Interpretable Graph Networks Formulate Universal Algebra Conjectures

Francesco Giannini, Stefano Fioravanti, Oguzhan Keskin, Alisia Maria Lupidi, Lucie Charlotte Magister, Pietro Lio, Pietro Barbiero

Keywords: explainable AI, universal algebra, concept-based models, graph neural networks, interpretablity

TL;DR: We propose the first-ever use of AI to investigate Universal Algebra's conjectures using interpretable graph neural networks

Abstract:

The use of AI in Universal Algebra (UA)---one of the fields laying the foundations of modern mathematics---is still completely unexplored.
While UA's topological representations would enable the analysis of such properties using graph neural networks, the limited transparency and brittle explainability of these models hinder their straightforward use to empirically validate existing conjectures or to formulate new ones.
To bridge these gaps, we generate AI-ready datasets based on UA's conjectures, and introduce a novel neural layer to build fully interpretable graph networks. The results of our experiments demonstrate that interpretable graph networks strongly generalize when predicting universal algebra's properties, and generate simple explanations that empirically validate existing conjectures.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 181