Towards Antisymmetric Neural Ansatz Separation

Abstract

We study separations between two fundamental models (or Ans\"atze) of antisymmetric functions, that is, functions f of the form f(x_(1), , x_(N)) = sign()f(x_1, , x_N), where 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 Ans\"atze: 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 Ans\"atze.

Tasks

Reproductions