{"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/hilbert-series-machine-learning-and","title":"Hilbert Series, Machine Learning, and Applications to Physics","arxiv_id":"2103.13436","date":"2021-03-24","proceeding":null,"authors":["Jiakang Bao","Yang-Hui He","Edward Hirst","Johannes Hofscheier","Alexander Kasprzyk","Suvajit Majumder"],"abstract":"We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\\sim}1$ mean absolute error, whilst classifiers predict dimension and Gorenstein index to $>90\\%$ accuracy with ${\\sim}0.5\\%$ standard error. Binary random forest classifiers managed to distinguish whether the underlying HS describes a complete intersection with high accuracies exceeding $95\\%$. Neural networks (NNs) exhibited success identifying HS from a Gorenstein ring to the same order of accuracy, whilst generation of 'fake' HS proved trivial for NNs to distinguish from those associated to the three-dimensional Fano varieties considered.","url_abs":"https://arxiv.org/abs/2103.13436v3","url_pdf":"https://arxiv.org/pdf/2103.13436v3.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":"hilbert-series-machine-learning-and","repo_url":"https://github.com/edhirst/HilbertSeriesML","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}