Exponential Negation of a Probability Distribution

TL;DR

This paper introduces an exponential negation operation for probability distributions, which acts as a geometric negation, increases entropy, and causes distributions to converge to uniformity after multiple iterations.

Contribution

It proposes a novel exponential negation method for probability distributions, analyzing its properties and demonstrating its convergence behavior and entropy-increasing effect.

Findings

The negation's fixed point is the uniform distribution.

Repeated negation increases entropy and leads to convergence.

Convergence speed is inversely proportional to the number of distribution elements.

Abstract

Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation is investigated, we find that the fix point is the uniform probability distribution. The negation is an entropy increase operation and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation.