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

2023/03/22 by Nilin Abrahamsen, Lin Lin, Abrahamsen, Nilin +1 · 1 citation
Computer Science · Materials Science · #Computational Drug Discovery Methods #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Neural Networks and Applications #Numerical Analysis (math.NA) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2303.12856

openalex publication_date 2023/03/22 · openalex created_date 2023/03/25 · openalex updated_date 2026/07/28

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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