Shallow ReLU${}^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization

Weizhao Li, Fanghui Liu, Lei Shi

This paper studies approximation by shallow ReLU${}^s$ networks, ${\sigma }_s(t)=\max \{0,t{\}}^s$, together with their generalization behavior under ${\ell }_1$ path-norm control. For the $L^p$-t…