On Representing Electronic Wave Functions with Sign Equivariant Neural
  Networks
Nicholas Gao Stephan Günnemann
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.