In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $O(1/\sqrt{m})$ where $m$ is the size of networks, which overcomes the curse of dimensionality. The key idea of the approximation is to define a Barron space of functionals.

翻译：在本文中,我们建立了一个近似功能的神经网络,这些功能是从无限的维空间到有限维空间的地图。神经网络的近似错误是$O(1/\sqrt{m})$($O),其中百万美元是网络的大小,克服了维度的诅咒。近似的关键理念是定义功能的边际空间。