This paper analyzes the generalization error of two-layer neural networks for computing the ground state of the Schr\”odinger operator on a $d$-dimensionalhypercube . We prove that the convergence rate of the error isindependent of the dimension $d$, under the a priori assumption that the groundstate lies in a spectral Barron space . We verify such assumption by proving anew regularity estimate for the groundState in the spectral Barron .

Author(s) : Jianfeng Lu, Yulong Lu

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Keywords : error - barron - groundstate - generalization - layer -

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