As a generalization of the work in [Lee et al., 2017], this note briefly discusses when the prior of a neural network output follows a Gaussian process, and how a neural-network-induced Gaussian process is formulated. The posterior mean functions of such a Gaussian process regression lie in the reproducing kernel Hilbert space defined by the neural-network-induced kernel. In the case of two-layer neural networks, the induced Gaussian processes provide an interpretation of the reproducing kernel Hilbert spaces whose union forms a Barron space.

翻译：作为[Lee等人,2017年]中工作的概述,本说明简要讨论了神经网络产出之前在高斯进程之后的时期,以及神经网络引起的高斯进程是如何形成的。这种高斯进程后端的中值功能在于由神经网络引起的内核所定义的再生内核Hilbert空间。在两层神经网络中,引导的高斯进程对形成Barron空间的再生产内核Hilbert空间提供了解释。