# Interpretable Graph Networks Formulate Universal Algebra Conjectures

arXiv: https://arxiv.org/abs/2307.11688 · HTML: https://mlsanity.com/paper/2307.11688/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [ProtGNN: Towards Self-Explaining Graph Neural Networks](https://mlsanity.com/paper/2112.00911/) (2021)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [GCExplainer: Human-in-the-Loop Concept-based Explanations for Graph Neural Networks](https://mlsanity.com/paper/2107.11889/) (2021)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Encoding Concepts in Graph Neural Networks](https://mlsanity.com/paper/2207.13586/) (2022)

## Built on by (most cited first, 4 of 4)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective](https://mlsanity.com/paper/2502.02719/) (2025)
- [Logic Explanation of AI Classifiers by Categorical Explaining Functors](https://mlsanity.com/paper/2503.16203/) (2025)
- [Iterative In-Context Learning to Enhance LLMs Abstract Reasoning: The Case-Study of Algebraic Tasks](https://mlsanity.com/paper/2509.01267/) (2025)

## Abstract (arXiv)

The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the foundations of modern mathematics -- is still completely unexplored. This work proposes the first use of AI to investigate UA's conjectures with an equivalent equational and topological characterization. While 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 propose a general algorithm generating 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: (i) enhance interpretability without sacrificing task accuracy, (ii) strongly generalize when predicting universal algebra's properties, (iii) generate simple explanations that empirically validate existing conjectures, and (iv) identify subgraphs suggesting the formulation of novel conjectures.