A New Information Theory of Certainty for Machine Learning

TL;DR

This paper introduces troenpy, a new measure dual to entropy, to quantify certainty in data distributions, with applications in document classification, language modeling, and quantum systems.

Contribution

It proposes troenpy as a novel concept dual to entropy, enabling new ways to model certainty in classical and quantum data.

Findings

Troenpy improves document classification weighting schemes.

Self-troenpy reduces perplexity in neural language models.

Quantum troenpy quantifies certainty in quantum systems.

Abstract

Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we propose a new concept troenpy,as the canonical dual of entropy, to quantify the certainty of the underlying distribution. We demonstrate two applications in machine learning. The first is for the classical document classification, we develop a troenpy based weighting scheme to leverage the document class label. The second is a self-troenpy weighting scheme for sequential data and show that it can be easily included in neural network based language models and achieve dramatic perplexity reduction. We also define quantum troenpy as the dual of the Von Neumann entropy to quantify the certainty of quantum systems.