On Representing Electronic Wave Functions with Sign Equivariant Neural Networks

Recent neural networks demonstrated impressively accurate approximations of electronic ground-state wave functions. Such neural networks typically consist of a permutation-equivariant neural network followed by a permutation-antisymmetric operation to enforce the electronic exchange symmetry. While accurate, such neural networks are computationally expensive. In this work, we explore the flipped approach, where we first compute antisymmetric quantities based on the electronic coordinates and then apply sign equivariant neural networks to preserve the antisymmetry. While this approach promises acceleration thanks to the lower-dimensional representation, we demonstrate that it reduces to a Jastrow factor, a commonly used permutation-invariant multiplicative factor in the wave function. Our empirical results support this further, finding little to no improvements over baselines. We conclude with neither theoretical nor empirical advantages of sign equivariant functions for representing electronic wave functions within the evaluation of this work.