Year: 2023
Author: Nilin Abrahamsen, Lin Lin
Journal of Machine Learning, Vol. 2 (2023), Iss. 3 : pp. 211–240
Abstract
Explicit antisymmetrization of a neural network is a potential candidate for a universal function approximator for generic antisymmetric functions, which are ubiquitous in quantum physics. However, this procedure is a priori factorially costly to implement, making it impractical for large numbers of particles. The strategy also suffers from a sign problem. Namely, due to near-exact cancellation of positive and negative contributions, the magnitude of the antisymmetrized function may be significantly smaller than before antisymmetrization. We show that the anti-symmetric projection of a two-layer neural network can be evaluated efficiently, opening the door to using a generic anti-symmetric layer as a building block in anti-symmetric neural network Ansatzes. This approximation is effective when the sign problem is controlled, and we show that this property depends crucially the choice of activation function under standard Xavier/He initialization methods. As a consequence, using a smooth activation function requires rescaling of the neural network weights compared to standard initializations.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jml.230703
Journal of Machine Learning, Vol. 2 (2023), Iss. 3 : pp. 211–240
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Fermions Sign problem Neural quantum states.