Graph Neural Networks and 3-dimensional topology
We test the efficiency of applying geometric deep learning to the problems in low-dimensional topology in a certain simple setting. Specifically, we consider the class of 3-manifolds described by plumbing graphs and use graph neural networks (GNN) for the problem of deciding whether a pair of graphs...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/acf097 |
| _version_ | 1797737587134169088 |
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| author | Song Jin Ri Pavel Putrov |
| author_facet | Song Jin Ri Pavel Putrov |
| author_sort | Song Jin Ri |
| collection | DOAJ |
| description | We test the efficiency of applying geometric deep learning to the problems in low-dimensional topology in a certain simple setting. Specifically, we consider the class of 3-manifolds described by plumbing graphs and use graph neural networks (GNN) for the problem of deciding whether a pair of graphs give homeomorphic 3-manifolds. We use supervised learning to train a GNN that provides the answer to such a question with high accuracy. Moreover, we consider reinforcement learning by a GNN to find a sequence of Neumann moves that relates the pair of graphs if the answer is positive. The setting can be understood as a toy model of the problem of deciding whether a pair of Kirby diagrams give diffeomorphic 3- or 4-manifolds. |
| first_indexed | 2024-03-12T13:30:29Z |
| format | Article |
| id | doaj.art-76d7b5b18c0442cd96c8d1d3d13bac9c |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-03-12T13:30:29Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-76d7b5b18c0442cd96c8d1d3d13bac9c2023-08-24T12:23:07ZengIOP PublishingMachine Learning: Science and Technology2632-21532023-01-014303502610.1088/2632-2153/acf097Graph Neural Networks and 3-dimensional topologySong Jin Ri0https://orcid.org/0000-0001-6513-0840Pavel Putrov1SISSA , Via Bonomea 265, Trieste 34136, Italy; ICTP , Strada Costiera 11, Trieste 34151, ItalyICTP , Strada Costiera 11, Trieste 34151, ItalyWe test the efficiency of applying geometric deep learning to the problems in low-dimensional topology in a certain simple setting. Specifically, we consider the class of 3-manifolds described by plumbing graphs and use graph neural networks (GNN) for the problem of deciding whether a pair of graphs give homeomorphic 3-manifolds. We use supervised learning to train a GNN that provides the answer to such a question with high accuracy. Moreover, we consider reinforcement learning by a GNN to find a sequence of Neumann moves that relates the pair of graphs if the answer is positive. The setting can be understood as a toy model of the problem of deciding whether a pair of Kirby diagrams give diffeomorphic 3- or 4-manifolds.https://doi.org/10.1088/2632-2153/acf097Graph neural networksplumbed 3-manifoldsreinforcement learningsupervised learning |
| spellingShingle | Song Jin Ri Pavel Putrov Graph Neural Networks and 3-dimensional topology Machine Learning: Science and Technology Graph neural networks plumbed 3-manifolds reinforcement learning supervised learning |
| title | Graph Neural Networks and 3-dimensional topology |
| title_full | Graph Neural Networks and 3-dimensional topology |
| title_fullStr | Graph Neural Networks and 3-dimensional topology |
| title_full_unstemmed | Graph Neural Networks and 3-dimensional topology |
| title_short | Graph Neural Networks and 3-dimensional topology |
| title_sort | graph neural networks and 3 dimensional topology |
| topic | Graph neural networks plumbed 3-manifolds reinforcement learning supervised learning |
| url | https://doi.org/10.1088/2632-2153/acf097 |
| work_keys_str_mv | AT songjinri graphneuralnetworksand3dimensionaltopology AT pavelputrov graphneuralnetworksand3dimensionaltopology |