# Tropical probability theory and an application to the entropic cone

## TL;DR

This paper summarizes the development of tropical probability theory and applies it to analyze the shape of the entropic cone, with implications for information theory and AI.

## Contribution

It introduces a tropical diagram framework for probability spaces and demonstrates its application to entropic cone dimension reduction.

## Key findings

- Tropical probability diagrams provide new insights into information optimization.
- The theory enables a dimension-reduction statement about the entropic cone.
- Potential applications in information theory and artificial intelligence.

## Abstract

In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.