the electronic
wavefunction. However, to date it is unclear if one can represent antisymmetric
functions of physical interest, and it is difficult to measure the
expressiveness of the antisymmetric layer. This work attempts to address this
problem by introducing explicitly antisymmetrized universal neural network
layers as a diagnostic tool. We first introduce a generic antisymmetric (GA)
layer, which we use to replace the entire antisymmetric layer of the highly
accurate ansatz known as the FermiNet. We demonstrate that the resulting
FermiNet-GA architecture can yield effectively the exact ground state energy
for small systems. We then consider a factorized antisymmetric (FA) layer which
more directly generalizes the FermiNet by replacing products of determinants
with products of antisymmetrized neural networks. Interestingly, the resulting
FermiNet-FA architecture does not outperform the FermiNet. This suggests that
the sum of products of antisymmetries is a key limiting aspect of the FermiNet
architecture. To explore this further, we investigate a slight modification of
the FermiNet called the full determinant mode, which replaces each product of
determinants with a single combined determinant. The full single-determinant
FermiNet closes a large part of the gap between the standard single-determinant
FermiNet and FermiNet-GA. Surprisingly, on the nitrogen molecule at a
dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can
significantly outperform the standard 64-determinant FermiNet, yielding an
energy within 0.4 kcal/mol of the best available computational benchmark.

本文提出了一种显式反对称通用神经网络层来替代高精度费米核（FermiNet）的整个反对称层，即 FermiNet-GA 结构，同时研究了差不多完全推导出基态能，即 full single-determinant FermiNet 模式以及另一个 FA 层，但发现这两者并没有超过 FermiNet 模式，说明反对称性的总和乘积是限制 FermiNet 的关键因素之一。