Universal approximation of symmetric and anti-symmetric functions [article]

Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, Linfeng Zhang
2022 arXiv   pre-print
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ϵ. While the approximation still suffers from the curse of dimensionality, to the best of our knowledge, these are the first results in the literature with explicit
more » ... rror bounds for functions with symmetry or anti-symmetry constraints.
arXiv:1912.01765v2 fatcat:flz4dlznwbhl3frstsxre7jwye