Machines and Mathematical Mutations: Using GNNs to Characterize Quiver Mutation Classes
Authors: Jesse He, Helen Jenne, Herman Chau, Davis Brown, Mark Raugas, Sara C. Billey, Henry Kvinge
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this work, we use graph neural networks to investigate quiver mutation... We train a graph neural network (GNN) on a dataset consisting of 70, 000 quivers labeled with one of six different types... We find that not only does the resulting model achieve high accuracy, it also extracts features from type D quivers that align with the characterization from (Vatne, 2010). |
| Researcher Affiliation | Academia | 1Halıcıo glu Data Science Institute, University of California San Diego, San Diego, CA, USA 2Pacific Northwest National Laboratory, Richland, WA, USA 3Department of Mathematics, University of Washington, Seattle, WA, USA. |
| Pseudocode | No | The paper describes the methods used for training the GNN and the explainability techniques, but it does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide an explicit statement or a link to its own source code for the methodology described. It mentions using PyTorch Geometric, which is a third-party library. |
| Open Datasets | No | The paper states, 'We generate data with Sage (The Sage Developers, 2023; Musiker & Stump, 2011), which we describe in greater detail in Appendix C.' This indicates they generated their own dataset using a software tool, but does not provide concrete access information for the specific dataset used in their experiments. |
| Dataset Splits | Yes | The training data consists of quivers of each type on 6, 7, 8, 9, and 10 nodes. The test set consists of quivers of types A, D, E, A, D on 11 nodes. (Type E is not defined on 11 nodes.) ... Table 2. Number of quivers of each type and size in train and test sets. |
| Hardware Specification | Yes | We train with the Adam optimizer for 50 epochs with a batch size of 32 using cross-entropy loss with L1 regularization (γ = 5 10 6) using an Nvidia RTX A2000 Laptop GPU. |
| Software Dependencies | Yes | Quivers were generated using Sage (The Sage Developers, 2023; Musiker & Stump, 2011). For training and inference, each quiver was converted to Py Torch Geometric (Fey & Lenssen, 2019). |
| Experiment Setup | Yes | We train a 4-layer Dir GINE GNN with a hidden layer width of 32 to classify quivers into types A, D, E, A, D, and E... We train with the Adam optimizer for 50 epochs with a batch size of 32 using cross-entropy loss with L1 regularization (γ = 5 10 6)... In our analysis, we use hyperparameter values α = 2.5 and β = 0.1. |