Learning Fast Monomial Orders for Gröbner Basis Computations

[2602.02972] Learning Fast Monomial Orders for Gröbner Basis Computations Skip to main content Search Submit Donate Log in Computer Science > Symbolic Computation arXiv:2602.02972 (cs) [Submitted on 3 Feb 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Learning Fast Monomial Orders for Gröbner Basis Computations Authors: R. Caleb Bunch , Alperen A. Ergür , Melika Golestani , Jessie Tong , Malia Walewski , Yunus E. Zeytuncu View PDF HTML (experimental) Abstract: The efficiency of Gröbner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum of possible monomial orders, most implementations rely on static heuristics such as GrevLex, guided primarily by expert intuition. We address this gap by casting the selection of monomial orderings as a reinforcement learning problem over the space of admissible orderings. Our approach leverages domain-informed reward signals that accurately reflect the computational cost of Gröbner basis computations and admits efficient Monte Carlo estimation. Experiments on benchmark problems from systems biology and computer vision show that the resulting learned policies consistently outperform standard heuristics, yielding substantial reductions in computational cost. Moreover, we find that these policies resist distillation into simple interpretable models, providing empirical evidence that deep reinforcement learning allows the agents to exploit non-linear geometric structure beyond the scope of traditional heuristics. Comments: added more experiments against baselines, corrected a few typos and cosmetics Subjects: Symbolic Computation (cs.SC) ; Machine Learning (cs.LG); Commutative Algebra (math.AC); Algebraic Geometry (math.AG) Cite as: arXiv:2602.02972 [cs.SC] (or arXiv:2602.02972v2 [cs.SC] for this version) https://doi.org/10.48550/arXiv.2602.02972 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alperen Ali Ergur [ view email ] [v1] Tue, 3 Feb 2026 01:17:18 UTC (1,780 KB) [v2] Fri, 28 Aug 2026 12:06:32 UTC (20,029 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.SC < prev | next > new | recent | 2026-02 Change to browse by: cs cs.LG math math.AC math.AG References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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