Efficient anti-symmetrization of a neural network layer by taming the sign problem
This addresses the challenge of approximating antisymmetric functions in quantum physics, offering a practical solution for large particle systems, though it is incremental as it builds on existing neural network methods with specific modifications.
The paper tackles the factorial cost and sign problem in antisymmetrizing neural networks for quantum physics by showing that the antisymmetric projection of a two-layer network can be evaluated efficiently, enabling its use as a building block, with effectiveness depending on activation function choice and requiring weight re-scaling for smooth functions.
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.