Cut-off Jastrow Factors and Spectral Barron Regularity of Coulombic Electronic Wave Functions

What the math gives to ML

The paper identifies Coulomb cusps as the precise obstruction to high global Fourier regularity and shows that a cutoff Jastrow conjugation raises spectral Barron regularity from every order below 1 to every order below 2. This suggests factoring known electron–nucleus and electron–electron cusp geometry out of a neural wavefunction before asking a network to represent the residual. The transferable asset is the Fourier-tail improvement of the residual, which should reduce high-frequency approximation burden and stabilize derivative-based energy training. The most direct test is to compare otherwise identical neural quantum states with and without the cusp factor on few-electron Coulomb systems.