Multiple Threshold Neural Logic

Abstract

We introduce a new Boolean computing element related to the Linear Threshold element, which is the Boolean version of the neuron. Instead of the sign function, it computes an arbitrary (with polynomialy many transitions) Boolean function of the weighted sum of its inputs. We call the new computing element an LT M element, which stands for Linear Threshold with Multiple transitions. The paper consists of the following main contributions related to our study of LTM circuits: (i) the creation of efficient designs of LTM circuits for the addition of a multiple number of integers and the product of two integers. In particular, we show how to compute the addition of m integers with a single layer of LT M elements. (ii) a proof that the area of the VLSI layout is reduced from O(n^2) in LT circuits to O(n) in LTM circuits, for n inputs symmetric Boolean functions, and (iii) the characterization of the computing power of LT M relative to LT circuits.

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