Risk Bounds for Multi-layer Perceptrons through Spectra of Integral Operators

We characterize the behavior of integral operators associated with multi-layer perceptrons in two eigenvalue decay regimes. We obtain as a result sharper risk bounds for multi-layer perceptrons highlighting their behavior in high dimensions. Doing so, we also improve on previous results on integral operators related to power series kernels on spheres, with sharper eigenvalue decay estimates in a wider range of eigenvalue decay regimes.