Serial binary addition with polynormally bounded weights

Abstract

This paper presents a new approach to the problem of serial binary addition with feed-forward neural networks. It is shown that the serial binary addition, an important component to a number of applications such signal processing, of two n-bit operands with carry can be done by a feed-forward linear threshold gate based network with polynomially bounded weights, i.e. in the order of O(n ^k), associated with small delay and size. In particular, it is shown that the overall delay for the serial addition is k log n + n/k log n serial cycles, with the serial cycle comprising a neuron and a latch. The implementation cost of the proposal is in the order of O(log n), in terms of linear threshold gates, and in the order of O(log² n), in terms of latches. The fan-in is in the order of O(log n).