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Randomized neural networks (randomized NNs), where only the terminal layer'sweights are optimized constitute a powerful model class to reduce computationaltime in training the neural network model. At the same time, these modelsgeneralize surprisingly well in various regression and classification tasks. Inthis paper, we give an exact macroscopic characterization (i.e., acharacterization in function space) of the generalization behavior ofrandomized, shallow NNs with ReLU activation (RSNs). We show that RSNscorrespond to a generalized additive model (GAM)-typed regression in whichinfinitely many directions are considered: the infinite generalized additivemodel (IGAM). The IGAM is formalized as solution to an optimization problem infunction space for a specific regularization functional and a fairly generalloss. This work is an extension to multivariate NNs of prior work, where weshowed how wide RSNs with ReLU activation behave like spline regression undercertain conditions and if the input is one-dimensional.

How (Implicit) Regularization of ReLU Neural Networks Characterizes the  Learned Function -- Part II: the Multi-D Case of Two Layers with Random First  Layer