  Fermionic neural network (FermiNet) is a recently proposed wavefunction
Ansatz, which is used in variational Monte Carlo (VMC) methods to solve the
many-electron Schr\"{o}dinger 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.
