Anti-symmetric Barron functions and their approximation with sums of determinants

• URL: http://arxiv.org/abs/2303.12856v1
• Date: Wed, 22 Mar 2023 18:31:15 GMT
• Title: Anti-symmetric Barron functions and their approximation with sums of determinants
• Authors: Nilin Abrahamsen, Lin Lin
• Abstract summary: A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. 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.
• Score: 1.8076403084528587
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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