A machine learning approach to commutative algebra: Distinguishing table vs non-table ideals

TL;DR

This paper introduces a machine learning framework to classify table and non-table ideals in commutative algebra, demonstrating that such a distinction can be effectively learned and proven using neural networks and decision trees.

Contribution

The paper presents the first application of machine learning algorithms to distinguish table ideals from non-table ideals, including the creation of a labeled dataset and novel theoretical results.

Findings

Neural networks and decision trees can accurately classify table vs non-table ideals.

Existence of an algorithm to distinguish table ideals is proven.

New properties of table ideals are established.

Abstract

We propose a novel approach to distinguish table vs non-table ideals by using different machine learning algorithms. We introduce the reader to table ideals, assuming some knowledge on commutative algebra and describe their main properties. We create a data set containing table and non-table ideals, and we use a feedforward neural network model, a decision tree and a graph neural networks for the classification. Our results indicate that there exists an algorithm to distinguish table ideals from non-table ideals, and we prove it along some novel results on table ideals.