  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.
