Function approximation and nonparametric regression with binary and ternary ReLU networks

Aleksandr Beknazaryan

paper

Function approximation and nonparametric regression with binary and ternary ReLU networks

arXiv:2206.13280

Abstract

We show that deep binary ReLU networks and deep sparse ternary ReLU networks can approximate $β$ -Hölder functions on $[0, 1]^{d}$ . We also show that deep sparse ternary ReLU networks can achieve, up to a logarithmic factor, the minimax rate of prediction of $β$ -smooth regression function.