The Sample Complexity of One-Hidden-Layer Neural Networks. (arXiv:2202.06233v2 [cs.LG] UPDATED)

We study norm-based uniform convergence bounds for neural networks, aiming at
a tight understanding of how these are affected by the architecture and type of
norm constraint, for the simple class of scalar-valued one-hidden-layer
networks, and inputs bounded in Euclidean norm. We begin by proving that in
general, controlling the spectral norm of the hidden layer weight matrix is
insufficient to get uniform convergence guarantees (independent of the network
width), while a stronger Frobenius norm control is sufficient, extending and …

arxiv complexity networks neural networks