{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/detecting-homeomorphic-3-manifolds-via-graph","title":"Detecting Homeomorphic 3-manifolds via Graph Neural Networks","arxiv_id":"2409.02126","date":"2024-09-01","proceeding":null,"authors":["Craig Lawrie","Lorenzo Mansi"],"abstract":"Motivated by the enumeration of the BPS spectra of certain 3d $\\mathcal{N}=2$ supersymmetric quantum field theories, obtained from the compactification of 6d superconformal field theories on three-manifolds, we study the homeomorphism problem for a class of graph-manifolds using Graph Neural Network techniques. Utilizing the JSJ decomposition, a unique representation via a plumbing graph is extracted from a graph-manifold. Homeomorphic graph-manifolds are related via a sequence of von Neumann moves on this graph; the algorithmic application of these moves can determine if two graphs correspond to homeomorphic graph-manifolds in super-polynomial time. However, by employing Graph Neural Networks (GNNs), the same problem can be addressed, at the cost of accuracy, in polynomial time. We build a dataset composed of pairs of plumbing graphs, together with a hidden label encoding whether the pair is homeomorphic. We train and benchmark a variety of network architectures within a supervised learning setting by testing different combinations of two convolutional layers (GEN, GCN, GAT, NNConv), followed by an aggregation layer and a classification layer. We discuss the strengths and weaknesses of the different GNNs for this homeomorphism problem.","url_abs":"https://arxiv.org/abs/2409.02126v1","url_pdf":"https://arxiv.org/pdf/2409.02126v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"detecting-homeomorphic-3-manifolds-via-graph","repo_url":"https://github.com/Lollo0900/Plumbed_3-Manifolds","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[{"method_slug":"gat","method_name":"GAT"},{"method_slug":"gcn","method_name":"GCN"},{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}