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

Nilin Abrahamsen; Lin Lin

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arXiv · 2303.12856

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

Nilin Abrahamsen·Lin Lin

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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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Nilin Abrahamsen, Lin Lin. 2023-03-22. Anti-symmetric Barron functions and their approximation with sums of determinants. https://arxiv.org/abs/2303.12856

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