Geodesic
Rectifier circuits of bounded depth
Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 1, pp. 120-141

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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.
Mots-clés : rectifier circuit
Keywords: complexity, depth. 
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     author = {I. S. Sergeev},
     title = {Rectifier circuits of bounded depth},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {120--141},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2018_25_1_a5/}
}
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I. S. Sergeev. Rectifier circuits of bounded depth. Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 1, pp. 120-141. http://geodesic.mathdoc.fr/item/DA_2018_25_1_a5/