{"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/machine-learning-sasakian-and-g-2-topology-on","title":"Machine learning Sasakian and $G_2$ topology on contact Calabi-Yau $7$-manifolds","arxiv_id":"2310.03064","date":"2023-10-04","proceeding":null,"authors":["Daattavya Aggarwal","Yang-Hui He","Elli Heyes","Edward Hirst","Henrique N. Sá Earp","Tomás S. R. Silva"],"abstract":"We propose a machine learning approach to study topological quantities related to the Sasakian and $G_2$-geometries of contact Calabi-Yau $7$-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-N\\\"ordstrom invariant of the natural $G_2$-structure of the $7$-dimensional link of a weighted projective Calabi-Yau $3$-fold hypersurface singularity, for 7549 of the 7555 possible $\\mathbb{P}^4(\\textbf{w})$ projective spaces. These topological quantities are then machine learnt with high performance scores, where learning the Sasakian Hodge numbers from the $\\mathbb{P}^4(\\textbf{w})$ weights alone, using both neural networks and a symbolic regressor which achieve $R^2$ scores of 0.969 and 0.993 respectively. Additionally, properties of the respective Gr\\\"obner bases are well-learnt, leading to a vast improvement in computation speeds which may be of independent interest. The data generation and analysis further induced novel conjectures to be raised.","url_abs":"https://arxiv.org/abs/2310.03064v2","url_pdf":"https://arxiv.org/pdf/2310.03064v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"machine-learning-sasakian-and-g-2-topology-on","repo_url":"https://github.com/TomasSilva/MLcCY7","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"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}