Polytopes and Machine Learning

TL;DR

This paper applies machine learning techniques to analyze lattice polytopes, achieving high accuracy in predicting properties like volume and reflexivity, especially for 2D and 3D cases using Plücker coordinates.

Contribution

It introduces a novel application of supervised learning to lattice polytope properties, outperforming traditional vertex-based methods.

Findings

Predicts properties with up to 100% accuracy

Plücker coordinates outperform vertex representation

Effective for 2D polygons and 3D polytopes

Abstract

We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d polygons and 3d polytopes with Pl\"ucker coordinates as input, which out-perform the usual vertex representation.