2022/05/24 by Abrahamsen, Nilin, Lin, Lin
#FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2205.12250
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 anti-symmetrization. We show that the anti-symmetric projection of a two-layer neural network can be evaluated efficiently, opening the door to using a generic antisymmetric 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 re-scaling of the neural network weights compared to standard initializations.