  Randomized neural networks (randomized NNs), where only the terminal layer's
weights are optimized constitute a powerful model class to reduce computational
time in training the neural network model. At the same time, these models
generalize surprisingly well in various regression and classification tasks. In
this paper, we give an exact macroscopic characterization (i.e., a
characterization in function space) of the generalization behavior of
randomized, shallow NNs with ReLU activation (RSNs). We show that RSNs
correspond to a generalized additive model (GAM)-typed regression in which
infinitely many directions are considered: the infinite generalized additive
model (IGAM). The IGAM is formalized as solution to an optimization problem in
function space for a specific regularization functional and a fairly general
loss. This work is an extension to multivariate NNs of prior work, where we
showed how wide RSNs with ReLU activation behave like spline regression under
certain conditions and if the input is one-dimensional.
