Efficient Threshold Circuits for Power Series

Abstract We show that functions with convergent real power series can be well approximated by two classes of polynomial-size small-weight threshold circuits: depth-three circuits with threshold gates on all levels and depth-four circuits with threshold gates on the first two levels and AND–OR gates on the last two. This is done without restricting the input to a fixed closed subinterval of the interval of convergence of the series. We also point out that rational functions and the logarithm of x in base b can be well approximated by the same classes of circuits when both x and b are given as input.