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.

翻译：量子物理学中的一个基本问题是对在全同粒子置换下完全反对称的函数进行编码。Barron空间由可通过具有单隐层的无限神经网络参数化的高维函数构成。通过显式编码反对称结构，我们证明了属于Barron空间的反对称函数可以用行列式之和进行高效逼近。与Barron空间中的标准表示相比，这带来了复杂度上的阶乘级改进，并为从头算量子化学中基于行列式的架构的有效性提供了理论解释。