@Article{JML-2-211,
author = {Abrahamsen , Nilin and Lin , Lin},
title = {Efficient Anti-Symmetrization of a Neural Network Layer by Taming the Sign Problem},
journal = {Journal of Machine Learning},
year = {2023},
volume = {2},
number = {3},
pages = {211--240},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2790-2048},
doi = {https://doi.org/10.4208/jml.230703},
url = {http://global-sci.org/intro/article_detail/jml/22013.html}
}