Anti-symmetric Barron functions and their approximation with sums of determinants
Numerical Analysis
2023-03-24 v1 Machine Learning
Numerical Analysis
Quantum Physics
Abstract
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite neural networks with one hidden layer. By explicitly encoding the anti-symmetric structure, we prove that the anti-symmetric functions which belong to the Barron space can be efficiently approximated with sums of determinants. This yields a factorial improvement in complexity compared to the standard representation in the Barron space and provides a theoretical explanation for the effectiveness of determinant-based architectures in ab-initio quantum chemistry.
Keywords
Cite
@article{arxiv.2303.12856,
title = {Anti-symmetric Barron functions and their approximation with sums of determinants},
author = {Nilin Abrahamsen and Lin Lin},
journal= {arXiv preprint arXiv:2303.12856},
year = {2023}
}