Energy-Efficient Threshold Circuits for Comparison Functions

Abstract

A threshold gate is a theoretical model of a neuron, and a threshold circuit is a theoretical model of a neural network. The energy e of a threshold circuit C is defined to be the maximum number of gates outputting ones, where the maximum is taken over all input assignments to C. In this paper, we prove that the comparison function of 2n variables is computable by a polynomial-weight threshold circuit C of energy e, size s = O(n/log n), depth d = O(n/(e log n)) for any e, 3 ≤ e ≤ n/⌈log n⌉. Our result implies that one can construct an energy-efficient circuit computing the comparison function if it is allowable to use large depth.