Rectifier circuits of bounded depth

Asymptotically tight bounds are obtained for the complexity of computation of the classes of $(m,n)$-matrices with entries from the set $\{0,1,\dots,q-1\}$ by rectifier circuits of bounded depth $d$, under some relations between $m,n$, and $q$. In the most important case of $q=2$, it is shown that the asymptotics of the complexity of Boolean $(m,n)$-matrices, $\log n=o(m)$, $\log m=o(n)$, is achieved for the circuits of depth $3$. Illustr. 1, bibliogr. 11.