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Rectifier Circuits of Bounded Depth

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Abstract

Asymptotically tight bounds are obtained for the complexity of computation of the classes of (m, n)-matrices with entries from the set {0, 1,..., 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), logm = o(n), is achieved for the circuits of depth 3.

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  1. Research Institute ‘Kvant,’, Chetvyortyi Likhachyovskii per. 15, Moscow, 125438, Russia

    I. S. Sergeev

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  1. I. S. Sergeev
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Correspondence to I. S. Sergeev.

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Original Russian Text © I.S. Sergeev, 2018, published in Diskretnyi Analiz i Issledovanie Operatsii, 2018, Vol. 25, No. 1, pp. 120–141.

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Sergeev, I.S. Rectifier Circuits of Bounded Depth. J. Appl. Ind. Math. 12, 153–166 (2018). https://doi.org/10.1134/S1990478918010143

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  • DOI: https://doi.org/10.1134/S1990478918010143

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