Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks

ArXi:2605.31152v1 Announce Type: cross This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions. When the error is measured in $L^p([0,1]^d)$ norm and the approximator is a network with width $W$ and depth $L$, recent works have proven the supper approximation rate $\mathcal{O}((WL)^{-2s/d})$ for Beso space $\mathcal{B}^s_{q,r}([0,1]^d)$ under the Sobole embedding condition $s/d>1/q-1/p$. In order to overcome the curse of dimensionality in this rate, we extent this result to anisotropic and mixed smooth function classes.