# Machines and Mathematical Mutations: Using GNNs to Characterize Quiver Mutation Classes

arXiv: https://arxiv.org/abs/2411.07467 · HTML: https://mlsanity.com/paper/2411.07467/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Evaluating Explainability for Graph Neural Networks](https://mlsanity.com/paper/2208.09339/) (2022)
- [Understanding Transformer Reasoning Capabilities via Graph Algorithms](https://mlsanity.com/paper/2405.18512/) (2024)
- [GraphFramEx: Towards Systematic Evaluation of Explainability Methods for Graph Neural Networks](https://mlsanity.com/paper/2206.09677/) (2022)
- [Graph Neural Networks are Dynamic Programmers](https://mlsanity.com/paper/2203.15544/) (2022)
- [Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability](https://mlsanity.com/paper/2305.08746/) (2023)
- [Grokking Group Multiplication with Cosets](https://mlsanity.com/paper/2312.06581/) (2023)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)

## Built on by (most cited first, 2 of 2)

- [Machine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematics](https://mlsanity.com/paper/2503.06366/) (2025)
- [Can Neural Networks Learn Small Algebraic Worlds? An Investigation Into the Group-theoretic Structures Learned By Narrow Models Trained To Predict Group Operations](https://mlsanity.com/paper/2601.21150/) (2026)

## Abstract (arXiv)

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze. In this work, we use graph neural networks to investigate quiver mutation -- an operation that transforms one quiver (or directed multigraph) into another -- which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics. In the study of cluster algebras, the question of mutation equivalence is of fundamental concern: given two quivers, can one efficiently determine if one quiver can be transformed into the other through a sequence of mutations? In this paper, we use graph neural networks and AI explainability techniques to independently discover mutation equivalence criteria for quivers of type tildeD. Along the way, we also show that even without explicit training to do so, our model captures structure within its hidden representation that allows us to reconstruct known criteria from type D, adding to the growing evidence that modern machine learning models are capable of learning abstract and parsimonious rules from mathematical data.