  Double-descent curves in neural networks describe the phenomenon that the
generalisation error initially descends with increasing parameters, then grows
after reaching an optimal number of parameters which is less than the number of
data points, but then descends again in the overparameterized regime. In this
paper, we use techniques from random matrix theory to characterize the spectral
distribution of the empirical feature covariance matrix as a width-dependent
perturbation of the spectrum of the neural network Gaussian process (NNGP)
kernel, thus establishing a novel connection between the NNGP literature and
the random matrix theory literature in the context of neural networks. Our
analytical expression allows us to study the generalisation behavior of the
corresponding kernel and GP regression, and provides a new interpretation of
the double-descent phenomenon, namely as governed by the discrepancy between
the width-dependent empirical kernel and the width-independent NNGP kernel.
