In this paper we investigate the reduction of the size for small depth feed-forward linear threshold networks performing binary addition, comparison, and related functions. For n bit operands we propose a depth-3 O( n 2 log n ) asymptotic size network for the binary addition with polynomially bounded weights. We propose also a depth-3 addition of optimal O(n) asymptotic size network and a depth-2 comparison of O( p n) asymptotic size network, both with O(2 p n ) asymptotic size of weight

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... For existing architectural formats we show that our schemes, with equal or smaller depth networks, substantially outperform existing schemes in terms of size and fan-in requirements and in occasions in weight requirements.