TY - JOUR T1 - Efficient Anti-Symmetrization of a Neural Network Layer by Taming the Sign Problem AU - Abrahamsen , Nilin AU - Lin , Lin JO - Journal of Machine Learning VL - 3 SP - 211 EP - 240 PY - 2023 DA - 2023/09 SN - 2 DO - http://doi.org/10.4208/jml.230703 UR - https://global-sci.org/intro/article_detail/jml/22013.html KW - Fermions, Sign problem, Neural quantum states. AB -

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.